the eighth international conference on scientific ...€¦ · the eighth international conference...

THE EIGHTH INTERNATIONAL CONFERENCE ONSCIENTIFIC COMPUTING AND APPLICATIONS

University of Nevada, Las VegasApril 1 – 4, 2012

Program and Abstracts

Department of Mathematical Sciences, University of Nevada, Las Vegas

Sponsors

National Science FoundationUSA

National Security TechnologiesLLC, USA

Table of Contents

Committees 1

Plenary Speakers 2

Schedule 3

Program 7Sunday, April 1, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Monday, April 2, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Tuesday, April 3, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Wednesday, April 4, 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Abstracts 29Plenary Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Walter Allegretto’s 70th Birthday . . . . . . . . . . . . . . . . . . . . . . . . 35Graeme Fairweather’s 70th Birthday . . . . . . . . . . . . . . . . . . . . . . 38Mini-symposia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Other Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

List of Participants 87

CBC and Hyatt Place 92

UNLV Campus Map 93

Committees

Scientific Committee

Randolph Bank, University of California - San Diego, USAGang Bao, Michigan State University, USARuss Caflisch, University of California - Los Angeles, USAZhangxing (John) Chen, University of Calgary, CanadaGraeme Fairweather, American Mathematical Society, USAMax Gunzburger, Florida State University, USAJan Hesthaven, Brown University, USAYunqing Huang, Xiangtan University, ChinaYoussuff Hussaini, Florida State University, USAJin-Fa Lee, Ohio State University, USAYanping Lin, The Hong Kong Polytechnic University, Hong KongChi-Wang Shu, Brown University, USATao Tang, The Hong Kong Baptist University, Hong KongRen-hong Wang, Dalian University of Technology, ChinaMary Wheeler, University of Texas at Austin, USAYau Shu Wong, University of Alberta, Canada

Organizing Committee

Yitung Chen, University of Nevada, Las Vegas, USADerrick Dubose, University of Nevada, Las Vegas, USAJichun Li (Co-Chair), University of Nevada, Las Vegas, USAEric Machorro, National Security Technologies, LLC, USAMonika Neda, University of Nevada, Las Vegas, USAPengtao Sun, University of Nevada, Las Vegas, USAHongtao Yang (Co-Chair), University of Nevada, Las Vegas, USA

1

Plenary Speakers

Todd Arbogast, University of Texas at Austin, USARandolph Bank, University of California - San Diego, USAGang Bao, Michigan State University, USAPavel Bochev, Sandia National Lab, USAZhangxing (John) Chen, University of Calgary, CanadaLeszek Demkowicz, University of Texas at Austin, USAGraeme Fairweather, American Mathematical Society, USAMax Gunzburger, Florida State University, USAJan Hesthaven, Brown University, USAYunqing Huang, Xiangtan University, ChinaChi-Wang Shu, Brown University, USAMary Wheeler, University of Texas at Austin, USAJinchao Xu, Pennsylvania State University, USAZhimin Zhang, Wayne State University, USA

2

Schedule

Sunday,

Apri

l1,

2012

8:00

AM

–8:

30A

MC

BC

AR

egis

trat

ion

8:40

AM

–9:

30A

MC

BC

A10

6M

ary

Whee

ler

(Chai

r:I.

Yot

ov)

Ple

nar

yT

alks

CB

CA

110

Jan

Hes

thav

en(C

hai

r:Jic

hun

Li)

9:30

AM

–10

:00

AM

Coff

eeB

reak

CB

CC

116

CB

CA

110

CB

CA

106

CB

CC

118

Con

curr

ent

Ses

sion

sM

S4:

Yan

zhi

Zhan

gC

hai

r:Jan

Hes

thav

enSS

for

Alleg

rett

oM

S9:

Kac

hro

o/M

achor

ro10

:00

AM

–10

:30

AM

Pei

jun

Li

Aih

ua

Wood

Op

ennin

gR

emar

ks

Jer

ome

Bla

ir10

:30

AM

–11

:00

AM

Mao

jun

Li

Vru

shal

iB

okil

Chia

raM

oce

nni

P.D

.Span

os11

:00

AM

–11

:30

AM

Ngh

iem

V.

Ngu

yen

Shao

zhon

gD

eng

Shuhua

Zhan

gA

aron

Lutt

man

11:2

0A

M–

12:0

0P

MY

anzh

iZ

han

gP

eiju

nL

iP

eter

Min

evA

.V.

Bal

akkri

shnan

12:0

0P

M–

2:00

PM

Lunch

atH

azel

M.

Wilso

nD

inin

gC

omm

ons

(DIN

)2:

00P

M–

2:50

PM

CB

CA

106

Max

Gunzb

urg

er(C

hai

r:H

onga

oY

ang)

Ple

nar

yT

alks

CB

CA

110

Jin

chao

Xu

(Chai

r:P

engt

aoSun)

CB

CC

116

CB

CA

110

CB

CA

106

CB

CC

118

Con

curr

ent

Ses

sion

sM

S8:

Bar

thet

al.

Chai

r:Jin

chao

Xu

SP

for

Alleg

rett

oM

S6:

Sun/C

hen

/Hu

3:00

PM

–3:

30P

MM

ats

Lar

son

Ran

isIb

ragi

mov

Ducc

ioP

apin

iL

ong

Chen

3:30

PM

–4:

00P

MP

aul

Hou

ston

Gra

ceF

.Jeff

erso

nL

iqun

Cao

Pen

gtao

Sun

4:00

PM

–4:

30P

MC

offee

Bre

akC

BC

C11

6C

BC

A11

0C

BC

A10

6C

BC

C11

8C

oncu

rren

tSes

sion

sM

S8:

Bar

thet

al.

MS2:

Chen

/Rin

gler

SP

for

Alleg

rett

oM

S9:

Kac

hro

o/M

achor

ro4:

30P

M–

5:00

PM

Luka

sK

orou

sA

nto

ine

Rou

ssea

uJia

ng

Zhu

Nev

een

Shla

yan

5:00

PM

–5:

30P

MP

avel

Sol

inL

eslie

Sm

ith

Kai

Huan

gD

anie

leSch

iava

zzi

5:30

PM

–6:

00P

MA

ugu

stJoh

anss

onM

ark

Tay

lor

Ray

mon

dC

han

Lillian

Rat

liff

3

ScheduleM

onday,

April

2,

2012

8:30A

M–

9:20A

MC

BC

A106

Zhim

inZ

han

g(C

hair:

Chi-W

ang

Shu)

Plen

aryT

alks

CB

CA

112Z

han

gxin

gC

hen

(Chair:

M.

Ned

a)C

BC

A106

CB

CC

116C

BC

A112

CB

CC

118C

oncu

rrent

Session

sC

hair:

Zhim

inZ

han

gC

hair:

W.

Lay

tonSS

forF

airweath

erC

hair:

Shan

gyouZ

han

g9:30

AM

–10:00

AM

Weim

inH

anJue

Yan

B.

Bialeck

iQ

iW

ang

10:00A

M–

10:30A

MSum

Chow

Jian

xian

Qiu

Xiao-C

huan

Cai

Chuan

juX

u10:30

AM

–11:00

AM

Coff

eeB

reakC

BC

C116

CB

CC

118C

BC

A112

CB

CA

106C

oncu

rrent

Session

sM

S8:

Barth

...C

hair:

A.

Wood

SS

forF

airweath

erM

S7:

Sun/L

i11:00

AM

–11:30

AM

Jeff

Ban

ks

Zhen

Pen

gR

.I.F

ernan

des

Erk

ki

Som

ersalo11:30

AM

–12:00

PM

Tim

Barth

Min

Hyung

Cho

Ray

mon

dC

han

Yin

gH

e12:00

PM

–12:30

PM

Murtazo

Nazarov

Shan

Zhao

Mich

aelM

cCou

rtX

iaJi

12:30P

M–

2:00P

ML

unch

atH

azelM

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ilsonD

inin

gC

omm

ons

(DIN

)2:00

PM

–2:50

PM

CB

CA

106C

hi-W

ang

Shu

(Chair:

Max

Gunzb

urger)

Plen

aryT

alks

CB

CA

112G

raeme

Fairw

eather

(Chair:

Mary

Wheeler)

CB

CC

116C

BC

C118

CB

CA

112C

BC

A106

Con

curren

tSession

sM

S1:

Zhan

gxin

gC

hen

MS5:

Ned

a/Man

icaSS

forF

airweath

erC

hair:

Weim

inH

an3:00

PM

–3:30

PM

Shuyu

Sun

Dan

ielaC

alvettiP

aul

Muir

NC

Lab

:P

avelSolin

3:30P

M–

4:00P

ME

.W.

Jen

kin

sT

raianIliescu

C.S

.C

hen

NC

Lab

:P

avelSolin

4:00P

M–

4:30P

MC

offee

Break

CB

CC

116C

BC

C118

CB

CA

112C

BC

A106

Con

curren

tSession

sM

S1:

Zhan

gxin

gC

hen

MS5:

Ned

a/Man

icaSS

forF

airweath

erM

S7:

Sun/L

i4:30

PM

–5:00

PM

Guan

griX

ue

William

Lay

tonW

eiwei

Sun

Jigu

ang

Sun

5:00P

M–

5:30P

MW

enyuan

Liao

Max

imO

lshan

skii

A.

Karageorgh

isT

.R.

Khan

5:30P

M–

6:00P

MX

iaofeng

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gQ

inShen

g6:30

PM

–9:30

PM

Ban

quet

atR

ichard

Tam

Alu

mni

Cen

ter(T

AC

)

4

Schedule

Tuesd

ay,

Apri

l3,

2012

8:30

AM

–9:

20A

MC

BC

A10

6P

avel

Boch

ev(C

hai

r:G

ang

Bao

)P

lenar

yT

alks

CB

CA

112

Les

zek

Dem

kow

icz

(Chai

r:Shuyu

Sun)

CB

CC

116

CB

CA

106

CB

CA

112

CB

CC

118

Con

curr

ent

Ses

sion

sM

S3:

Eva

ns/

Per

ego

Chai

r:P

avel

Boch

evM

S6:

Sun/C

hen

/Hu

Chai

r:H

uoy

uan

Duan

9:30

AM

–10

:00

AM

Dan

iel

Mar

tin

Zhij

ian

Wu

Min

gW

ang

R.B

.K

earf

ott

10:0

0A

M–

10:3

0A

MH

elen

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ouss

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iA

.T

oiva

nen

Chen

song

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gF

atih

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iker

10:3

0A

M–

11:0

0A

MC

offee

Bre

akC

BC

C11

6C

BC

A10

6C

BC

A11

2C

BC

C11

8C

oncu

rren

tSes

sion

sM

S3:

Eva

ns/

Per

ego

MS2:

Chen

/Rin

gler

MS6:

Sun/C

hen

/Hu

Chai

r:Q

iW

ang

11:0

0A

M–

11:3

0X

yla

rA

say-D

avis

Rob

ert

Hig

don

Liu

qia

ng

Zhon

gZ

hip

ing

Li

11:3

0A

M–

12:0

0C

arl

Gla

dis

hR

amN

air

Shan

you

Sco

ttZ

han

gIv

anY

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12:0

0P

M–

12:3

0G

uilla

um

eJou

vet

Wei

Len

gY

unro

ng

Zhu

Huoy

uan

Duan

12:3

0P

M–

2:00

PM

Lunch

atH

azel

M.

Wilso

nD

inin

gC

omm

ons

(DIN

)2:

00P

M–

2:50

PM

CB

CA

106

Gan

gB

ao(C

hai

r:E

ric

Mac

hor

ro)

Ple

nar

yT

alks

CB

CA

112

Todd

Arb

ogas

t(C

hai

r:L

ong

Chen

CB

CC

116

CB

CA

106

CB

CA

112

CB

CC

118

Con

curr

ent

Ses

sion

sM

S3:

Eva

ns/

Per

ego

MS5:

Ned

a/M

anic

aM

S6:

Sun/C

hen

/Hu

Chai

r:P

avel

Sol

in3:

00P

M–

3:30

PM

Tob

inIs

aac

Jas

onH

owel

lX

iaoz

he

Hu

Cri

stin

aC

orci

no

3:30

PM

–4:

00P

MJed

Bro

wn

Ale

xan

der

Lab

ovsk

yJun

Hu

Mik

eD

amer

on4:

00P

M–

4:30

PM

Coff

eeB

reak

CB

CC

116

CB

CA

106

CB

CA

112

CB

CC

118

Con

curr

ent

Ses

sion

sC

hai

r:T

odd

Arb

ogas

tM

S5:

Ned

a/M

anic

aM

S6:

Sun/C

hen

/Hu

Chai

r:R

.B.

Kea

rfot

t4:

30P

M–

5:00

PM

Die

goA

ssen

cio

Hye

suk

Lee

Win

g-C

heo

ng

(Jon

)L

oA

.W

arzy

nsk

i5:

00P

M–

5:30

PM

Mat

thew

Hubbar

dC

arol

ina

Man

ica

Xin

feng

Liu

He

Yan

g5:

30P

M–

6:00

PM

Xu

Zhan

gM

onik

aN

eda

Lili

Ju

Rob

erto

Cor

cino

5

Schedule

Wednesd

ay,

April

4,

2012

8:30A

M–

9:20A

MC

BC

A106

Ran

dolp

hB

ank

(Chair:

Yan

pin

gL

in)

Plen

aryT

alks

CB

CA

112Jich

un

Li

(Chair:

Yau

Shu

Won

g)C

BC

C116

CB

CA

106C

BC

A112

Con

curren

tSession

sC

hair:

Shuhua

Zhan

gM

S5:

Ned

a/Man

icaM

S6:

Sun/C

hen

/Hu

9:300A

M–

10:00A

MM

artinSty

nes

Abigail

Bow

ersJam

esB

rannick

10:00A

M–

10:30A

MT

ong

Kan

gL

eoR

ebholz

Jeff

reyO

vall10:30

AM

–11:00

AM

Coff

eeB

reakC

BC

C116

CB

CA

106C

BC

A112

Con

curren

tSession

sC

hair:

Martin

Sty

nes

MS5:

Ned

a/Man

icaM

S6:

Sun/C

hen

/Hu

11:00A

M–

11:30A

MY

anpin

gC

hen

Hoan

gT

ranH

enggu

ang

Li

11:30A

M–

12:00P

MT

odd

Rin

glerN

icholas

Wilson

Hualon

gF

eng

12:00P

M–

12:30P

MD

omin

ikSch

oetzau

Wen

xian

gZ

hu

12:30P

M–

2:00P

ML

unch

atH

azelM

.W

ilsonD

inin

gC

omm

ons

(DIN

)

6

Program

Sunday, April 1, 2012

8:00 AM – 8:30 AM: Registration at CBC A

8:40 AM – 9:30 AM: Two Concurrent Plenary Talks

Room: CBC A106Chair: Ivan Yotov, University of Pittsburgh, USACoupling Compositional Flow, Transport, and Mechanics in Porous Media forModeling Carbon Sequestration in Saline Aquifers (p. 33)Mary F. Wheeler, The University of Texas at Austin, USA

Room: CBC A110Chair: Jichun Li, University of Nevada, Las Vegas, USAReduced Models You can Believe in (p. 32)Jan S. Hesthaven, Brown University, USA

9:30 AM – 10:00 AM: Coffee Break

10:00 AM – 12:00 PM: Four Concurrent Sessions

Room: CBC C116Mini-symposium 4Advances in analytical and computational techniques for nonlinear wavesOrganizer: Yanzhi Zhang, Missouri University of Science and Technology, USA10:00 AM – 10:30 AM Analysis of electromagnetic cavity scattering problems (p. 50)

Peijun Li, Purdue University, USA10:30 AM – 11:00 AM Central discontinuous Galerkin methods for shallow water waves

(p. 50)Maojun Li, Rensselaer Polytechnic Institute, USA

7


11:00 AM – 11:30 AM Global existence for a system of Schrodinger equations withpower-type nonlinearities (p. 51)Nghiem V. Nguyen, Utah State University, USA

11:30 AM – 12:00 PM Numerical methods for rotating dipolar BEC based on a rotatingLagrange coordinate (p. 51)Yanzhi Zhang, Missouri University of Science and Technology,USA

Room: CBC A110Chair: Jan Hesthaven, Brown University, USA10:00 AM – 10:30 AM Topics on electromagnetic scattering from cavities (p. 77)

Aihua W. Wood, Air Force Institute of Technology, USA10:30 AM – 11:00 AM High Order Finite Difference Methods for Maxwell’s Equations

in Dispersive Media (p. 69)Vrushali Bokil, Oregon State University, USA

11:00 AM – 11:30 AM Generalized image charge solvation model for electrostatic inter-actions in molecular dynamics simulations of aqueous solutions(p. 70)Shaozhong Deng, UNC Charlotte, USA

11:30 AM – 12:00 PM Generalized Foldy-Lax Formulation and its Application to theInverse Scattering (p. 73)Peijun Li, Purdue University, USA

Room: CBC A106A Special Session in Honor of Walter Allegretto’s 70th BirthdayChair: Hong Xie, Manulife Financial, Canada10:00 AM – 10:30 AM Openning Remarks10:30 AM – 11:00 AM Homogenization and parameter estimation of reaction-diffusion

systems with rough boundaries (p. 36)Chiara Mocenni, University of Siena, Italy

11:00 AM – 11:30 AM A Front-fixing Finite Element Method for the Valuation of Amer-ican Options with Regime Switching (p. 37)Shuhua Zhang, Tianjin University of Finance and Economics,China

11:30 AM – 12:00 PM A Direction Splitting Algorithm for Flow Problems in Com-plex/Moving Geometries (p. 35)Peter Minev, University of Alberta, Edmonton, Canada

Room: CBC C118Mini-symposium 9Uncertainty Quantification For Signal Processing and Inverse ProblemsOrganizers: Pushkin Kachroo, University of Nevada, Las Vegas, USAEric Machorro, National Security Technologies, LLC, USA

8


10:00 AM – 10:30 AM Estimating the bias of local polynomial approximation methodsusing the Peano kernel (p. 66)Jerome Blair, Keystone International and NSTec, USA

10:30 AM – 11:00 AM Hybrid Numerical Techniques for Efficient Determination ofstochastic Nonlinear Dynamic Responses via harmonic Wavelets(p. 67)P.D. Spanos, Rice University, USA

11:00 AM – 11:30 AM Computational Methods for Analyzing Fluid Flow Dynamicsfrom Digital Imagery Authors (p. 67)Aaron Luttman, National Security Technologies LLC, USA

11:30 AM – 12:00 PM Application of Random Field Theory (p. 67)A.V. Balakkrishnan, University of California, Los Angeles,USA

12:00 PM – 2:00 PM: Lunch at Hazel M. Wilson Dining Commons

2:00 PM – 2:50 PM: Two Concurrent Plenary Talks

Room: CBC A106Chair: Hongtao Yang, University of Nevada, Las Vegas, USAEfficient Numerical Approaches for the Simulation and Control of PDEs withRandom Inputs (p. 32)Max Gunzburger, Florida State University, USA

Room: CBC A110Chair: Pengtao Sun, University of Nevada, Las Vegas, USAOptimal Discretization, Adaptation and Iterative Solver for High Order PartialDifferential Equations (p. 33)Jinchao Xu, Penn State University, USA

3:00 PM – 4:00 PM: Four Concurrent Sessions

Room: CBC C116Mini-symposium 8Recent Developments in Adaptivity and A Posteriori Error AnalysisOrganizers: Tim Barth, NASA, USAPaul Houston, University of Nottingham, UKMats Larson, University of Umea, Sweden

9


3:00 PM – 3:30 PM Adaptive Model Reduction for Coupled Thermoelastic Problems(p. 63)Mats Larson, Umea University, Sweden

3:30 PM – 4:00 PM Two-Grid hp–Adaptive Discontinuous Galerkin Finite ElementMethods for Second–Order Quasilinear Elliptic PDEs (p. 64)Paul Houston, University of Nottingham, UK

Room: CBC A110Chair: Jinchao Xu, Pennsylvania State University, USA3:00 PM – 3:30 PM Lie Group Analysis – a microscope of physical and engineering

sciences (p. 80)Ranis N. Ibragimov, University of Texas at Brownsville, USA

3:30 PM – 4:00 PM Higher and Approximate Symmetries of Differential EquationsUsing MAPLE (p. 84)Grace Jefferson, Deakin University, Australia

Room: CBC A106A Special Session in Honor of Walter Allegretto’s 70th BirthdayChair: Raymond Chan, The Chinese University of Hong Kong, Hong Kong3:00 PM – 3:30 PM Periodic solutions to nonlinear equations with oblique boundary

conditions (p. 36)Duccio Papini, Universita degli Studi di Siena, Italy

3:30 PM – 4:00 PM A Molecular Dynamics-Continuum Coupled Model for HeatTransfer in Composite Materials (p. 35)Liqun Cao, Chinese Academy of Sciences, China

Room: CBC C118Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China3:00 PM – 3:30 PM A Robust and Efficient Method for Steady State Patterns in

Reaction-Diffusion Systems (p. 59)Wing-Cheong (Jon) Lo, The Ohio State University, USA

3:30 PM – 4:00 PM Dirichlet/Robin iteration-by-subdomain Schwarz-DDM for mul-tiphase fuel cell model with micro-porous layer (p. 60)Pengtao Sun, University of Nevada Las Vegas, USA

4:00 PM – 4:30 PM: Coffee Break

10


4:30 – 6:00 PM: Four concurrent sessions

Room: CBC C116Mini-symposium 8Recent Developments in Adaptivity and A Posteriori Error AnalysisOrganizers: Tim Barth, NASA, USAPaul Houston, University of Nottingham, UKMats Larson, University of Umea, Sweden4:30 PM – 5:00 PM Advanced Aspects of Adaptive Higher-Order Methods (p. 64)

Lukas Korous, Charles University, Prague5:00 PM – 5:30 PM Adaptive Higher-Order Finite Element Methods for Transient

PDE Problems Based on Embedded Higher-Order ImplicitRunge-Kutta Methods (p. 65)Pavel Solin, University of Nevada, Reno, USA

5:30 PM – 6:00 PM Blockwise Adaptivity for Time Dependent Problems Based onCoarse Scale Adjoint Solutions (p. 65)August Johansson, University of California, Berkeley, USA

Room: CBC A110Mini-symposium 2Insight Into Geophysical Fluid Dynamics Through Analysis and ComputationOrganizers: Qingshan Chen and Todd Ringler, Los Alamos National Laboratory, USA4:30 PM – 5:00 PM On the quasi-hydrostatic ocean models (p. 45)

Antoine Rousseau, INRIA, France5:00 PM – 5:30 PM Tropical Cyclogenesis and Vertical Shear in a Moist Boussinesq

Model (p. 45)Leslie Smith, University of Wisconsin, Madison, USA

5:30 PM – 6:00 PM A Spectral Element Method for the Community AtmosphereModel (p. 46)Mark Taylor, Sandia National Laboratory, USA

Room: CBC A106A Special Session in Honor of Walter Allegretto’s 70th BirthdayChair: Peter Minev, University of Alberta, Edmonton, Canada4:30 PM – 5:00 PM Mixed finite element analysis of thermally coupled non-

Newtonian flows (p. 37)Jiang Zhu, Laboratorio Nacional de Computacao Cientıfica,Brazil

5:00 PM – 5:30 PM Instant System Availability (p. 71)Kai Huang, Florida International University, USA

11


5:30 PM – 6:00 PM A Variational Approach for Exact Histogram Specification (p. 35)Raymond Chan, The Chinese University of Hong Kong, HongKong

Room: CBC C118Mini-symposium 9Uncertainty Quantification For Signal Processing and Inverse ProblemsOrganizers: Pushkin Kachroo, University of Nevada, Las Vegas, USAEric Machorro, National Security Technologies, LLC, USA4:30 PM – 5:00 PM Analysis and Methods for Time Resolved Neutron Detection

(p. 67)Neveen Shlayan, Singapore-MIT Alliance for Research & Tech-nology, MIT, USA

5:00 PM – 5:30 PM Stochastic Spectral Approximation with Redundant Multiresolu-tion Dictionaries for Uncertainty Quantification (p. 68)Daniele Schiavazzi, Stanford University, USA

5:30 PM – 6:00 PM Conservation Law Methods for Uncertainty Propagation in Dy-namic Systems (p. 68)Lillian Ratliff, UC Berkeley, USA

12

Program

Monday, April 2, 2012

8:30 AM – 9:20 AM: Two concurrent plenary talks

Room: CBC A106Chair: Chi-Wang Shu, Brown University, USAUnclaimed Territories of Superconvergence I: Spectral and Spectral CollocationMethods (p. 34)Zhimin Zhang, Wayne State University, USA

Room: CBC A112Chair: Monika Neda, University of Nevada, Las Vegas, USAChallenges in Numerical Simulation of Unconventional Oil and Gas Reservoirs(p. 30)Zhangxing Chen, University of Calgary, Canada

9:30 – 10:30: Four concurrent sessions

Room: CBC A106Chair: Zhimin Zhang9:30 AM – 10:00 AM On A Family of Models in X-ray Dark-field Tomography (p. 71)

Weimin Han, University of Iowa, USA10:00 AM – 10:30 AM Multi-frequency methods for an inverse source problem (p. 69)

Sum Chow, Brigham Young University, USA

Room: CBC C116Chair: William Layton, University of Pittsburgh, USA9:30 AM – 10:00 AM Direct Discontinuous Galerkin method and Its Variations for Dif-

fusion Problems (p. 78)Jue Yan, Iowa State University, USA

13


10:00 AM – 10:30 AM Hybrid weighted essentially non-oscillatory schemes with differ-ent indicators (p. 74)Jianxian Qiu, Xiamen University, China

Room: CBC A112A Special Session in Honor of Graeme Fairweather’s 70th BirthdayChair: C.S. Chen, University of Southern Mississippi, USA9:30 AM – 10:00 AM Orthogonal Spline Collocation for Quasilinear Parabolic Prob-

lems with Nonlocal Boundary Conditions (p. 38)B. Bialecki∗, Colorado School of Mines, USA

10:00 AM – 10:30 AM A Space-time Domain Decomposition Method for StochasticParabolic Problems (p. 38)Xiao-Chuan Cai, University of Colorado at Boulder, USA

Room: CBC C118Chair: Shangyou Zhang, University of Delaware, USA9:30 AM – 10:00 AM Multiphase complex fluid models and their applications to com-

plex biological systems (p. 76)Qi Wang, University of South Carolina, USA

10:00 AM – 10:30 AM Fractional Differential Equations: Modeling and Numerical So-lutions (p. 78)Chuanju Xu, Xiamen University, China


11:00 AM – 12:30 PM: Four concurrent sessions

Room: CBC C116Mini-symposium 8Recent Developments in Adaptivity and A Posteriori Error AnalysisOrganizers: Tim Barth, NASA, USAPaul Houston, University of Nottingham, UKMats Larson, University of Umea, Sweden11:00 AM – 11:30 AM A Posteriori Error Estimation via Nonlinear Error Transport

(p. 65)Jeff Banks, Lawrence Livermore National Laboratory, USA

11:30 AM – 12:00 PM Dual Problems in Error Estimation and Uncertainty Propagationfor Hyperbolic Problems (p. 65)Tim Barth, NASA Ames Research Center Moffett Field, USA

14


12:00 PM – 12:30 PM A Posteriori Error Estimation for Compressible Flows using En-tropy Viscosity (p. 66)Murtazo Nazarov, Texas A&M University, USA

Room: CBC C118Chair: Aihua Wood, Air Force Institute of Technology, USA11:00 AM – 11:30 AM A Scalable Non-Conformal Domain Decomposition Method For

Solving Time-Harmonic Maxwell Equations In 3D (p. 72)Zhen Peng, Ohio State University, USA

11:30 AM – 12:00 PM A Fast Volume Integral Solver for 3-D Objects Embedded in Lay-ered Media (p. 79)Min Hyung Cho, The University of North Carolina at Char-lotte, USA

12:00 PM – 12:30 PM High order interface methods for electromagnetic systems in dis-persive inhomogeneous media (p. 78)Shan Zhao, University of Alabama, USA

Room: CBC A112A Special Session in Honor of Graeme Fairweather’s 70th BirthdayChair: Andreas Karageorghis, University of Cyprus, Cyprus11:00 AM – 11:30 AM ADI Orthogonal Spline Collocation Method on Non-rectangular

Regions (p. 39)R. I. Fernandes, The Petroleum Institute, UAE

11:30 AM – 12:00 PM Linearized alternating direction method for constrained linearleast-squares problem (p. 38)Raymond Chan, The Chinese University of Hong Kong, HongKong

12:00 PM – 12:30 PM Stable Computations with Gaussians (p. 40)Michael McCourt, Cornell University, USA

Room: CBC A106Mini-symposium 7Direct and Inverse Scattering for Wave PropagationOrganizers: Jiguang Sun, Delaware State University, USAPeijun Li, Purdue University, USA11:00 AM – 11:30 AM Statistical methods applied to the inverse problem in electroneu-

rography (p. 61)Erkki Somersalo, Case Western Reserve University, USA

11:30 AM – 12:00 PM An Efficient and Stable Spectral Method for ElectromagneticScattering from a Layered Periodic Structure (p. 62)Ying He - Purdue University, USA

15


12:00 PM – 12:30 PM A Schwarz generalized eigen-oscillation spectral element method(GeSEM) for 2-D high frequency electromagnetic scattering indispersive inhomogeneous media (p. 62)Xia Ji, Chinese Academy of Sciences, China


2:00 PM – 2:50 PM: Two concurrent plenary talks

Rom: CBC A106Chair: Max Gunzburger, Florida State University, USADiscontinuous Galerkin Method for Hamilton-Jacobi Equations and Front Prop-agation with Obstacles (p. 32)Chi-Wang Shu, Brown University, USA

Room: CBC A112Chair: Mary Wheeler, University of Texas at Austin, USAAlternating Direction Implicit (ADI) Methods – a Personal Retrospective (p. 31)Graeme Fairweather, American Mathematical Society, USA

3:00 PM 00 4:00 PM: Four concurrent sessions

Room: CBC C116Mini-symposium 1Computational Methods for Multiphase Flow in Porous MediaOrganizer: Zhangxing Chen, University of Calgary, Canada3:00 PM – 3:30 PM Simulation of Multiphase Flow in Porous Media using Locally

Conservative Finite Element Methods (p. 43)Shuyu Sun, KAUST, Kingdom of Saudi Arabia

3:30 PM – 4:00 PM Mathematical Analysis of Problems in Filtration Applications(p. 43)E.W. Jenkins, Clemson University, USA

Room: CBC C118Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil

16


3:00 PM – 3:30 PM Bayesian source separation in MEG (p. 52)Daniela Calvetti, Case Western Reserve University, USA

3:30 PM – 4:00 PM Approximate Deconvolution Large Eddy Simulation of aBarotropic Ocean Circulation Model (p. 52)Traian Iliescu, Virginia Tech, USA

Room: CBC A112A Special Session in Honor of Graeme Fairweather’s 70th BirthdayChair: Yanping Lin, The Hong Kong Polytechnic University, Hong Kong3:00 PM – 3:30 PM B-Spline Collocation Software for PDEs with Efficient

Interpolation-Based Spatial Error Estimation (p. 40)Paul Muir, Saint Mary’s University, Canada

3:30 PM – 4:00 PM Fast Solution of the Method of Fundamental Solutions for Mod-ified Helmholtz Equations (p. 39)C.S. Chen, University of Southern Mississippi, USA

Room: CBC A106Chair: Weimin Han, University of Iowa, USA3:00 PM – 4:00 PM Networked Computing Laboratory (NCLab) (p. 75)

Pavel Solin, University of Nevada – Reno, USA


4:30 PM – 6:00 PM: Four concurrent sessions

Room: CBC C116Mini-symposium 1Computational Methods for Multiphase Flow in Porous MediaOrganizer: Zhangxing Chen, University of Calgary, Canada4:30 PM – 5:00 PM Recent Developments in Multipoint Flux Mixed Finite Elements

(p. 42)Guangri Xue (Gary), Shell, USA

5:00 PM – 5:30 PM A numerical method for solving 3D elastic wave equation inanisotropic heterogeneous medium (p. 42)Wenyuan Liao, University of Calgary, Canada

17


Room: CBC C118Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil4:30 PM – 5:00 PM Modern ideas in turbulence confront legacy codes (p. 53)

William Layton, University of Pittsburgh, USA

5:00 PM – 5:30 PM Numerical free surface flows on dynamic octree meshes (p. 53)Maxim Olshanskii, Moscow State University, Russia

5:30 PM – 6:00 PM The dynamics of two phase complex fluids: dropformation/pinch-off (p. 55)Xiaofeng Yang, University of South Carolina, USA

Room: CBC A112A Special Session in Honor of Graeme Fairweather’s 70th BirthdayChair: B. Bialecki, Colorado School of Mines, US4:30 PM – 5:00 PM A Legendre-Galerkin method of the Helmholtz Equation for Elec-

tromagnetics Cavity Problem (p. 40)Weiwei Sun, City University of Hong Kong, Hong Kong

5:00 PM – 5:30 PM The method of fundamental solutions for the solution of inverseproblems (p. 39)Andreas Karageorghis, University of Cyprus, Cyprus

5:30 PM – 6:00 PM Expectations and Limitations of the Compact Splitting Methodfor Quenching-combustion Problems (p. 41)Qin Sheng, Baylor University, USA

Room: CBC A106Mini-symposium 7Direct and Inverse Scattering for Wave PropagationOrganizers: Jiguang Sun, Delaware State University, USAPeijun Li, Purdue University, USA4:30 PM – 5:00 PM An eigenvalue method using multiple frequency data (p. 63)

Jiguang Sun, Delaware State University, USA5:00 PM – 5:30 PM Sparse reconstruction in diffuse optical tomography (p. 63)

Taufiquar Rahman Khan, Clemson University, USA

6:30 PM – 9:30 PM: Banquet at Richard Tam Alumni Center

18

Program

Tuesday, April 3, 2012


Room: CBC A112Chair: Shuyu Sun, KAUST, Kingdom of Saudi ArabiaDiscrete Stability, DPG Method and Least Squares (p. 31)L. Demkowicz, ICES, UT Austin, USA

Room: CBC A106Chair: Gang Bao, Michigan State University, USAOptimization-Based Methods for Conservative and Monotone Transport andRemap (p. 30)Pavel Bochev, Sandia National Laboratories, USA

9:30 AM – 10:30 AM: Four concurrent sessions

Room: CBC C116Mini-symposium 3Developing ice-sheet models for the next generation climate simulationOrganizers: Katherine J. Evans, Oak Ridge National Laboratory, USAMauro Perego, Florida State University, USA9:30 AM – 10:00 AM BISICLES – progress on a higher-order adaptive mesh refinement

ice-sheet model (p. 47)Daniel Martin, Lawrence Berkeley National Lab, USA

10:00 AM – 10:30 AM A simple approach to modeling multi-physics coupled models,application to large-scale ice sheet models (p. 47)Helene Seroussi, Caltech-Jet Propulsion Laboratory, USA andEcole Centrale Paris, Chatenay-Malabry, France

19


Room: CBC A106Pavel Bochev, Sandia National Laboratories, USA9:30 AM – 10:00 AM Most Likely Paths of Shortfalls in Long-Term Hedging with

Short-Term FuturesZhijian Wu, University of Alabama, USA

10:00 AM – 10:30 AM Pricing Options under Jump-diffusion ModelsJari Toivanen, Stanford University, Stanford, USA

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China9:30 AM – 10:00 AM Cell conservative flux recovery and a posteriori error estimate of

high order finite volume methods (p. 60)Ming Wang, University of California at Irvine, USA and PekingUniversity, China

10:00 AM – 10:30 AM A parallel geometric-algebraic multigrid solver for the Stokesproblem (p. 60)Chensong Zhang, Chinese Academy of Sciences, China

Room: CBC C118Chair: Huoyuan Duan, Nankai University, China9:30 AM – 10:00 AM Optimization Under Uncertainty: Models and Computational

TechniquesRalph Baker Kearfott, University of Louisiana at Lafayette,USA

10:00 AM – 10:30 AM HDG methods for Reissner-Mindlin platesFatih Celiker, Wayne State University, USA


11:00 AM – 12:30 PM: Four concurrent sessions

Room: CBC C116Mini-symposium 3Developing ice-sheet models for the next generation climate simulationOrganizers: Katherine J. Evans, Oak Ridge National Laboratory, USAMauro Perego, Florida State University, USA

20


11:00 AM – 11:30 AM A method for simulating dynamic ice shelves in global ocean mod-els (p. 48)Xylar Asay-Davis, Los Alamos National Laboratory, USA

11:30 AM – 12:00 PM Which physics for coupled ice sheet and ocean models? Lessonslearned from Petermann Glacier (p. 48)Carl Gladish, New York University, USA

12:00 PM – 12:30 PM A geometrical multigrid method for shallow ice models based onan energy minimization approach (p. 49)Guillaume Jouvet, Free University of Berlin, Germany

Room: CBC A106Mini-symposium 2Insight Into Geophysical Fluid Dynamics Through Analysis and ComputationOrganizers: Qingshan Chen and Todd Ringler, Los Alamos National Laboratory, USA11:00 AM – 11:30 AM Multiple Time Scales and Time Stepping for Ocean Circulation

Models (p. 44)Robert L. Higdon, Oregon State University, USA

11:30 AM – 12:00 PM Non-Oscillatory Central Finite-Volume Schemes for AtmosphericNumerical Modeling (p. 45)Ram Nair, National Center for Atmospheric Research, USA

12:00 PM – 12:30 PM Earth core thermal convection simulation using high-order finiteelement (p. 44)Wei Leng, Chinese Academy of Sciences, China

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China11:00 AM – 11:30 AM A BPX preconditioner for the symmetric discontinuous Galerkin

methods on graded meshes (p. 61)Liuqiang Zhong, South China Normal University, China andThe Chinese University of Hong Kong, Hong Kong

11:30 AM – 12:00 PM On a Robin-Robin domain decomposition method with optimalconvergence rate (p. 61)Shangyou Zhang, University of Delaware, USA

12:00 PM – 12:30 PM Adaptive finite element techniques for Einstein constraints (p. 61)Yunrong Zhu, University of California at San Diego, USA

21


Room: CBC C118Chair: Qi Wang, University of South Carolina, USA11:00 AM – 11:30 AM A Multiple-Endpoints Chebysheve Collocation Method For High

Order Problems (p. 73)Zhiping Li, Peking University, China

11:30 AM – 12:00 PM Mortar multiscale methods for Stokes-Darcy flows in irregulardomains (p. 77)Ivan Yotov, University of Pittsburgh, USA

12:00 PM – 12:30 PM L2 Projected C0 Elements for non H1 Very Weak Solution of curland div Operators (p. 70)Huoyuan Duan, Nankai University, China


2:00 PM – 2:50 PM: Two concurrent plenary talks

Room: CBC A106Chair: Aaron Luttman, National Security Technologies, LLC, USAFuture Directions for Inverse Scattering Problems (p. 29)Gang Bao, Zhejiang University, China and Michigan State University, USA

Room: CBC A112Chair: Long Chen, University of California, USAMultiscale Mixed Methods for Heterogeneous Elliptic Problems (p. 29)Todd Arbogast, UT Austin, USA


Room: CBC C116Mini-symposium 3Developing ice-sheet models for the next generation climate simulationOrganizers: Katherine J. Evans, Oak Ridge National Laboratory, USAMauro Perego, Florida State University, USA3:00 PM – 3:30 PM Advanced ice sheet modeling: scalable parallel adaptive full

Stokes solver and inversion for basal slipperiness and rheologi-cal parameters (p. 49)Tobin Isaac, The University of Texas at Austin, USA

22


3:30 PM – 4:00 PM Scalable and composable implicit solvers for polythermal ice flowwith steep topography (p. 50)Jed Brown, Argonne National Laboratory, USA

Room: CBC A106Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil3:00 PM – 3:30 PM Dual-mixed finite element methods for the Navier-Stokes equa-

tionsJason Howell, Clarkson University, USA

3:30 PM – 4:00 PM An efficient and accurate numerical method for high-dimensionalstochastic partial differential equationsAlexander Labovsky, Michigan Technological University, USA

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China3:00 PM – 3:30 PM Algebraic Multigrid Methods for Petroleum Reservoir Simulation

Xiaozhe Hu, The Pennsylvania State University, USA3:30 PM – 4:00 PM The adaptive nonconforming finite element method for the fourth

order problemJun Hu, Peking University, China

Room: CBC C118Chair: Pavel Solin, University of Nevada Reno, USA3:00 PM – 3:30 PM Asymptotic Formulas for the Generalized Stirling Numbers of the

Second Kind with Integer Parameters (p. 81)Cristina B. Corcino, De La Salle University, Philippines

3:30 PM – 4:00 PM Effects of Rotation on Energy Stabilization of Internal GravityWaves Confined in a Cylindrical Basin (p. 83)Michael Dameron, University of Texas at Brownsville, USA.



23


Room: CBC C116Chair: Todd Arbogast, University of Texas at Austin, USA4:30 PM – 5:00 PM Second Order Virtual Node Algorithms for Stokes Flow Problems

with Interfacial Forces and Irregular Domains (p. 79)Diego C. Assencio, University of California, Los Angeles, USA

5:00 PM – 5:30 PM Unconditionally Positive Residual Distribution Schemes for Hy-perbolic Conservation Laws (p. 79)M.E.Hubbard, University of Leeds, UK

5:30 PM – 6:00 PM Immerse Finite Element Methods for Solving Parabolic TypeMoving Interface Problems (p. 85)Xu Zhang, Virginia Tech, USA

Room: CBC A106Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil4:30 PM – 5:00 PM Numerical and analytical study for viscoelastic flow in a moving

domain (p. 54)Hyesuk Lee, Clemson University, USA

5:00 PM – 5:30 PM Stability and Convergence Analysis: Leray-Iterated-TikhonovNSE with Time Relaxation (p. 54)Carolina Manica, Universidade Federal do Rio Grande do Sul,Brasil

5:30 PM – 6:00 PM Sensitivity Analysis and Computations for Regularized Navier-Stokes Equations (p. 55)Monika Neda, University of Nevada Las Vegas, USA

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China4:30 PM – 5:00 PM Multigrid Methods for Stokes Equation based on Distributive

Gauss-Seidel Relaxation (p. 56)Long Chen, University of California at Irvine, USA

5:00 PM – 5:30 PM Operator splitting methods for stiff convection-reaction-diffusionequations (p. 58)Xinfeng Liu, University of South Carolina, USA

5:30 PM – 6:00 PM Covolume-Upwind Finite Volume Approximations for Linear El-liptic Partial Differential Equations (p. 58)Lili Ju, University of South Carolina, USA

24


Room: CBC C118Chair: R. Baker Kearfott, Uiversity of Louisiana at Lafayette, USA4:30 PM – 5:00 PM Discontinuous-in-Space Explicit Runge-Kutta Residual Distribu-

tion Schemes for Hyperbolic Conservation Laws (p. 82)A. Warzynski, University of Leeds, UK

5:00 PM – 5:30 PM Dispersion and Dissipation Analysis of Two Fully Discrete Dis-continuous Galerkin Methods (p. 84)He Yang, Rensselaer Polytechnic Institute, USA

5:30 PM – 6:00 PM On Generalized Bell Numbers for Complex Argument (p. 81)Roberto B. Corcino, De La Salle University, Philippines

25

Program

Wednesday, April 4, 2012


Room: CBC A106Chair: Yanping Lin, The Hong Kong Polytechnic University, Hong KongSome Algorithmic Aspects of hp-Adaptive Finite Elements (p. 29)Randolph E. Bank, University of California at San Diego, USA

Room: CBC A112Chair: Yau Shu Wong, University of Alberta, CanadaFinite element analysis of electromaganetics in metamaterials (p. 32)Jichun Li, University of Nevada, Las Vegas, USA

9:30 – 10:30: Three concurrent sessions

Room: CBC C116Chair: Shuhua Zhang, Tianjin University of Economy and Finance, China9:300 AM – 10:00 AM A balanced finite element method for singularly perturbed

reaction-diffusion problems (p. 76)M. Stynes, National University of Ireland, Ireland

10:00 AM – 10:30 AM A Potential-based Finite Element Scheme with CGM for EddyCurrent Problems (p. 82)Tong Kang, Communication University of China, China

Room: CBC A106Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil

26


9:300 AM – 10:00 AM On the Leray regularization with fine mesh filtering (p. 53)Abigail Bowers, Clemson University, USA

10:00 AM – 10:30 AM Linear solvers for incompressible flow simulations using Scott-Vogelius elements (p. 55)Leo Rebholz, Clemson University, USA

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China9:300 AM – 10:00 AM An Algebraic Multilevel Preconditioner for Graph Laplacians

based on Matching of Graphs (p. 56)James Brannick, The Pennsylvania State University, USA

10:00 AM – 10:30 AM Toward a robust hp-adaptive method for elliptic eigenvalue prob-lems (p. 59)Jeffrey S. Ovall, University of Kentucky, USA


11:00 AM – 12:30 PM: Three concurrent sessions

Room: CBC C116Chair: Martin Stynes, National University of Ireland, Cork, Ireland11:00 AM – 11:30 AM Spectral Collocation Methods for Volterra Integro-Differential

Equations (p. 69)Yanping Chen, South China Normal University, China

11:30 AM – 12:00 PM A High-Order Transport Scheme for Unstructured Atmosphereand Ocean Climate Models (p. 74)Todd Ringler, Los Alamos National Laboratory, USA

12:00 PM – 12:30 PM A mixed finite element method with exactly divergence-free ve-locities for incompressible magnetohydrodynamics(p. 75)Dominik Schoetzau, University of British Columbia, Canada

Room: CBC A106Mini-symposium 5Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, Brasil

27


11:00 AM – 11:30 AM Analysis of stability and errors of IMEX methods for MHD equa-tions (p. 55)Hoang Tran, University of Pittsburgh, USA

11:30 AM – 12:00 PM Physics based filtering for the incompressible Leray-α Magneto-hydrodynamics equations (p. 55)Nicholas Wilson, Clemson University, USA

Room: CBC A112Mini-symposium 6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, China11:00 AM – 11:30 AM New multigrid methods for the Stokes and linear elasticity prob-

lems (p. 58)Hengguang Li, Wayne State University, USA

11:30 AM – 12:00 PM A treecode elastostatics computation (p. 58)Hualong Feng, Illinois Institute of Technology, USA

12:00 PM – 12:30 PM Axially symmetric volume constrained anistropic mean curvatureflow (p. 61)Wenxiang Zhu, Iowa State University, USA


28

Abstracts

Plenary Talks

Multiscale Mixed Methods for Heterogeneous Elliptic ProblemsTodd Arbogast, UT Austin, USAAbstract. We consider a second order elliptic problem with a heterogeneous coefficient writ-ten in mixed form. Multiscale approximation methods for these problems can be viewed inone of three equivalent frameworks: as a Galerkin or finite element method with nonpolyno-mial basis functions, as a variational multiscale method with standard finite elements, or asa domain decomposition method with restricted degrees of freedom on the interfaces. Eachis valuable for devising effective local multiscale methods. Taking a nonoverlapping domaindecomposition view, we define a new multiscale mortar space that incorporates informationfrom homogenization theory to better approximate the solution along the interfaces withjust a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient ofperiod ε, the new method achieves both optimal order error estimates in the discretizationparameters and convergence when ε is small, with no numerical resonance, despite the factthat our method is purely locally defined. Moreover, we present numerical examples to assessits performance when the coefficient is not obviously locally periodic. We show that the newmortar method works well, and better than polynomial mortar spaces.

Some Algorithmic Aspects of hp-Adaptive Finite ElementsRandolph E. Bank, University of California at San Diego, USAAbstract. We will discuss our on-going investigation of hp-adaptive finite elements. Wewill focus on a posteriori error estimates based on superconvergent derivative recovery. Be-sides providing both global error estimates and local error indicators, this family of errorestimates also provides information that forms the basis of our hp-adaptive refinement andcoarsening strategies. In particular, these a posteriori error estimates address in a cost ef-ficient and natural way the critical issue of deciding between h or p refinement/coarsening.Some numerical examples will be provided.

Joint with Hieu Nguyen, University of California at Davis, USA.

Future Directions for Inverse Scattering ProblemsGang Bao, Zhejiang University, China and Michigan State University, USAAbstract. A survey on the recent progress of our research group on three classes of inversescattering problems in wave propagation, namely inverse medium scattering, inverse sourcescattering, and inverse obstacle scattering, will be presented. Issues on numerical solution,mathematical analysis, as well as applications will be discussed. Future directions on theinverse scattering problems and significant new applications will be highlighted.

29

Plenary Talks

Optimization-Based Methods for Conservative and Monotone Transport andRemapPavel Bochev, Sandia National Laboratories, USAAbstract. We describe a new optimization-based modeling (OBM) strategy for compatiblediscretizations and demonstrate its effectiveness by constructing monotone optimization-based transport (OBT) and remap (OBR) schemes without limiters.

OBM is a “divide-and-conquer” approach which separates preservation of properties suchas discrete maximum principle, local bounds, or monotonicity from the discretization pro-cess. In so doing, our approach obviates severe constraints on mesh geometry and fieldrepresentations, thereby greatly improving flexibility of resulting schemes.

In particular, optimization-based transport and remap (OBT/OBR) is formulated as thesolution of a global convex optimization problem in which accuracy considerations, handledby an objective functional, are separated from monotonicity considerations, handled by acarefully defined set of inequality constraints.

The resulting methods are provably linearity preserving on grids with arbitrary cell shapesunder more permissive conditions on the mesh motion than a standard explicit trans-port/remap scheme with, e.g., Van Leer limiting. We demonstrate the scheme on a seriesof standard test problems on non-uniform, unstructured grids. This is joint work with D.Ridzal, K. Peterson, and J. Young.

Challenges in Numerical Simulation of Unconventional Oil and Gas ReservoirsZhangxing Chen, University of Calgary, CanadaAbstract. Mathematical models have widely been used to predict, understand, and optimizecomplex physical processes in modeling and simulation of multiphase fluid flow in petroleumreservoirs. These models are important for understanding the fate and transport of chemicalspecies and heat. With this understanding the models are then applied to the needs of thepetroleum industry to design enhanced oil and gas recovery strategies.

While mathematical modeling and computer simulation have been successful in their appli-cation to the recovery of conventional oil and gas, there still exist a lot of challenges in theirapplication to unconventional oil and gas modeling. As conventional oil and gas reservesdwindle and oil prices rise, the recovery of unconventional oil and gas (such as heavy oil,oil sands, tight gas, and shale gas) is now the center stage. For example, enhanced heavyoil recovery technologies are an intensive research area in the oil industry, and have recentlygenerated a battery of recovery methods, such as cyclic steam stimulation (CSS), steamassisted gravity drainage (SAGD), vapor extraction (VAPEX), in situ combustion (ISC),hybrid steam-solvent processes, and other emerging recovery processes. This presentationwill give an overview on challenges encountered in modeling and simulation of these recoveryprocesses: insufficient physics/chemistry in current models, multi-scale phenomena, phasebehavior, geomechanics, assisted history matching with closed-loop optimization, transportof solvents, wellbore modeling, and four-phase flow. It will also present some case studiesfor the applications of these recovery processes to real heavy oilfields.

30

Plenary Talks

Discrete Stability, DPG Method and Least SquaresL. Demkowicz, ICES, UT Austin, USAAbstract. Ever since the ground breaking paper of Ivo Babuska [1], everybody from FiniteElement (FE) community has learned the famous phrase: “Discrete stability and approx-imability imply convergence.” The challenge in establishing convergence comes from thefact that, except for a relative small class of “safe” coercive (elliptic) problems, continuousstability DOES NOT imply discrete stability. In other words, the problem of interest maybe well posed at the continuous level but this does not imply that the corresponding FEdiscretization will automatically be stable. No wonder then that the FE numerical analysiscommunity spent the last 40+ years coming up with different ideas how to generate dis-cretely stable schemes coming up with such famous results as Mikhlin’s theory of asymptoticstability for compact perturbations of coercive problems, Brezzi’s theory for problems withconstraints, concept of stabilized methods starting with SUPG method of Tom Hughes, thebubble methods, stabilization through least-squares, stabilization through a proper choice ofnumerical flux including a huge family of DG methods starting with the method of Cockburnand Shu, and a more recent use of exact sequences.

In the first part of my presentation I will recall Babuska’s Theorem and review shortly themilestones in designing various discretely stable methods listed above.

In the second part of my presentation, I will present the Discontinuous Petrov-Galerkinmethod developed recently by Jay Gopalakrishnan and myself [2]. The main idea of themethod is to employ (approximate) optimal test functions that are computed on the flyat the element level using Bubnov-Galerkin method and an enriched space. If the errorin approximating the optimal test functions is negligible, the method AUTOMATICALLYguarantees the discrete stability, provided the continuous problem is well posed. And thisholds for ANY linear problem. The result is shocking until one realizes that we are workingwith a unconventional least squares method. The twist lies in the fact that the residual livesin a dual space and it is computed using dual norms.

The method turns out to be especially suited for singular perturbation problems where onestrives not only for stability but also for ROBUSTNESS, i.e. a stability UNIFORM withrespect to the perturbation parameter. I will use an important model problem: convection-dominated diffusion to outline a general strategy for constructing a robust DPG method andreport on recent results obtained in collaboration with Norbert Heuer [3].

References

[1] I. Babuska, Error-bounds for Finite Element Method. Numer. Math, 16, 1970/1971.

[2] L. Demkowicz, J. Gopalakrishnan. A Class of Discontinuous Petrov-Galerkin Methods.Part II: Optimal Test Functions. Numer. Meth. Part. D. E., 27, 70-105, 2011.

[3] L. Demkowicz, N. Heuer, Robust DPG Method for Convection-Dominated DiffusionProblems. ICES Report 2011-33, submitted to SIAM J. Num. Anal.

Alternating Direction Implicit (ADI) Methods – a Personal RetrospectiveGraeme Fairweather, American Mathematical Society, USAAbstract. For more than half a century, alternating direction implicit (ADI) methods haveproved to be effective techniques for the solution of various multidimensional time–dependent

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Plenary Talks

problems. Their attraction lies in the fact that they reduce such a problem to the solutionof systems of independent one–dimensional problems. First formulated for finite differencemethods, ADI methods were subsequently extended to various other spatial discretizationsincluding finite element Galerkin methods, spectral methods and orthogonal spline colloca-tion methods. In this talk, some milestones in their development will be discussed as wellsome of their recent applications.

Efficient Numerical Approaches for the Simulation and Control of PDEs withRandom InputsMax Gunzburger, Florida State University, USAAbstract. We discuss three problems involving the numerical solution of PDEs with randominputs. First, we consider an approach for PDEs driven by white noise in which the problemis transformed into one driven by correlated noise which can then be efficiently treated using,e.g., Karhunen-Loeve expansions and sparse grid methods. We then discuss the replacementof white noise forcing with the perhaps more physically relevant pink noise of, more generally,1/fα noise. We also discussed methods for discretizing these noises. Finally, we discussmethods for treating control and optimization problems constrained by PDEs with randominputs. Collaborators in this work include John Burkardt, Steven Hou, Ju Ming, MiroslavStoyanov, Catalin Trenchea, and Clayton Webster.

Reduced Models You can Believe inJan S Hesthaven, Brown University, USAAbstract. In this talk we present an overview of recent and ongoing efforts to developreduced basis methods for which one can develop a rigorous a posteriori theory, hence cer-tifying the accuracy of the reduced model for parametrized linear PDEs. This is in contrastto most previous attempts to develop reduced complexity methods that, while used widelyand of undisputed value, are often heuristic in nature and the validity and accuracy of theoutput is often unknown. This limits the predictive value of such models.

We shall outline the theoretical and computational developments of certified reduced basismethods, drawing from problems in electromagnetics and acoustics, given both on differentialand integral form. The performance of the certified reduced basis model will be illustratedthrough a number of examples to highlight the significant advantages of the proposed ap-proach and we discuss extensions and challenges associated with high-dimensional problemsto the extend time permits.

Finite element analysis of electromaganetics in metamaterialsJichun Li, University of Nevada, Las Vegas, USAAbstract. In this talk we will report some recent advances in finite element analysis andsimulation of electromaganetics wave propagation in metamaterials. The stability proper-ties, optimal error estimates and superconvergence are considered for various fully discreteschemes. Numerical tests are presented not only for theoretical justification, but also forsome interesting metamaterial phenomena such as invisibility cloak, and backward wavepropagation etc.

This talk is based on the joint work with Yunqing Huang and Wei Yang.

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Plenary Talks

Discontinuous Galerkin Method for Hamilton-Jacobi Equations and Front Prop-agation with ObstaclesChi-Wang Shu, Brown University, USAAbstract. In this talk we will first describe a discontinuous Galerkin (DG) method for solv-ing Hamilton-Jacobi equations, including those for front propagation problems. This methodsolves the Hamilton-Jacobi equations directly, without first converting them to conservationlaw systems, can be proved to converge optimally in L2 for smooth solutions, and performnicely for viscosity solutions with singularities. We then extend the DG method to frontpropagation problems in the presence of obstacles. We follow the formulation of Bokanowskiet al. leading to a level set formulation driven by min(ut + H(x,∇u), u− g(x)) = 0, whereg(x) is an obstacle function. The DG scheme is motivated by the variational formulationwhen the Hamiltonian H is a linear function of ∇u, corresponding to linear convectionproblems in presence of obstacles. The scheme is then generalized to nonlinear equations,resulting in an explicit form which is very efficient in implementation. Stability analysis areperformed for the linear case with Euler forward, a second and third order SSP Runge-Kuttatime discretization, and convergence is proved for the linear case with Lipschitz continuousand piecewise smooth data. Numerical examples are provided to demonstrate the robust-ness of the method. Finally, a narrow band approach is considered in order to reduce thecomputational cost. This is a joint work with Yingda Cheng (the design of the scheme), TaoXiong (error estimates for smooth solutions), and Olivier Bokanowski and Yingda Cheng(front propagation without and with obstacles).

Coupling Compositional Flow, Transport, and Mechanics in Porous Media forModeling Carbon Sequestration in Saline AquifersMary F. Wheeler, The University of Texas at Austin, USAAbstract. A key goal of our work is to produce a prototypical computational system toaccurately predict the fate of injected CO2 in conditions governed by multiphase flow, rockmechanics, multi-component transport, thermodynamic phase behavior, chemical reactionswithin both the fluid and the rock, and the coupling of all these phenomena over multipletime and spatial scales. Even small leakage rates over long periods of time can unravel thepositive effects of sequestration. This effort requires high accuracy in the physical modelsand their corresponding numerical approximations. For example, an error of one percent peryear in a simulation may be of little concern when dealing with CO2 oil recovery flooding,but such an inaccuracy for sequestration will lead to significantly misleading results thatcould fail to produce any long-term predictive capability. It is important to note that veryfew parallel commercial and/or research software tools exist for simulating complex processessuch as coupled multiphase flow with chemical transport and geomechanics.

Here we discuss modeling multicomponent, multiscale, multiphase flow and transport throughporous media and through wells and that incorporate uncertainty and history matching andinclude robust solvers. The coupled algorithms must be able to treat different physicalprocesses occurring simultaneously in different parts of the domain, and for computationalaccuracy and efficiency, should also accomodate multiple numerical schemes. We present anew multipint flux mixed finite element method for compositional flow as well as discusssome carbon seqestration results in saline aquifers.

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Plenary Talks

Optimal Discretization, Adaptation and Iterative Solver for High Order PartialDifferential EquationsJinchao Xu, Penn State University, USAAbstract. In this talk, I should discuss about an universal construction of finite elementdiscretization methods for high order PDEs in any dimensions (joint work with M. Wang),optimal grid adaptation (joint work with J. Hu) and optimal algebraic solvers (joint workwith S. Zhang) for these finite elements.

Unclaimed Territories of Superconvergence I: Spectral and Spectral CollocationMethodsZhimin Zhang, Wayne State University, USAAbstract. In numerical computation, we often observe that the convergent rate exceedsthe best possible global rate at some special points. Those points are called superconvergentpoints, and the phenomenon is called superconvergence phenomenon, which is well under-stood for the h-version finite element method. However, the relevant study for the p-versionfinite element method and the spectral method is lacking.

In this work, superconvergence properties for some high-order orthogonal polynomial in-terpolations are studied. The results are twofold: When interpolating function values, weidentify those points where the first and second derivatives of the interpolant converge faster;When interpolating the first derivative, we locate those points where the function value ofthe interpolant superconverges. For both cases we consider various Chebyshev polynomials,but for the latter case, we also include the counterpart Legendre polynomials.

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A Special Session in Honor of Walter Allegretto’s 70th

Birthday

Organizers: Yau Shu Wong, University of Alberta, CAHongtao Yang, University of Nevada, Las Vegas, USA

A Molecular Dynamics-Continuum Coupled Model for Heat Transfer in Com-posite MaterialsJizu Huang, Chinese Academy of Sciences, ChinaLiqun Cao∗, Chinese Academy of Sciences, ChinaSam Yang, Clayton South MDC, AustraliaAbstract. In this talk, we discuss the heat transfer problem in composite materials whichcontain the nano-scale interface. A molecular dynamics-continuum coupled model is devel-oped to study the heat transport from the macroscale to the microscale. The model includesfour major steps: (1) A reverse non-equilibrium molecular dynamics (RNEMD) is used tocalculate some physical parameters such as the thermal conductivities on the interface. (2)The homogenization method is applied to compute the homogenized thermal conductivitiesof composite materials. (3) We employ the multiscale asymptotic method for the macro-scopic heat transfer equation to compute the temperature field in the global structure ofcomposite materials. (4) We develop a molecular dynamics-continuum coupled model toreevaluate the temperature field of composite materials, in particular, the local temperaturefield near the interface. The numerical results in one-, two- and three-dimensional structuresof composite materials including the nano-scale interface are given. Good agreement betweenthe numerical results of the proposed coupled algorithm and those of the full MD simulationis found, demonstrating the accuracy of the present method and its potential applicationsin the thermal engineering of composite materials.

A Variational Approach for Exact Histogram SpecificationRaymond Chan∗, Mila Nikolova, and You-Wei Wen, The Chinese University of Hong Kong,Hong KongAbstract. We focus on exact histogram specification when the input image is quantified.The goal is to transform this input image into an output image whose histogram is exactlythe same as a prescribed one. In order to match the prescribed histogram, pixels with thesame intensity level in the input image will have to be assigned to different intensity levels inthe output image. An approach to classify pixels with the same intensity value is to constructa strict ordering on all pixel values by using auxiliary attributes. Local average intensitiesand wavelet coefficients have been used by the past as the second attribute. However,these methods cannot enable strict-ordering without degrading the image. In this paper, wepropose a variational approach to establish an image preserving strict-ordering of the pixelvalues. We show that strict-ordering is achieved with probability one. Our method is imagepreserving in the sense that it reduces the quantization noise in the input quantified image.Numerical results show that our method gives better quality images than the preexistingmethods.

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A Special Session in Honor of Walter Allegretto’s 70th Birthday

A Direction Splitting Algorithm for Flow Problems in Complex/Moving Geome-triesPeter Minev, University of Alberta, Edmonton, CanadaAbstract. An extension of the direction splitting method for the incompressible Navier-Stokes equations proposed in [1], to flow problems in complex, possibly time dependentgeometries will be presented. The idea stems from the idea of the fictitious domain/penaltymethods for flows in complex geometry. In our case, the velocity boundary conditions onthe domain boundary are approximated with a second-order of accuracy while the pressuresubproblem is harmonically extended in a fictitious domain such that the overall domainof the problem is of a simple rectangular/parallelepiped shape. The new technique is stillunconditionally stable for the Stokes problem and retains the same convergence rate in both,time and space, as the Crank-Nicolson scheme. A key advantage of this approach is thatthe algorithm has a very impressive parallel performance since it requires the solution ofone-dimensional problems only, which can be performed very efficiently in parallel by adomain-decomposition Schur complement approach. Numerical results illustrating the con-vergence of the scheme in space and time will be presented. Finally, the implementation ofthe scheme for particulate flows will be discussed and some validation results for such flowswill be presented.

[1] J.L. Guermond, P.D. Minev, A new class of massively parallel direction splitting forthe incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics andEngineering, 200 (2011), 2083–2093.

Homogenization and parameter estimation of reaction-diffusion systems withrough boundariesChiara Mocenni, University of Siena, ItalyAbstract. The talk addresses the problem of parametrizing the boundary data for reaction-diffusion partial differential equations associated to distributed systems that possess roughboundaries. The boundaries are modeled as fast oscillating periodic structures and areendowed with Neumann or Dirichlet boundary conditions. Using techniques from homog-enization theory and multiscale analysis we derive the effective equations and boundaryconditions that are satisfied by the homogenized solution. Numerical simulations that vali-date the theoretical results are presented and compared with the alternative approach basedon solving the same equation with a smoothed version of the boundary. We numericallyexplore the dynamics of the homogenized solutions and show dynamical regime shifts thatinclude the anticipation of pattern formation as a result of the variation of the diffusioncoefficient. The problem of estimating the diffusion parameter of the homogenized system isfinally addressed by means of a nonlinear identification procedure and a linear least squareapproach applied to finite element discretized equations.

Joint work with Emiliano Sparacino (Department of Information Engineering, University ofSiena, Italy) and Jorge Passamani Zubelli (IMPA, Rio de Janeiro, Brasil)

Periodic solutions to nonlinear equations with oblique boundary conditionsWalter Allegretto, University of Alberta, CanadaDuccio Papini∗, Universita degli Studi di Siena, ItalyAbstract. We study the existence of positive periodic solutions to nonlinear elliptic and

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A Special Session in Honor of Walter Allegretto’s 70th Birthday

parabolic equations with oblique and dynamical boundary conditions and non-local terms.We observe that the oblique boundary conditions problems we consider would arise in sit-uations where the motion due to diffusion induced an effect in a different direction, forexample in the situation of charged bacteria moving in a magnetic field. On the other hand,the dynamic boundary condition could be used to model situations where the biologicalspecies was stored and released depending on conditions at the boundary. The results areobtained through fixed point theory, topological degree methods and properties of relatedlinear elliptic problems with natural boundary conditions and possibly non-symmetric prin-cipal part. As immediate consequences, we also obtain estimates on the principal eigenvaluefor non-symmetric elliptic eigenvalue problems.

A Front-fixing Finite Element Method for the Valuation of American Optionswith Regime SwitchingA. D. Holmes, Deloitte & Touche LLP, Houston, USAHongtao Yang, University of Nevada, Las Vegas, USAShuhua Zhang∗, Tianjin University of Finance and Economics, ChinaAbstract. American option problems under regime switching model are considered in thispaper. The conjectures about the position of early exercise prices are proved, which gener-alize the results in the previous literature by allowing the interest rates are different in twostates. A front-fixing finite element method for the free boundary problems are proposed andimplemented. Its stability is established under reasonable assumptions. Numerical resultsare given to examine the rate of convergence of our method and compare it with the usualfinite element method.

Mixed finite element analysis of thermally coupled non-Newtonian flowsJiansong Zhang, China University of Petroleum, ChinaJiang Zhu∗, Laboratorio Nacional de Computacao Cientıfica, BrazilXijun Yu, Chinese Academy of Sciences, ChinaF. D. Loula, Laboratorio Nacional de Computacao Cientıfica, BrazilAbstract. In this paper, we consider an incompressible non-Newtonian flow with a tem-perature dependent viscosity obeying a power law, and the thermal balance includes viscousheating. The corresponding mathematical model can be written as:

−2∇· (µ(θ)|D(u)|r−2D(u)) +∇p = f in Ω∇· u = 0 in Ω−∆θ = µ(θ)|D(u)|r in Ω

u = 0 on Γθ = 0 on Γ

where u : Ω→ IRd is the velocity, p : Ω→ IR is the pressure, θ : Ω→ IR is the temperature,Ω is a bounded open subset of IRd, d = 2 or 3, Γ its boundary. The viscosity µ is a functionof θ, µ = µ(θ). D(u) = 1

2(∇u +∇uT ) is the strain rate tensor, and 1 < r <∞.

We first establish existence and uniqueness of the weak solution of the system of equations.Next, we propose mixed finite element approximation combined with a fixed point algorithm.Finally we present convergence analysis with an error estimate between continuous solutionand its iterative finite element approximation.

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A Special Session in Honor of Graeme Fairweather’s

70th Birthday

Organizers: Yanping Lin, The Hong Kong Polytechnic University, Hong KongAndreas Karageorghis, University of Cyprus, Cyprus

Orthogonal Spline Collocation for Quasilinear Parabolic Problems with NonlocalBoundary ConditionsB. Bialecki∗, Colorado School of Mines, USAG. Fairweather, American Mathematical Society, USAJ. C. Lopez-Marcos, Universidad de Valladolid, SpainAbstract. We formulate and analyze the extrapolated Crank-Nicolson orthogonal splinecollocation method for the solution of quasilinear parabolic problems in one space variablewith nonlocal boundary conditions involving integrals of the unknown solution over thespatial interval. Using an extension of the analysis of Douglas and Dupont for Dirichletboundary conditions, we derive optimal order error estimates in the discrete maximum normin time and the continuous maximum norm in space. We discuss the solution of the linearsystem arising at each time level via the capacitance matrix technique and the packageCOLROW for solving almost block diagonal linear systems. We present numerical examplesthat confirm the theoretical error estimates.

A Space-time Domain Decomposition Method for Stochastic Parabolic ProblemsXiao-Chuan Cai, University of Colorado at Boulder, USAAbstract. We discuss an implicit space-time approach for solving stochastic parabolicPDEs. We first decouple the space-time discretized stochastic equation into some uncoupleddeterministic systems by using a Karhunen-Loeve expansion and double orthogonal polyno-mials. And then a multilevel overlapping domain decomposition method is combined with arecycling GMRES method to solve the large number of systems with similar structures. Wereport experiments obtained on a parallel computer with a large number of processors. Thisis a joint work with Cui Cong.

Linearized alternating direction method for constrained linear least-squares prob-lemRaymond H. Chan∗, The Chinese University of Hong Kong, Shatin, NT, Hong Kong,ChinaMin Tao, Nanjing University of Posts and Telecommunications, ChinaXiaoming Yuan, Hong Kong Baptist University, Hong Kong, ChinaAbstract. We apply the alternating direction method (ADM) to solve a constrained linearleast-squares problem where the objective function is a sum of two least-squares terms andthe constraints are box constraints. Using ADM, we decompose the original problem intotwo easier least-squares subproblems at each iteration. To speed up the inner iteration, welinearize the subproblems whenever their closed-form solutions do not exist. We prove theconvergence of the resulting algorithm and apply it to solve some image deblurring problems.We show the efficiency of our algorithm by comparing it with Newton-type methods.

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A Special Session in Honor of Graeme Fairweather’s 70th Birthday

The research is supported in part by HKRGC Grant No. CUHK400510 and CUHK DirectAllocation Grant 2060408, the Scientific Research Foundation of Nanjing University of Postsand Telecommunications (NY210049), and a General Research Fund grant of Hong Kong

Fast Solution of the Method of Fundamental Solutions for Modified HelmholtzEquationsC.S. Chen, University of Southern Mississippi, USAX.R. Jiang and Wen Chen, Hohai University, ChinaAbstract. Since 1990s, the method of fundamental solutions (MFS) has re-emerged as an ef-fective meshless method. Instead of boundary discretization as classical BEM, the boundarycollocation points were used in the solution process of the MFS. In the MFS, the singularityis avoided by the use of fictitious boundary outside the domain. One of the reasons that theMFS is getting popular is due to its simplicity. By coupling the method of particular solu-tions (MPS), the MFS has been successfully extended to solving inhomogeneous problems.In the MFS-MPS approach, two dense matrix systems need to be solved. The developmentof the compactly supported radial basis functions (CS-RBFs) has made it possible for for-mulate the sparse matrix in the context of the MFS. It is desirable that MFS-MPS has thecombined features of ‘sparse’ and ‘meshless’. It is the purpose of this presentation to showhow the sparse formulation of the MFS for the modified Helmholtz equation can be achieved.

ADI Orthogonal Spline Collocation Method on Non-rectangular RegionsR. I. Fernandes∗, The Petroleum Institute, UAEB. Bialecki, Colorado School of Mines, USAAbstract. The alternating direction implicit (ADI) method is a highly efficient techniquefor solving multi-dimensional problems on rectangles. When the ADI technique is coupledwith orthogonal spline collocation (OSC) we not only obtain the global solution efficientlybut also observe superconvergence phenomena, that is, at certain points of the domain thederivative values converge to that of the exact solution at a rate higher than one wouldexpect from the spline approximation.

In a recent paper (SISC, v. 28 (2006), pp. 1054-1077), we used a Crank Nicolson ADI OSCmethod for solving general nonlinear parabolic problems with Robin’s boundary conditionson rectanglular polygons and demonstrated numerically the accuracy and superconvergencephenomena in various norms. A natural question that arises is: Does this technique have anatural extension to non-rectangular regions? In this talk, we present a simple idea of howthe ADI OSC technique can be extended to some such regions. Our approach depends onthe fourth order transfer of Dirichlet boundary conditions in the solution for a two-pointboundary value problem using a non-uniform grid. We illustrate our idea for the solution ofthe heat equation on the unit disc.

The method of fundamental solutions for the solution of inverse problemsAndreas Karageorghis, University of Cyprus, CyprusAbstract. The method of fundamental solutions (MFS) is a relatively new techniquewhich can be used for the numerical solution of certain boundary value problems and ini-tial/boundary value problems. The ease with which it can be implemented and its effec-tiveness have made it very popular for the solution of a large variety of problems arising

39


in science and engineering. Recently, it has been used extensively for a particular class ofsuch problems, namely inverse problems. We attempt to review the applications of the MFSto the various classes of inverse and related problems, over the last few years. Some of theseveral issues related to the implementation of the MFS to such problems are discussed andsome representative numerical results are presented.

Stable Computations with GaussiansMichael McCourt, Cornell University, USAAbstract. Radial basis functions (RBFs), or kernels, are used in machine learning, geo-statistics, computer graphics, boundary value problems and many other applications. Theirpractical application is often impeded by ill-conditioning present for certain choices of RBF.The most common choice, the Gaussian, is optimal for approximating sufficiently smoothfunctions, but also the most susceptible to conditioning issues and thus the least trustworthyin many circumstances. This work provides a new way to compute and evaluate GaussianRBF interpolants in a stable way in arbitrary dimensions with a focus on increasingly flatkernels. Motivated by the pioneering research of Bengt Fornberg and his co-workers, aneigenfunction (or Hilbert-Schmidt) expansion of the Gaussian is used to isolate ill-conditionedterms analytically. In addition to obtaining the true RBF interpolant, this technique canalso be used to produce a highly accurate least-squares approximation at significantly lesscost. Interpolation and regression results will be presented, as well as collocation results forboundary value problems.

B-Spline Collocation Software for PDEs with Efficient Interpolation-Based Spa-tial Error Estimation

Paul Muir, Saint Mary’s University, Canada

Abstract. BACOL, recently developed collocation software for 1D parabolic PDEs, hasbeen shown to be efficient, reliable and robust, especially for problems with solutions ex-hibiting sharp layers, and for stringent tolerances. The software features adaptive control ofestimates of the spatial and temporal errors. While the BACOL spatial error estimates aregenerally quite reliable, the error estimation algorithm involves the (expensive) computationof two collocation solutions of orders p and p + 1. (The solution of order p + 1 is used toprovide a spatial error estimate for the solution of order p.) This talk will discuss recentwork investigating more efficient spatial error estimation algorithms based on (i) an orderp + 1 (superconvergent) interpolant that allows us to avoid the computation of the higherorder collocation solution, and (ii) an order p interpolant, whose error agrees asymptoticallywith the error of the order p collocation solution, that allows us to avoid the computationof the lower order collocation solution. We have implemented a new, more efficient versionof BACOL based on these new error estimation schemes that we call BACOLI. We providenumerical results comparing the original version of BACOL with this new version and showthat BACOLI is about twice as fast as the original code.

This is joint work with Tom Arsenault, University of Western Ontario, Tristan Smith, Bankof Nova Scotia, Jack Pew, Saint Mary’s University, and Zhi Li, Saint Mary’s University.

A Legendre-Galerkin method of the Helmholtz Equation for Electromagnetics

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Cavity ProblemWeiwei Sun, City University of Hong Kong, Hong KongAbstract. We study the TM (transverse magnetic) case of the electromagnetic scatteringfrom a two-dimensional large rectangular open cavity embedded in an infinite ground plane.By introducing a non-local transparent boundary condition on the aperture, the governingequation for this open cavity problem is then reduced to a Holmholtz equation in the rectan-gular cavity. A Legendre-Gauss interpolatory approximation is devised for the evaluation ofthe hyper-singular integral operator, and a Legendre-Galerkin scheme is proposed for solvingthe reduced Helmholtz equation. The existence and the uniqueness of the approximationsolution are established for arbitrary wave numbers. The stability and the spectral conver-gence of the approximation scheme are then proved. Illustrative numerical results, which arein agreement with the theoretical estimates, are presented.

Expectations and Limitations of the Compact Splitting Method for Quenching-combustion ProblemsQin Sheng∗ and Matt Beauregard, Baylor University, USAAbstract. This talk is based on a collaborated endeavor with a family of compact split-ting schemes for solving two-dimensional singular reaction-diffusion equations for combustionsimulations. While a temporal adaption is utilized, uniform grids are enforced in the space.We will show that the compact splitting scheme is numerically stable and convergent whenits dimensional Courant numbers are within certain frames of windows determined by thegiven spatial domain. Though such a window poses a considerable restriction on decomposedcompact computations, the interesting combination of different computational technologiesis in fact highly efficient and reliable for a variety of combustion applications. Some ex-perimental results will be given to illustrate our conclusions and concerns. We will alsoshow that the compact splitting method studied is sufficiently accurate in determining themost important key characteristics such as the quenching time, critical domain and blow-upprofiles.

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Mini-symposia

Mini-symposium 1:Computational Methods for Multiphase Flow in Porous MediaOrganizer: Zhangxin Chen, University of Calgary, Canada

Recent Developments in Multipoint Flux Mixed Finite ElementsGuangri Xue (Gary), Shell, USAAbstract. We report recent developments in multipoint flux mixed finite element (MFMFE)method on flow in porous media. The MFMFE method gives a cell-centered scheme basedon an appropriate choice of numerical quadrature and degrees of freedom. In addition, themethod is shown to be accurate on highly distorted quadrilaterals and hexahedral grids.Theoretical results indicate first-order convergence for the pressure and face flux. Numericalresults on single and two-phase flow will be presented. If time allows, the coupling of flowand elasticity will be also demonstrated.

This is joint work with M. Wheeler and I. Yotov.

A numerical method for solving 3D elastic wave equation in anisotropic hetero-geneous mediumWenyuan Liao, University of Calgary, CanadaAbstract. It is well-known that the acoustic isotropic models of the earth do not adequatelydescribe the seismic wave propagation in realistic cases, as some important information ofthe media is lost when such simplifications were taken. To address these issues, one shouldconsider elastic wave equation and remove the standard assumption of isotropy of the earth.Such changes result in better description of the medium properties but meanwhile makethe numerical simulation a computationally challenging task. In this talk a new numericalmethod that combines a second-order finite difference approximation in spatial derivativesand Rosenbrock method for time integration will be introduced to solve the 3D elastic waveequation in anisotropic medium. We first transform the second-order (in time) elastic waveequation into a coupled first-order system, which is discretized in space then the semi-discreteODE system is solved by high-order Rosenbrock method. We investigate in great details onthe stability, convergence, computational efficiency and numerical dispersion of the newmethod. Several numerical examples are conducted to valid the theoretical analysis.

Based on Expert Knowledge and Topological SimilaritiesJiang Xie and Wu Zhang∗, Shanghai University, ChinaAbstract. Similarities between different biomolecular networks have important significancein studies of diseases and evolution. Bio-molecular networks are complex networks. Searchinga sub-network which is most similar to a target is a NP-complete problem. It involveslarge-scale computations and is time consuming. A new algorithm is developed to searchsimilar sub-network in one or between two species biomolecular networks. Models of bothmathematics and computation are studied for the searching problem, and the highlights ofthe new algorithm are based on expert knowledge and average topological similarities, so asto improve accuracy of computational results. The range of the free parameter ω is given

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Mini-symposia

when searching by neighbors-in-first, which can reduce computational complexity. To dealwith large- scale biomolecular networks, the GPU algorithm is also introduced here.

Mathematical Analysis of Problems in Filtration ApplicationsE.W. Jenkins∗ and V.J. Ervin, Clemson University, USAAbstract. Filtration applications appear in a variety of physical settings; among themare industrial filtration for polymer processing, protein separation in pharmaceutical drugpurification, and oil and air filtration in the automotive industry. Effective filters removelarge amounts of debris, but cost considerations warrant filters that have long lifetimes.Thus, one must balance the need for effective filters against the costs of replacement; filtersthat trap everything would have short life spans. Alternatively, one could make a filter lastforever by trapping nothing.

Filter design can be evaluated using computational simulators and optimization tools thatbalance these competing objectives. We have used population-based methods, e.g. geneticalgorithms, to evaluate the competing objectives in one-layer filter designs. These methodsthoroughly search the design space to generate a Pareto set of optimal solutions, makingthem computationally expensive. Accurate and efficient simulation tools are required toimprove the validity of the solutions generated as well as reduce the computational timerequired as we move to more complicated filter designs.

In this talk, we present our work on several mathematical problems that have been moti-vated by filtration applications. In particular, we discuss results on coupled Stokes/Darcysystems for generalized, non-Newtonian fluids, and results from optimization studies we haveperformed using an existing computational tool for simulation of filtration processes. Wealso discuss our current research directions for this class of problems.

Simulation of Multiphase Flow in Porous Media using Locally Conservative Fi-nite Element MethodsShuyu Sun, KAUST, Kingdom of Saudi ArabiaAbstract. Multiphase flow in porous media has important applications in petroleum reser-voir engineering and environmental science. Modeling equation system of such multiphaseflow can be generally split into 1) an elliptic partial differential equation (PDE) for the pres-sure and 2) one or multiple convection dominated convection-diffusion PDE for the saturationor for the chemical composition. Accurate simulation of the phenomena not only requireslocal mass conservation to be retained in discretization, but it also demands steep gradientsto be preserved with minimal oscillation and numerical diffusion. The heterogeneous per-meability of the media often comes with spatially varied capillary pressure functions, bothof which impose additional difficulties to numerical algorithms. To address these issues,we solve the saturation equation (or species transport equation) by discontinuous Galerkin(DG) method, a specialized finite element method that utilizes discontinuous spaces to ap-proximate solutions. Among other advantages, DG possesses local mass conservation, smallnumerical diffusion, and little oscillation. The pressure equation is solved by either a mixedfinite element (MFE) scheme or a Galerkin finite element method with local conservativepostprocessing. In this talk, we will present the theory and numerical examples of thiscombined finite element approach for simulating subsurface multiphase flow.

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Mini-symposium 2:Insight Into Geophysical Fluid Dynamics Through Analysis and ComputationOrganizers: Qingshan Chen and Todd Ringler, Los Alamos National Laboratory, USAAbstract. Climate modeling is a multi-facet endeavor. The exponential growth in com-putational resources encourages ultra high resolution numerical simulations of the globalclimate system, which has led to manifestation of unprecedented detail on both global andlocal scales. On the other hand, alternatives to ultra high resolution simulations are beingactively pursued. The alternatives include, but not limited to, multi-resolution simulations,development of scale-invariant subgrid closure schemes, and design of hierarchical concep-tual models. One classical research direction that has proven critical for advances in climatemodeling is the discovery of new numerical techniques in spatial discretization and timestepping schemes. These new techniques may lead to a high-order accuracy, or to certaindesirable conservative properties. On the other front, mathematicians have been studyingthe geophysical flows from a dynamical point of view for a long time. Dynamical theorycan qualitatively predict the long time behaviors of the climate system, or the bifurcationand/or phase transition in the system.

The purpose of this mini-symposium is to bring together researchers working on climatemodeling from a plethora of approaches, and thus to encourage discussions regarding theadvantage and disadvantage of each approach. This conference is primarily on applied andcomputational mathematics. Having a mini-symposium on climate modeling within thisconference will help to expose the abundance of problems in climate modeling to the generalcommunity of applied and computational mathematicians.

Multiple Time Scales and Time Stepping for Ocean Circulation ModelsRobert L. Higdon, Oregon State University, USAAbstract. Numerical ocean models admit motions that vary on a wide range of time scales.For reasons of computational efficiency, it is common practice to split the dynamics into twosubsystems that are solved by different techniques. A vertically-integrated two-dimensionalsubsystem can be used to model the fast external waves, and the remaining slow motionscan be modeled with a three-dimensional system that is solved explicitly with a long timestep. A successful implementation of this idea requires a derivation of sufficiently accuratesplit equations, combined with proper communication between the two subsystems whenthese subsystems are discretized numerically. The latter is partly a matter of the basictime-stepping schemes that are used, and partly a matter of details of communication. Forexample, the algorithms for mass conservation in the two subsystems must yield consistentresults, and the enforcement of this consistency has the effect of filtering the fast motionsfrom the 3-D mass conservation equations, so that a long time step can be used for the 3-Dequations. This talk will provide a survey of previous and upcoming work on the aboveissues.

Earth core thermal convection simulation using high-order finite elementWei Leng, State Key Laboratory of Scientific and Engineering Computing, Chinese Academyof Sciences, ChinaAbstract. Earth core thermal convection simulation is a basic part of the magnetohydrody-

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namics simulation of the Earth’s magnetic field. In the numerical simulation of core thermalconvection problem, highly accurate numerical results, including the rotation speed, areobtained using high-order finite element discretization. A special preconditioner which com-bines the PCD (pressure Convection Diffusion) preconditioner and the geometric multigridpreconditioner is designed, to circumvent the difficulties in solving the linear systems of equa-tions which contain the anti-symmetric part caused by the Coriolis force term. Numericalexperiments show that our preconditioning strategy is highly efficient.

Non-Oscillatory Central Finite-Volume Schemes for Atmospheric Numerical Mod-elingRam Nair, National Center for Atmospheric Research, USAAbstract. The central finite-volume (FV) schemes are a subset of Godunov-type methodsfor solving hyperbolic conservation laws. Unlike the upwind methods,the central schemesdo not require characteristic decomposition of the hyperbolic system or expensive Riemannsolvers. A semi-discretized central finite-volume scheme has been developed for atmosphericmodeling applications. The non-oscillatory property of the scheme is achieved by employinghigh-order weighted essentially non-oscillatory (WENO) reconstruction method, and time in-tegration relies on explicit Runge-Kutta method.The scheme is computationally efficient anduses a compact computational stencil, amenable to parallel implementation. The central FVscheme has optional monotonic (positivity-preserving) filter, which is highly desirable for at-mospheric tracer transport problems. The scheme has been validated for several benchmarkadvection tests on the cubed-sphere. A global shallow-water model and a 2D non-hydrostaticEuler solver are also developed based on the same central finite-volume scheme, the resultswill be presented in the seminar.

On the quasi-hydrostatic ocean modelsAntoine Rousseau, INRIA, FranceAbstract. In this talk, we want to study the influence of the so-called traditional ap-proximation in the equations of large scale ocean. We will distinguish three main models:the (traditional) hydrostatic equations (also called primitive equations), the non-hydrostaticequations, and an intermediate model called quasi-hydrostatic. The quasi-hydrostatic modelconsists in adding nontraditional Coriolis terms to the traditional primitive equations. Wewill see that we can extend well-posedness results previously established for the primitiveequations, and the corresponding quasi-geostrophic regime will be studied, leading to a newtilted QG model.

Tropical Cyclogenesis and Vertical Shear in a Moist Boussinesq ModelLeslie Smith∗ and Qiang Deng, University of Wisconsin, Madison, USAAndrew J. Majda, Courant Institute for Mathematical Sciences, NYU, USAAbstract. Tropical cyclogenesis is studied in the context of idealized three-dimensionalBoussinesq dynamics with a simple self-consistent model for bulk cloud physics. With low-altitude input of water vapor, numerical simulations capture the formation of vortical hottowers. From measurements of water vapor, vertical velocity, vertical vorticity and rain, it isdemonstrated that the structure, strength and lifetime of the hot towers is similar to resultsfrom models including more detailed cloud microphysics. The effects of low-altitude verticalshear are investigated by varying the initial zonal velocity profile. In the presence of weak

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low-level vertical shear, the hot towers retain the low-altitude monopole cyclonic structurecharacteristic of the zero-shear case (starting from zero velocity). Some initial velocityprofiles with small vertical shear can have the effect of increasing cyclonic predominance ofindividual hot towers in a statistical sense, as measured by the skewness of vertical vorticity.Convergence of horizontal winds in the atmospheric boundary layer is mimicked by increasingthe frequency of the moisture forcing in a horizontal sub-domain. When the moisture forcingis turned off, and again for zero shear or weak low-level shear, merger of cyclonic activityresults in the formation of a larger-scale cyclonic vortex. An effect of the shear is to limit thevertical extent of the resulting depression vortex. For stronger low-altitude vertical shear, theindividual hot towers have a low-altitude vorticity dipole rather than a cyclonic monopole.The dipoles are not conducive to the formation of larger-scale depressions, and thus strongenough low-level shear prevents the vortical-hot-tower route to cyclogenesis. The resultsindicate that the simplest condensation and evaporation schemes are useful for exploratorynumerical simulations aimed at better understanding of competing effects such as low-levelmoisture and vertical shear.

A Spectral Element Method for the Community Atmosphere ModelMark Taylor, Sandia National Laboratory, USAAbstract. We will describe our experience with the spectral element method in the Com-munity Atmosphere Model (CAM). CAM is the the atmospheric component of CommunityEarth System Model, one of the flagship U.S. global climate change models. The spectralelement method is a numerically efficient way to obtain a high-order accurate, explicit-in-time numerical method. It retains these properties on the unstructured and block structuredgrids needed for spherical geometry. Because of its reliance on quadrilateral elements andtensor-product Gauss-Lobatto quadrature, its fundamental computational kernels look likedense matrix-vector products which map well to upcoming computer architectures. Herewe will describe our work adapting the spectral element method for atmospheric modeling:obtaining conservation and non-oscillatory advection. For conservation we have developeda mimetic/compatible formulation of the method, which allows for exact conservation (ma-chine precision) of quantities solved in conservation form, and semi-discrete conservation(exact with exact time-discretization) of other quantities such as energy and potential vor-ticity. For tracer advection in CAM, the spectral element mimetic formulation allows usto introduce a family of locally bounds preserving limiters. The limiters require solving acontained optimization problem that is local to each element.

This is a joint work with K.J. Evans, A. Fournier, O. Guba, P. H. Lauritzen and M. Levy.

Mini-symposium 3:Developing ice-sheet models for the next generation climate simulationOrganizers: Katherine J. Evans, Oak Ridge National Laboratory, USAMauro Perego, Florida State University, USAAbstract. The need for accurate, feasible and reliable ice-sheet numerical Simulations atthe continental scale creates significant mathematical and computational challenges. In thismini-symposium we focus on several aspects of ice sheet numerical simulations ranging fromparallel high performance computing to uncertainty quantification and parameter estimation.

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In particular we will address the design of efficient parallel solvers for large scale simulations(Greenland and Antarctica ice-sheets); the quantification of uncertainty of numerical solu-tions and the estimation of model parameters including ice viscosity and bedrock boundaryconditions. Also, we address the problem of coupling ice-sheet model with other climatesub-models (e.g. ice-ocean coupling).

BISICLES – progress on a higher-order adaptive mesh refinement ice-sheetmodelDaniel Martin, Lawrence Berkeley National Lab, USAAbstract. Ice sheets require fine resolution to resolve the dynamics of features such asgrounding lines and ice streams. However, ice sheets also have large regions where such highresolution is unnecessary (much of East Antarctica, for example). Ice sheets are thereforeideal candidates for adaptive mesh refinement (AMR).

As the Berkeley ISICLES (BISICLES) project, in collaboration with the University of Bristolin the U.K., we have developed an ice sheet model which uses adaptive mesh refinement in thehorizontal directions to locally refine the computational mesh in regions where fine resolutionis required to accurately resolve ice sheet dynamics. Using coarser meshes in regions wheresuch fine resolution is unnecessary allows for substantial savings in computational effort.In addition, the use of the vertically-integrated momentum approximation of Schoof andHindmarsh (2010) allows still greater computational efficiency.

We present recent progress and demonstrate the effectiveness of our approach, includingapplication to regional and continental-scale modeling.

This is a joint work with Stephen Cornford (University of Bristol, UK) and Esmond Ng(Lawrence Berkeley National Lab, USA).

A simple approach to modeling multi-physics coupled models, application tolarge-scale ice sheet modelsHelene Seroussi, Caltech-Jet Propulsion Laboratory, USA and Ecole Centrale Paris, Chatenay-Malabry, FranceAbstract. The recent development of new higher-order, higher-resolution ice sheet modelshas shown that sophisticated models are essential to model some areas of the ice sheets,including the grounding line region. These areas are critical for ice flow projections andare best simulated using full 3d models. Higher-order models are well suited to ice streamdynamics, whereas the shallow-shelf approximation is sufficient for modeling ice shelf flow.Higher-order and full-Stokes model are computationally intensive and prohibitive for large-scale modeling. There is therefore a strong need to combine such different models in orderto balance computational cost and physical accuracy for the whole ice sheet.

Here we present a new methodology, the Tiling method, adapted from the Arlequin frame-work (Ben Dhia, 1998) to couple finite element shelfy-stream, higher-order and Full-Stokesmodels. It is achieved by strongly coupling the different approximations within the samelarge-scale simulation. This technique is applied to synthetic and real geometries; we com-pare the results for different hybrid models and single-model approaches.

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This work was performed at the California Institute of Technology’s Jet Propulsion Labora-tory and Ecole Centrale Paris under a contract with the National Aeronautics and Space Ad-ministration’s Modeling, Analysis and Prediction (MAP) Program (http://issm.jpl.nasa.gov/).

This is a joint work with Mathieu Morlighem (Caltech-Jet Propulsion Laboratory, USA andEcole Centrale Paris, France), Eric Larour (Caltech-Jet Propulsion Laboratory, USA), EricRignot (Caltech-Jet Propulsion Laboratory, USA and University of California Irvine, USA)and Hachmi Ben Dhia (Ecole Centrale Paris, Chatenay-Malabry, France).

A method for simulating dynamic ice shelves in global ocean modelsXylar Asay-Davis, Los Alamos National Laboratory, USAAbstract. Ice sheets are expected to contribute a major fraction of 21st century sea-levelrise, partly because of nonlinear feedbacks between climate and ice-sheet dynamics. Therate of ice mass loss is strongly influenced by interactions between the ocean and ice shelves,huge tongues of floating ice attached to the ice sheet. Theoretical arguments and numericalsimulations indicate that marine ice sheets (those lying on bedrock below sea level) aresubject to an instability that can lead to rapid ice retreat when the bedrock slopes downwardaway from the ocean, as is the case in much of West Antarctica. Accurate representationof the geometry and physics at the ice shelf/ocean interface is critical to capturing thesedynamics.

We are developing a method for simulating dynamic ice/ocean interaction in a global oceanmodel, the Parallel Ocean Program (POP). The interface between ice and ocean can berepresented using stair-steps (partial cells) or using a ghost-cell immersed boundary method(IBM). In the near future, POP and the Community Ice Sheet Model (CISM) will be coupledin the Community Earth System Model (CESM); the coupler will handle passing and inter-polating fields between models. CISM will dynamically update the geometry of the ice/oceaninterface and POP will supply heat and freshwater fluxes across the interface to CISM. Thepartial cells representation of the ice/ocean interface is relatively easy to implement and hasbeen used to represent ocean bathymetry for more than a decade. The IBM is less provenbut is designed to handle moving boundaries and more accurate in its representation of thegeometry and boundary conditions.

Which physics for coupled ice sheet and ocean models? Lessons learned fromPetermann GlacierCarl Gladish, New York University, USAAbstract. Coupling ice sheet and ocean models to investigate their behavior in changingclimate conditions requires careful consideration of the possible physics involved. At themarine boundaries of the Antarctic and Greenland ice sheets, mass loss due to both ice-berg calving and melting is important. Calving, being episodic in time, probably involvesmaterial properties of ice and timescales that are not usually represented in ice sheet mod-els. On the other hand, our numerical simulations of ice shelf melting show that complexchannelized morphology can arise at very small spatial scales in ice shelves that are floatingin relatively warm water. These exploratory simulations were performed using a version ofthe Glimmer-CISM ice sheet model coupled to a plume ocean model and the cases studiedwere idealizations motivated by Petermann Glacier in Greenland and Pine Island Glacier inAntarctica. The results of our study of the interplay between melting and ice geometry will

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be presented with an emphasis on principles that could be useful to others working towardscontinental scale modeling using coupled, state-of-the-art ice sheet and ocean models. Inparticular, we will present results on the important role of ocean mixed-layer physics, theeffect of ocean temperature perturbations on simulated melt rates and also the significanceof sub-glacial discharge of fresh water.

This is a joint work with David Holland (New York University, USA) and Paul Holland(British Antarctic Survey, Cambridge, UK).

A geometrical multigrid method for shallow ice models based on an energy min-imization approachGuillaume Jouvet, Free University of Berlin, GermanyAbstract. We consider a model for the time evolution of ice sheets and ice shelves thatcombines the Shallow Ice Approximation (SIA) for the slow deformation of ice and the Shal-low Shelf Approximation (SSA) for the fast basal sliding. At each time step, we have to solveone scalar generalized p-Laplace problem with obstacle and p > 2 (SIA) and one vectorialp-Laplace problem with 1 < p < 2 (SSA). Both problems can be advantageously rewrittenby minimising suitable, convex non-smooth energies. By exploiting such formulations, weimplement a fast and robust Newton multigrid method, the convergence being naturallycontrolled by the energy. Local non-smoothness are treated by truncation rather than byregularisation which might affect the solution in an arbitrary way. To update the ice sheetgeometry, we implement the method of characteristics using an recent algorithm of optimalcomplexity. In contrast with most of existing numerical models based on finite differences,our approach has no theoretical restriction on the time-step and allows a wide choice ofunstructured meshes to be used. As an illustration, we present numerical results based onthe exercises of the Marine Ice Sheet Model Inter-comparison Project (MISMIP).

This is a joint work with Ed Bueler (University of Alaska, USA) and Carsten Graser (FreeUniversity of Berlin, Germany).

Advanced ice sheet modeling: scalable parallel adaptive full Stokes solver andinversion for basal slipperiness and rheological parametersCarsten Burstedde, Rheinische Friedrich-Wilhelms-Universitt Bonn, GermanyOmar Ghattas, Tobin Isaac∗, Noemi Petra, Georg Stadler, and Hongyu Zhu, TheUniversity of Texas at Austin, USAAbstract. We present a parallel, adaptive mesh, high-order finite element solver for the 3Dfull Stokes equations with Glen’s flow law rheology. The adaptive mesh capabilities allowfor efficiently capturing the wide range of length scales with localized features present inice sheet dynamics. We solve the equations using a globalized Newton-Krylov method withblock, multilevel preconditioning. We set up realistic calculations using SeaRISE datasets.Numerical results from these calculations indicate scalability of the algorithm and the im-plementation for realistic full continent ice sheet simulations.

Additionally, we formulate an inverse problem to infer the basal slipperiness and rheologi-cal parameters from surface observations. For this purpose, we minimize the misfit betweenobserved and modeled surface flow velocities. The resulting least squares minimization prob-lem is solved using an adjoint-based inexact Newton method. Numerical inversion studies

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demonstrate the influence of prior knowledge on the model parameters for addressing ill-posedness of the inverse problem and to handling noise present in the observations. Wepresent preliminary work on inverting for basal slipperiness parameters on a continentalscale.

Scalable and composable implicit solvers for polythermal ice flow with steeptopographyJed Brown, Argonne National Laboratory, USAAbstract. Ice flow adds additional nonlinearities and a transport-dominated system tothe Stokes problem for ice flow. The heat transport equation has very different spectralproperties from the Stokes system, which preconditioners must respect in order to performwell. This is achieved using field-split preconditioning composed with geometric and algebraicmultigrid methods. We evaluate the robustness of several preconditioning and nonlinearsolution techniques for the coupled problem and discuss efficient implementation on modernhardware.

This is a joint work with Matt Knepley (University of Chicago, USA), Dave May (ETH,Zurich, Switzerland) and Barry Smith (Argonne National Laboratory, USA).

Mini-symposium 4:Advances in analytical and computational techniques for nonlinear wavesOrganizer: Yanzhi Zhang, Missouri University of Science and Technology, USAAbstract. Recently, research on nonlinear waves has been dramatically expanding andnumerous exciting phenomena have been discovered in this field. This mini-symposium aimsto survey recent advances on various aspects of nonlinear wave studies. The scope of topicsincludes the analytical methods and computational techniques used for studying nonlinearwaves, as well as their applications in physical systems.

Analysis of electromagnetic cavity scattering problemsPeijun Li, Purdue University, USAAbstract. In this talk, we consider the scattering of a time-harmonic electromagnetic planewave by an open cavity embedded in a perfect electrically conducting infinite ground plane,where the electromagnetic wave propagation is governed by the Maxwell equations. Giventhe incident field, the direct problem is to determine the field distribution from the knownshape of the cavity; while the inverse problem is to determine the shape of the cavity fromthe measurement of the field on the open aperture of the cavity. We will discuss both thedirect and inverse scattering problems. The existence and uniqueness of the weak solutionfor the direct model problem will be shown by using a variational approach. The perfectlymatched layer method will be investigated to truncate the unbounded electromagnetic cavityscattering problem. Results on a global uniqueness and a local stability will be presentedfor the inverse problem.

Central discontinuous Galerkin methods for shallow water wavesMaojun Li∗ and Liwei Xu, Rensselaer Polytechnic Institute, USAAbstract. Green-Naghdi equations and standard shallow water wave equations are two

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types of models describing the propagation of shallow water waves. We first develop acoupling scheme of central discontinuous Galerkin methods and finite element methods forthe solution of Green-Naghdi equations with flat bottom. The numerical scheme is basedon a reduction of the original Green-Naghdi model to a system of hyperbolic equationstogether with a stationary elliptic equation. Then, we develop a well-balanced high-orderpositivity-preserving central discontinuous Galerkin method solving standard shallow waterwave equations with non-flat bottom. Numerical results will be presented to illustrate theaccuracy and efficiency of the methods.

Global existence for a system of Schrodinger equations with power-type nonlin-earitiesNghiem V. Nguyen, Utah State University, USAAbstract. In this talk, consideration is given to the Cauchy problem for a Schrodingersystem with power-type nonlinearities

i∂

∂tuj + ∆uj +

m∑k=1

ajk|uk|p|uj|p−2uj = 0,

uj(x, 0) = ψj0(x),

(1)

where uj : RN ×R→ C, ψj0 : RN → C for j = 1, 2, . . . ,m and ajk = akj are real numbers. Asharp form of vector-valued Gagliardo-Nirenberg inequality is first established which yields apriori estimate needed for global existence of solutions in the sub-critical case, along with thebest embedding constant for the Gagliardo-Nirenberg inequality. Using this best embeddingconstant, global existence for small initial data is next shown for the critical exponent case.The finite time blow-up as well as stability of solution in the critical case are then discussed.

Numerical methods for rotating dipolar BEC based on a rotating Lagrange co-ordinateYanzhi Zhang, Missouri University of Science and Technology, USAAbstract. In this talk, we discuss an efficient numerical method for simulating the rotat-ing dipolar Bose-Einstein condensates (BEC), which is described by the Gross-Pitaevskiiequation (GPE) with an angular momentum rotation term as well as a dipolar interactionterm. Both terms bring significant difficulties in the analysis and simulations of rotatingdipolar BEC. We apply a rotating Lagrange coordinate to resolve the angular momentumterm; while the dipolar interaction potential is decoupled into local and nonlocal interactionswhich results in a Gross-Pitaevskii-Poisson equation. An efficient and accurate numericalmethod is introduced to solve the coupled system. Some analytical and numerical resultswill be discussed in this talk.

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Mini-symposium 5:Numerical Analysis and Computations of Fluid Flow ProblemsOrganizers: Monika Neda, University of Nevada Las Vegas, USACarolina Manica, Universidade Federal do Rio Grande do Sul, BrasilAbstract. Fluid flow problems occur in numerous applications in science and engineering.Enhancement of physical properties in fluid modeling (such as conservation laws), achieve-ment of long term stability and accuracy of models approximated numerical solutions areessential. This special session will focus on recent advances in modeling fluid flow dynam-ics and in numerical methods to compute the approximated solutions of fluid flow models.Contributions can range from fundamental numerical studies for improvement of models atcontinuous and discretized level, and applications to industrial processes. Theoretical andcomputational studies based on related physical models are welcome too.

Bayesian source separation in MEGDaniela Calvetti, Case Western Reserve University, USAAbstract. Magnetoencephalography (MEG) is a completely non-invasive brain-mappingmodality which uses measurements of the magnetic field outside the head induced by elec-trical brain activity to localize and characterize the activity inside the brain. Potentially, itis particularly useful in the study of epilepsy as a tool for localizing the focii of the onset ofseizures. A key issue in MEG is the separation of sources of a different nature. Non-focalsources from both inside and outside of the brain produce interference, making the inverseproblem of identifying the focal source signal extremely difficult. In this talk we show howBayesian methods can be used to address this issue. In particular, we illustrate how a mixedprior distribution is able to separate sources which are statistically different from each other.Furthermore, we propose using a depth scan to identify activity from deep focal sources.Numerical simulations are used to generate controlled data in order to validate the model.

Approximate Deconvolution Large Eddy Simulation of a Barotropic Ocean Cir-culation ModelTraian Iliescu, Virginia Tech, USAAbstract. This talk introduces a new large eddy simulation closure modeling strategy fortwo-dimensional turbulent geophysical flows. This closure modeling approach utilizes ap-proximate deconvolution, which is based solely on mathematical approximations and doesnot employ phenomenological arguments, such as the concept of energy cascade. The newapproximate deconvolution model is tested in the numerical simulation of the wind-drivencirculation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics.The model employs the barotropic vorticity equation driven by a symmetric double-gyrewind forcing, which yields a four-gyre circulation in the time mean. The approximate de-convolution model yields the correct four-gyre circulation structure predicted by a directnumerical simulation, on a much coarser mesh and at a fraction of the computational cost.This first step in the numerical assessment of the new model shows that approximate decon-volution could represent a viable alternative to standard eddy viscosity parameterizations inthe large eddy simulation of more realistic turbulent geophysical flows.

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Modern ideas in turbulence confront legacy codesWilliam Layton, University of Pittsburgh, USAAbstract. The accurate, efficient and reliable simulation of turbulent flows in complexgeometries and modulated by other effects is a recurring challenge. Often these simulationsmust be done with legacy codes written a generation of programmers ago. The questionthen becomes: How are modern models and methods to be used in such a setting? Thistalk will present one path to doing so. The new algorithms involved lead to new models ofturbulence and these lead inevitably to new analysis questions.

Numerical free surface flows on dynamic octree meshesMaxim Olshanskii, Moscow State University, RussiaAbstract. In the talk, we present an approach for numerical simulation of free surface flowsof viscous Newtonian and viscoplastic incompressible fluids. The approach is based on thelevel set method for capturing free surface evolution and features compact finite differenceapproximations of fluid and level set equations on locally refined and dynamically adaptedoctree cartesian grids. Several important choices have to be made and tools to be developedfor the entire simulations to be predictive and efficient: spacial disretization, time stepping,handling non-differentiable constitutive relations, surface reconstruction, re-initialization ofthe level set function, curvature evaluation, etc. These building blocks will be discussed inthe talk. Numerical examples will demonstrate the performance of the approach for a rangeof problems, starting from academic benchmark tests and ending with applications to fluidanimation, catastrophe modelling, and in food industry.

This is a part of the joint research with Kirill Nikitin, Kirill Terehov, and Yuri Vassilevskifrom Inst. Numer. Math. RAS in Moscow.

On the Leray regularization with fine mesh filteringAbigail Bowers, Clemson University, USAAbstract. We study a numerical method for the Leray-alpha regularization model thatapplies the spacial filtering on a finer mesh than is used to resolve the model. Analysis ofthis method reveals an optimal scaling between the coarse and fine mesh widths, and thefiltering radius. Moreover, the analysis also shows that polynomials of one lower degree canbe used to resolve the filter problem, making for only a small extra cost associated with thefine mesh filter solve. Numerical experiments are given that confirm the theory, and showthe effectiveness of the method on benchmark problems.

Dual-mixed finite element methods for the Navier-Stokes equationsJason Howell, Clarkson University, USAAbstract. Accurate and efficient numerical methods to approximate fluid flows are impor-tant to researchers in many fields, including mechanical, materials, and biomedical engineer-ing. In many applications within these fields, it is of paramount importance to accuratelypredict fluid stresses. However, most existing numerical schemes for fluids are formulatedwith velocity as the primary unknown of interest, and computation of the fluid stress requiresexpensive and potentially inaccurate postprocessing techniques. In this talk, a dual-mixedvariational formulation for the Navier-Stokes equations, in which the stress is a primaryunknown of interest, is derived and analyzed. Using results that provide equivalent sets

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of inf-sup conditions for twofold saddle point problems, it is shown that a finite elementscheme for this method can be constructed from existing schemes for elasticity problemswith weak symmetry of the stress. The extension of this method to non-Newtonian fluids isalso discussed.

An efficient and accurate numerical method for high-dimensional stochastic par-tial differential equationsAlexander Labovsky, Michigan Technological University, USAAbstract. The Analysis of Variance (ANOVA) expansion is often used to represent multi-variate functions in high dimensions. Using the anchored (Dirac) ANOVA expansion resultsin a substantially reduced cost of evaluation of such functions. However, this approach hastwo significant flaws. First, the accuracy of the approximation is sensitive to the choice of theanchor point, which is hard to make a priori. Secondly, when the number of the parametersis large, the construction of the ANOVA expansion becomes prohibitively expensive. In thiscase, efforts were made to recognize which input dimensions have the largest effect upon theoutput, and the ANOVA expansion was built using only these important inputs and theirinteractions. However, we show that such a simplification can result in a loss of accuracy,since unimportant inputs often have important interactions. We propose a method for repre-sentation of multivariate functions, which does not depend on the choice of the anchor point,and tracks all the important inputs and important interactions, therefore constructing theexpansion with the exact minimum of the needed terms. We also provide an example of areal life application where our method is not only computationally attractive, but it is theonly approach capable of approximating the given multivariate function with the expectedaccuracy.

Numerical and analytical study for viscoelastic flow in a moving domainHyesuk Lee, Clemson University, USAAbstract. In this talk the problem of a viscoelastic fluid flow in a movable domain is consid-ered. A numerical approximation scheme is developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. The spatial discretization is accomplishedby the finite element method, and time-stepping schemes satisfying the geometric conserva-tion law are discussed. We also present some results of viscoelastic flow interacted with anelastic structure.

Stability and Convergence Analysis: Leray-Iterated-Tikhonov NSE with TimeRelaxationCarolina Manica, Universidade Federal do Rio Grande do Sul, BrasilAbstract. We present a general theory for regularization models of the Navier-Stokesequations based on the Leray deconvolution model with a general deconvolution operatordesigned to fit a few important key properties. We provide examples of this operator, suchas the Tikhonov-Lavrentied and Iterated Tikhonov-Lavrentiev operators, and study theirmathematical properties. An existence theory is derived for the family of models and arigorous convergence theory is derived for the resulting algorithms.

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Sensitivity Analysis and Computations for Regularized Navier-Stokes EquationsMonika Neda, University of Nevada Las Vegas, USAAbstract. We study the sensitivity of the regularized Navier-Stokes equations that arebased on filtering and deconvolution. The sensitivity studies are based on the sensitivityequation method, where the corresponding differentiation of the model equations is done.We apply the finite element method to the model and sensitivity equations, and investigateits algorithm theoretically and computationally.

Linear solvers for incompressible flow simulations using Scott-Vogelius elementsLeo Rebholz, Clemson University, USAAbstract. We investigate linear solvers for the saddle point linear systems arising in((Pk)

d, P disck−1 ) Scott-Vogelius finite element implementations of the incompressible Navier-

Stokes equations. We discuss the advantages of static condensation applied to these systemsto dramatically reduce the system sizes, and then test direct solvers, several implementationsof augmented Lagrangian preconditioners with GMRES, HLU preconditioned GMRES onthe condensed and uncondensed systems for four test problems.

Analysis of stability and errors of IMEX methods for MHD equationsHoang Tran, University of Pittsburgh, USAAbstract. We analyze the stability and accuracy of several implicit-explicit (IMEX) meth-ods for the MHD equations. At small magnetic Reynolds numbers, the methods can beevolved in time by calls to the NSE and Maxwell codes, each possibly optimized for thesubproblem’s respective physics.

This work is in collaboration with William Layton and Catalin Trenchea

Physics based filtering for the incompressible Leray-α MagnetohydrodynamicsequationsNicholas Wilson, Clemson University, USAAbstract. The incompressible magnetohydrodynamics equations (MHD) are derived bycoupling the Navier-Stokes equations (NSE) with Maxwell’s equations. They model fluidflows in the presence of a magnetic field, when the fluid is electrically conductive but notmagnetic (e.g. salt water). The complexity of these flows do not allow for efficient directnumerical simulation, which motivates the use of regularization models. The Leray-α MHDmodel uses the Helmoholtz filter to remove under resolved scales from the velocity andmagnetic fields. filtered the entire velocity and magnetic fields. To date the velocity andmagnetic fields are filtered entirely. However, recent work for the Leray-α NSE model hasshown that nonlinear filtering that locally chooses the filtering radius based on physics mayimprove solutions. We develop physics based criterion for filtering the velocity and magneticfield for MHD flows, and provide numerical experiments.

The dynamics of two phase complex fluids: drop formation/pinch-offXiaofeng Yang, University of South Carolina, USAAbstract. We present an energetic variational phase-field model for the two-phase incom-pressible flow with one phase being the nematic liquid crystal. The model leads to a couplednonlinear system satisfying an energy law. An efficient and easy-to-implement numerical

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scheme is presented for solving the coupled nonlinear system. We use this scheme to sim-ulate two benchmark experiments: one is the formation of a bead-on-a-string phenomena,and the other is the dynamics of drop pinching-off. We investigate the detailed dynamicalpinch-off behavior, as well as the formation of the consequent satellite droplets, by varyingorder parameters of liquid crystal bulk and interfacial anchoring energy constant. Qualitativeagreements with experimental results are observed.

Mini-symposium #6Multilevel and Adaptive Methods for Solving Complex SystemsOrganizers: Pengtao Sun, University of Nevada Las Vegas, USALong Chen, University of California, USAJun Hu, Peking University, ChinaAbstract. This mini-symposium is motivated by recent advances on multilevel adaptivemesh method, multigrid method, domain decomposition method, multiscale method, phasefield/level set method, Newton-Krylov method and their applications on multidimensional,multiphysics and/or multiphase convection-diffusionreaction problems arising from complexfluids, fluid-structure coupling, mathematical biology, electromagnetics, renewable energy(fuel cell, solar cell and battery innovations) and etc. We expect to communicate and discussthe recent novel techniques/ideas achieved on the modeling and numerical methods aboutthese topics. More beyond, the related physical models and the corresponding computationalmethods will not be limited to aforementioned topics only, any efficient and robust numericaltechniques for solving significant complex systems are welcome to be presented in this session.

An Algebraic Multilevel Preconditioner for Graph Laplacians based on Matchingof GraphsJames Brannick, The Pennsylvania State University, USAAbstract. We present an algebraic multilevel method for solving Ax = f where A is thegraph Laplacian of an unweighted graph G. We estimate the convergence rate of a two levelmethod where the coarser level operator is the graph Laplacian of the reduced graph, whichis formed by aggregation where each aggregate contains two or more vertices in the graphG. We show a general approach of estimating the convergence rate of the corresponding twolevel method. Then we constructed a multilevel hierarchy and used Algebraic MultilevelIterations (AMLI) in the solving phase. Such combination is proved to have nearly optimalconvergence and time/space complexity on graph Laplacians corresponding to structuredgrids, and numerical results indicate good performance on other type of graphs.

This is a joint work with Johannes Kraus (RICAM), and Ludmil Zikatanov (The Pennsyl-vania State University).

Multigrid Methods for Stokes Equation based on Distributive Gauss-Seidel Re-laxationLong Chen, University of California at Irvine, USAAbstract. A major difficulty for the numerical simulation of incompressible flows is thatthe velocity and the pressure are coupled by the incompressibility constraint. Distributive

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Gauss-Seidel (DGS) relaxation introduced by Achi Brandt and Nathan Dinar is known to bean efficient decoupled smoothing method for the staggered grid discretization (MAC scheme)of Stokes equations. In this work, we attempt to design DGS relaxation for discontinuouspressure finite element approximations of Stokes equations on rectangular grid. We proposea two-level solver based on DGS smoothing on the fine space and use V-cycle for MACscheme as coarse space correction solver. Numerical experiments show that the new solverachieves the textbook multigrid efficiency.

This is a joint work with Ming Wang (UC Irvine, USA and Peking University, China).

The adaptive nonconforming finite element method for the fourth order problemJun Hu, Peking University, ChinaAbstract. For the fourth order elliptic problem, most of popular finite element methodsin the literature are the nonconforming finite element method. The partial reason maylie in that it is actually very difficult to design conforming finite element spaces consistingof piecewise polynomials. There are a lot of papers concerning a priori analysis of thenonconforming finite elements in the literature. However, there are few works concerningthe adaptive nonconforming finite element methods of the fourth order problem.

In the first part of the talk, we present the a posteriori error estimator of some nonconformingelements for the Kirchhoff-Love plate problem. We overcome the key difficulty due to thelack of proper conforming subspaces and prove that the usual residual-based error estimatoris reliable and efficient for these methods. The main ingredient is the tool used for a priorerror analysis by exploring carefully the continuity condition of these elements.

In the second part of the talk, we address the convergence and optimality of the adaptiveMorley element method for the fourth order elliptic problem. We develop a new technique toestablish a quasi-orthogonality which is crucial for the convergence analysis of the adaptivenonconforming method. By introducing a new prolongation operator and further establishinga discrete reliability property, we show the sharp convergence and optimality estimates forthe fourth order elliptic problem.

Algebraic Multigrid Methods for Petroleum Reservoir SimulationXiaozhe Hu, The Pennsylvania State University, USAAbstract. The most time-consuming part of modern Petroleum Reservoir Simulation (PRS)is solving a sequence of large-scale and ill-conditioned Jacobian systems. In this work, wedevelop new effective preconditioners based on Algebraic Multigrid (AMG) Methods forsolving these Jacobian systems. Following the auxiliary space preconditioning framework,the new preconditioning technique chooses appropriate auxiliary problems according to thedifferent properties of the equations in the black oil model, and designs robust and efficientAMG methods for each auxiliary problem. By combining the new preconditioners withKrylov subspace iterative methods, we construct efficient and robust solvers, which can begeneralized to more complicated models for enhanced oil recovery. Numerical experimentsincluding preliminary parallel implementations demonstrate the effectiveness and robustnessof our new solvers for PRS.

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Covolume-Upwind Finite Volume Approximations for Linear Elliptic Partial Dif-ferential EquationsLili Ju, University of South Carolina, USAAbstract. In this talk, we discuss covolume-upwind finite volume methods on rectangularmeshes for solving linear elliptic partial differential equations with mixed boundary con-ditions. To avoid non-physical numerical oscillations for convection-dominated problems,nonstandard control volumes (covolumes) are generated based on local Peclet’s numbers andthe upwind principle for finite volume approximations. Two types of discretization schemeswith mass lumping are developed with use of bilinear or biquadratic basis functions as thetrial space respectively. Some stability analyses of the schemes are presented for the modelproblem with constant coefficients. Various examples are also carried out to numericallydemonstrate stability and optimal convergence of the proposed methods.

New multigrid methods for the Stokes and linear elasticity problemsHengguang Li, Wayne State University, USAAbstract. We have developed new smoothers for the Stokes and linear elasticity problems.Using the multigrid Poisson solve, we precondition the indefinite system from the finiteelement discretization of these saddle point problems. We prove the resulting multigridalgorithms are contractions with the contraction number depending on the regularity of thesolution but independent of the mesh level.

A treecode elastostatics computationHualong Feng, Illinois Institute of Technology, USAAbstract. We describe an O(N logN) adaptive treecode for elastostatics computation. Thecode is tested both with randomly generated data and in a spectrally accurate method formaterials science problems. It is shown that the code scales like O(N logN) asymptotically,and at the same time fulfills stringent precision requirements prescribed by the spectralmethod. We also present a parallelized version of the treecode. The new version is relativelyeasier to implement than the previous versions, because it entails less communication betweenprocessors. For non-uniform data, data locality is necessary for load balancing to ensurespeed, and we use the Hilbert curve ordering to implement data locality. We show thatthe parallel version scales linearly with the number of processors for both uniform and non-uniform data.

This is a joint work with Shuwang Li, Amlan Barua, and Xiaofan Li.

Operator splitting methods for stiff convection-reaction-diffusion equationsXingfeng Liu, University of South Carolina, USAAbstract. Implicit integration factor (IIF) method, a class of efficient semi-implicit tempo-ral scheme, was introduced recently for stiff reaction-diffusion equations. Advection-reaction-diffusion equations are traditionally difficult to handle numerically. For reaction-diffusionsystems with both stiff reaction and diffusion terms, implicit integration factor (IIF) methodand its high dimensional analog compact form (cIIF) serve as an efficient class of time-stepping methods. For nonlinear hyperbolic equations, front tracking method is one of themost powerful tools to dynamically track the sharp interfaces. Meanwhile, weighted essen-tially non-oscillatory (WENO) methods are a class of start-of-the-art schemes with uniform

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high order of accuracy in smooth regions of the solution, which can also resolve the sharpgradient in accurate and essentially non-oscillatory (ENO) fashion. In this talk, IIF/cIIFis coupled with front tracking or WENO by the second-order symmetric operator splittingapproach to solve advection-reaction-diffusion equations. In the methods, IIF/cIIF meth-ods treat the stiff reaction-diffusion equations, and front tracking/WENO methods handlehyperbolic equations that arise from the advection part. In addition, we shall introduce amethod for integrating IIF/cIIF with adaptive mesh refinement (AMR) to take advantage ofthe excellent stability condition for IIF/cIIF. The applications of these numerical methodsto fluid mixing and cell signaling will also be presented.

A Robust and Efficient Method for Steady State Patterns in Reaction-DiffusionSystemsWing-Cheong (Jon) Lo, The Ohio State University, USAAbstract. An inhomogeneous steady state pattern of nonlinear reaction-diffusion equa-tions with no-flux boundary conditions is usually computed by solving the correspondingtime-dependent reaction-diffusion equations using temporal schemes with a careful choice ofinitial condition, which is often estimated through stability analysis. Nonlinear solvers (e.g.Newton’s method) take less CPU time in direct computing the steady state, however, theirconvergence is sensitive to the initial guess, often leading to divergence or convergence to spa-tially homogeneous solution. Systematic exploration of spatial patterns of reaction-diffusionequations under different parameter regimes through numerical simulations requires that thenumerical method be efficient and be robust in terms of initial condition or initial guess, andit has better likelihood of convergence to inhomogeneous pattern than convergence to spa-tially constant solutions. In this study, we present a new approach that combines advantageof temporal schemes in robustness and advantage of Newton’s method in fast convergence insolving steady states of reaction-diffusion equations. The new iterative procedure is basedon implicit Euler method but without solving the implicit equation exactly at each timestep. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is foundto be much more efficient than temporal schemes and to be more robust in convergence thantypical nonlinear solvers (e.g. Newton’s method) in finding the inhomogeneous pattern.

Toward a robust hp-adaptive method for elliptic eigenvalue problemsJeffrey S. Ovall, University of Kentucky, USAAbstract. We discuss progress toward a robust hp-adaptive method for approximatingcollections of eigenvalues of self-adjoint elliptic operators and their associated invariant sub-spaces. The robustness is with respect to discontinuities in the coefficients of the differentialoperator and the resultant low-regularity of eigenfunctions, as well as the possibility of de-generate or “nearly-degenerate” eigenvalues. Theoretical and computational results of theseauthors will be discussed for two hp-adaptive discretizations: one employing a discontinuousGalerkin approach, with goal-oriented adaptivity designed for these types of problems; theother using a continuous Galerkin approach, with adaptivity based on an operator-theoreticapproach to a posteriori error analysis, and the use of standard hp-residual error estimates.It is the latter of these approaches which will be pursued in further research, and indica-tions will be provided of where (and roughly how) improvements are expected in theory andpractice.

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This is a joint work with Luka Grubisic (University of Zagreb, Croatia) and Stefano Giani(University of Nottingham, United Kingdom).

Dirichlet/Robin iteration-by-subdomain Schwarz-DDM for multiphase fuel cellmodel with micro-porous layerPengtao Sun, University of Nevada Las Vegas, USAAbstract. In this talk, an efficient numerical method for a three-dimensional, two-phasetransport model is presented for polymer electrolyte membrane fuel cell (PEMFC) includ-ing multi-layer diffusion media, composed of two or more layers of porous materials havingdifferent pore sizes and/or wetting characteristics. Particularly, capillary pressure is contin-uous, whereas liquid saturation is discontinuous, across the interface of gas diffusion layer(GDL) and micro-porous layer (MPL), which can improve liquid-water transport in theporous electrode. We design a nonlinear Dirichlet/Robin iteration-by-subdomain Schwarz-domain decomposition method to deal with water transport in such multi-layer diffusionmedia, where Kirchhoff transformation and its inverse techniques are employed to conquerthe discontinuous water diffusivity in the coexisting single- and two-phase regions. In addi-tion, the conservation equations of mass, momentum, charge, hydrogen and oxygen transportare numerically solved by finite element-upwind finite volume method. Numerical simula-tions demonstrate that the presented techniques are effective to obtain a fast and convergentnonlinear iteration for a 3D full PEFC model within around a hundred steps. A seriesof numerical convergence tests are carried out to verify the efficiency and accuracy of ournumerical algorithms and techniques.

Cell conservative flux recovery and a posteriori error estimate of high order finitevolume methodsMing Wang, University of California at Irvine, USA and Peking University, ChinaAbstract. A cell conservative flux recovery technique is developed for vertex-centered finitevolume methods of second order elliptic equations. It is based on solving a local Neumannproblem on each control volume using mixed finite element methods. The recovered flux isused to construct a constant free a posteriori error estimator which is proven to be reliableand efficient. Some numerical tests are presented to confirm the theoretical results.

We emphasize that our method works for general order finite volume methods and therecovery-based and residual-based a posteriori error estimators is apparently the first resultson a posteriori error estimators for high order finite volume methods.

This is a joint work with Long Chen (UC Irvine, USA).

A parallel geometric-algebraic multigrid solver for the Stokes problemChensong Zhang, LSEC, Institute of Computational Mathematics, Chinese Academy ofSciences, ChinaAbstract. We propose a scalable parallel solver for the discrete systems from the generalizedStokes equation discretized by the Taylor-Hood finite element methods. We will analyze ageometric-algebraic multigrid (GAMG) method for high-order finite element methods forthe Laplacian problem which makes a key ingredient of the preconditioner. We will alsodescribe details for the parallel implementation and show this algorithm is user-friendly. Wetest serial and parallel version of the proposed method with 3D Poisson and Stokes problems

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on unstructured grids; preliminary numerical results show the advantages of the proposedalgorithm.

On a Robin-Robin domain decomposition method with optimal convergence rateShangyou Zhang, University of Delaware, USAAbstract. In this talk, we shall answer a long-standing question: Is it possible that theconvergence rate of the Lions’ Robin-Robin nonoverlapping domain decomposition method isindependent of the mesh size h? The traditional Robin-Robin domain decomposition methodconverges at a rate of 1 − O(h1/2), even under the optimal parameter. We shall design atwo-parameter Robin-Robin domain decomposition method. It is shown that the new DDmethod is optimal, which means the convergence rate is independent of the mesh size h.

A BPX preconditioner for the symmetric discontinuous Galerkin methods ongraded meshesLiuqiang Zhong, South China Normal University, China and The Chinese University ofHong Kong, ChinaAbstract. A multilevel BPX preconditioner for the symmetric discontinuous Galerkin meth-ods on graded meshes is presented. An arbitrary order discontinuous finite element is consid-ered and the resulting preconditioned system is uniformly well conditioned. The theoreticalresults are illustrated by numerical experiments.

Adaptive finite element techniques for Einstein constraintsYunrong Zhu, University of California at San Diego, USAAbstract. In this talk, we present adaptive finite element approximation techniques for theconstraints arising from the Einstein equations in general relativity. We first derive a prioriL∞ bounds of the discrete solution, without using the restrictive angle condition. Then wegive the adaptive algorithm based on a posteriori error indicator and refinement of simplextriangulations of the domain, and show that the algorithm converges.

Axially symmetric volume constrained anistropic mean curvature flowWenxiang Zhu, Idaho State University, USAAbstract. We study the long time existence theory for a non local flow associated to a freeboundary problem for a trapped nonliquid drop. The drop has free boundary componentson two horizontal plates and its free energy is anisotropic and axially symmetric. For axiallysymmetric intial surfaces with sufficiently large volume, we show the flow exists for all time.We will also talk about the numerical computations of this flow, especially via the approachesof front tracking method and the phase field method.

Mini-symposium #7Direct and Inverse Scattering for Wave PropagationOrganizers: Jiguang Sun, Delaware State University, USAPeijun Li, Purdue University, USA

Statistical methods applied to the inverse problem in electroneurographyErkki Somersalo, Case Western Reserve University, USA

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Abstract. Electroneurography (ENG) is a method of recording neural activity withinnerves. Using nerve electrodes with multiple contacts the activation patterns of individ-ual neuronal fascicles can be estimated by measuring the surface voltages induced by theintraneural activity. The information about neuronal activation can be used for functionalelectric stimulation (FES) of patients suffering of spinal chord injury, or to control a roboticprosthetic limb of an amputee. However, the ENG signal estimation is a severely ill-posedinverse problem due to uncertainties in the model, low resolution due to limitations of thedata, geometric constraints, and the difficulty to separate the signal from biological andexogenous noise. In this article, a reduced computational model for the forward problem isproposed, and the ENG problem is addressed by using beamformer techniques. It is shownthat the beamformer algorithm can be interpreted as a version of the classical Backus-Gilbertalgorithm. Furthermore, we show that using a hierarchical statistical model, it is possibleto develop an adaptive beamformer algorithm that estimates directly the source variancesrather than the voltage source itself. The advantage of this new algorithm, e.g., over a tra-ditional adaptive beamformer algorithms is that it allows a very stable noise reduction byaveraging over a time window. In addition, a new projection technique for separating sourcesand reducing cross-talk between different fascicle signals is proposed. The algorithms aretested on a computer model of realistic nerve geometry and time series signals.

An Efficient and Stable Spectral Method for Electromagnetic Scattering from aLayered Periodic StructureYing He - Purdue University, USAAbstract. The scattering of acoustic and electromagnetic waves by periodic structures playsan important role in a wide range of problems of scientific and technological interest. Thiscontribution focuses upon the stable and high order numerical simulation of the interactionof time harmonic electromagnetic waves incident upon a periodic doubly layered dielectricmedia with sharp, irregular interface. We describe a Boundary Perturbation Method forthis problem which avoids not only the need for specialized quadrature rules but also thedense linear systems characteristic of Boundary Integral/Element Methods. Additionally,it is a provably stable algorithm as opposed to other Boundary Perturbation approachessuch as Bruno & Reitich’s Method of Field Expansions” or Milder’s Method of OperatorExpansions.” Our spectrally accurate approach is a natural extension of the Method ofTransformed Field Expansions” originally described by Nicholls & Reitich (and later renedto other geometries by the authors) in the single layer case.

A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for2-D high frequency electromagnetic scattering in dispersive inhomogeneous me-diaXia Ji, LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences,ChinaAbstract. In this paper, we propose a parallel Schwarz generalized eigen-oscillation spec-tral element method (GeSEM) for 2-D complex Helmholtz equations in high frequency wavescattering in dispersive inhomogeneous media. This method is based on the spectral expan-sion of complex generalized eigen-oscillations for the electromagnetic fields and the Schwarznon-overlapping domain decomposition iteration method. The GeSEM takes advantages

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of a special real orthogonality property of the complex eigen-oscillations and a new radia-tion interface condition for the system of equations for the spectral expansion coefficients.Numerical results validate the high resolution and the flexibility of the method for variousmaterials.

Sparse reconstruction in diffuse optical tomographyTaufiquar Rahman Khan, Clemson University, USAAbstract. In this talk, a short overview of the basics of image reconstructio n in diffuseoptical tomography (DOT) will be presented. Extension of the distinguish-ability criteria ofIsaacson and Knowles to opti mal source in DOT will be discussed. A sparsity constrainedreconstruction problem in DOT for determining the optical parameters from bou ndarymeasurements will be presented. The sparsity of the inclusion with resp ect to a particularbasis is assumed a priori. The proposed approach is based on a sparsity promoting l1-penaltyterm similar to the approach of Jin et al. for electrical impedance tomography [Journal ofInverse and Ill-Posed Problems].

An eigenvalue method using multiple frequency dataJiguang Sun, Delaware State University, USAAbstract. Dirichlet and transmission eigenvalues have important applications in qualitativemethods in inverse scattering. Motivated by the fact that these eigenvalues can be obtainedfrom scattering data, we propose a new eigenvalue method using multiple frequency data(EM2F). The method detects eigenvalues and builds indicator functions to reconstruct thesupport of the target. Numerical reconstruction is quite satisfactory. Estimation of Dirichletor transmission eigenvalues is obtained. Furthermore, reconstruction of D and estimationof eigenvalues can be combined together to distinguish between the sound soft obstacle andnon-absorbing inhomogeneous medium.

Mini-symposium #8Recent Developments in Adaptivity and A Posteriori Error AnalysisOrganizers: Tim Barth, NASA, USAPaul Houston, University of Nottingham, UKMats Larson, University of Umea, SwedenAbstract. The exploitation of computable a posteriori error bounds within adaptive mesh-refinement strategies is of fundamental importance to guarantee the reliable and efficientnumerical simulation of mathematical models arising in computational science and engi-neering. The objective of this minisymposium is to present recent work undertaken in thisfield; in particular, topics of interest will include: dual-weighted-residual error estimation,adaptive model reduction, error estimation of time-dependent problems, and hp-adaptiverefinement strategies.

Adaptive Model Reduction for Coupled Thermoelastic ProblemsMats Larson, Umea University, SwedenAbstract. In this contribution we develop adaptive model reduction for coupled thermoe-lastic problems.The adaptive method is based on a discrete a posteriori error estimate for

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a thermoelastic model problem discretized using a reduced finite element method. We firstconsider the case when the problem is one-way coupled in the sense that heat transfer affectselastic deformation, but not vice versa. Then we extend our analysis to the fully coupledcase with temperature dependent material parameters. A reduced model is constructed us-ing component mode synthesis (CMS) in each of the heat transfer and linear elastic finiteelement solvers. The error estimate bounds the difference between the reduced and the stan-dard finite element solution in terms of discrete residuals and corresponding dual weights.A main feature with the estimate is that it automatically gives a quantitative measure ofthe propagation of error between the solvers with respect to a certain computational goal.Based on the estimates we design adaptive algorithms that enable automatic tuning of thenumber of modes required in each substructure. The analytical results are accompanied bynumerical examples.

This is a joint work with H. Jakobsson (Umea University).

Two-Grid hp–Adaptive Discontinuous Galerkin Finite Element Methods for Second–Order Quasilinear Elliptic PDEsPaul Houston, University of Nottingham, UKAbstract. In this talk we present an overview of some recent developments concerningthe a posteriori error analysis and adaptive mesh design of h– and hp–version discontinuousGalerkin finite element methods for the numerical approximation of second–order quasilinearelliptic boundary value problems. In particular, we consider the derivation of computablebounds on the error measured in terms of an appropriate (mesh–dependent) energy normin the case when a two-grid approximation is employed. In this setting, the fully nonlin-ear problem is first computed on a coarse finite element space VH,P . The resulting ‘coarse’numerical solution is then exploited to provide the necessary data needed to linearise theunderlying discretization on the finer space Vh,p; thereby, only a linear system of equationsis solved on the richer space Vh,p. Here, an adaptive hp–refinement algorithm is proposedwhich automatically selects the local mesh size and local polynomial degrees on both thecoarse and fine spaces VH,P and Vh,p, respectively. Numerical experiments confirming thereliability and efficiency of the proposed mesh refinement algorithm are presented.

Advanced Aspects of Adaptive Higher-Order MethodsLukas Korous, Charles University, PragueAbstract. In this presentation we give a survey of our recent results in adaptive hp-FEM andhp-DG methods. The presentation has four parts. In part 1 we illustrate the importance offully anisotropic hp refinements and present a new suite of benchmark problems that can beused to assess anisotropic capabilities of adaptive hp-FEM codes. In part 2 we present a novelPDE-independent hp-adaptive multimesh discretization method for multiphysics coupledproblems. In contrast to operator-splitting methods, our approach preserves the couplingstructure of all physical fields on the discrete level, which results into better accuracy andstability of the approximation. In part 3 we mention a monolithic multimesh discretizationof problems involving compressible inviscid flow where the flow part is discretized using hp-DG and second-order equations are discretized using hp-FEM. In part 4 we introduce theHermes library for rapid development of space- and space-time adaptive hp-FEM and hp-DGsolvers.

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Adaptive Higher-Order Finite Element Methods for Transient PDE ProblemsBased on Embedded Higher-Order Implicit Runge-Kutta MethodsPavel Solin, University of Nevada, Reno, USAAbstract. We present a new class of adaptivity algorithms for time-dependent partialdifferential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM)in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time.Weak formulation is only created for the stationary residual, and the Runge-Kutta methodsare specified via their Butcher’s tables. Around 30 Butcher’s tables for various Runge-Kutta methods with numerically verified orders of local and global truncation errors areprovided. A time-dependent benchmark problem with known exact solution that containsa sharp moving front is introduced, and it is used to compare the quality of seven em-bedded implicit higher-order Runge-Kutta methods. Numerical experiments also include acomparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes.All numerical results presented in this paper were obtained using the open source libraryHermes (http://hpfem.org/hermes) and they are reproducible in the Networked ComputingLaboratory (NCLab) at http://nclab.com.

This is a joint work with Lukas Korous (Charles University, Prague, Czech Republic).

Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Ad-joint SolutionsAugust Johansson, University of California, Berkeley, USAAbstract. We describe and test an adaptive algorithm for evolution problems that employsa sequence of ”blocks” consisting of fixed, though nonuniform, space meshes. This approachoffers the advantages of adaptive mesh refinement but with reduced overhead costs. A keyissue with a block adaptive approach is determining block discretizations from coarse scalesolution information that achieve the desired accuracy. We describe several strategies forachieving this goal using adjoint-based a posteriori error estimates, and we demonstrate thebehaviour of the proposed algorithms in various examples, such as a coupled PDE-ODEsystem.

A Posteriori Error Estimation via Nonlinear Error TransportJeff Banks, Lawrence Livermore National Laboratory, USAAbstract. Error estimation for time dependent hyperbolic problems is challenging for the-oretical and practical reasons. In these systems, error can propagate long distances andproduces effects far from the point of generation. In addition, nonlinear interactions of er-ror, as well as nonlinear discretizations can play important roles and should be addressed.In this talk we investigate the use of error equations for a posteriori error estimation. Weextend the existing work using linear error transport equations, and discuss situations wherethe this approach is found to be deficient. In particular, we investigate the effects of non-linearities in the error equations, which are particularly important for situations where localerrors become large such as near captured shocks. The auxiliary PDEs are treated numeri-cally to yield field estimates of error and we discuss subtleties associated with the numericaltreatment of the nonlinear error transport equations.

Dual Problems in Error Estimation and Uncertainty Propagation for HyperbolicProblems

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Tim Barth, NASA Ames Research Center Moffett Field, USAAbstract. Dual problems arise in a number of computational settings including a-posteriorierror estimation, mesh adaptivity, sensitivity analysis, uncertainty propagation, and opti-mization. Even so, computational demands placed on the dual problem may differ signif-icantly for each computational setting. We have developed a general software frameworkfor error estimation, solution adaptivity, and uncertainty propagation. This software frame-work been successfully applied to numerical computations of compressible Navier-Stokesflow, hypersonic Navier-Stokes flow with finite-rate chemistry, magnetohydrodynamics, andEuler-Maxwell flow. In this presentation, we will discuss this software framework, showcomputational applications for hyperbolic problems, and discuss outstanding problems andfuture challenges.

A Posteriori Error Estimation for Compressible Flows using Entropy ViscosityMurtazo Nazarov∗, Jean-Luc Guermond, Bojan Popov, Texas A&M University, USAAbstract. We present a goal-oriented adaptive finite element method for the compressibleEuler/Navier-Stokes equations using continuous Galerkin finite elements. The mesh adaptionrelies on a duality-based a posteriori error estimation of the output functional. We derivea posteriori error estimations of the quantity of interest in terms of a dual problem for thelinearized Euler equations. The primal and the dual problems are solved by using an entropybased artificial viscosity method which we call entropy viscosity. The numerical viscosityis proportional to the entropy residual in the primal problem and proportional to the dualresidual in the dual problem. Both problems are solved using continuous piecewise linearfinite elements in space and explicit Runge-Kutta methods in time. The implementation intwo and three space dimensions as well as different boundary conditions are discussed. Anumber of benchmark problems are solved to validate the performance of the method.

Mini-symposium #9Uncertainty Quantification For Signal Processing and Inverse ProblemsOrganizers: Pushkin Kachroo, University of Nevada, Las Vegas, USAEric Machorro, National Security Technologies, LLC, USA

Estimating the bias of local polynomial approximation methods using the PeanokernelJerome Blair*, Keystone International and NSTec, USAEric Machorro, National Security Technologies, LLC, USAAbstract. The determination of uncertainty of an estimate requires both the variance andthe bias of the estimate. Calculating the variance of local polynomial approximation (LPA)estimates is straightforward. We present a method, using the Peano kernel, to estimate thebias of LPA estimates and show how this can be used to optimize the LPA parameters interms of the bias-variance tradeoff. Figures of merit are derived and values calculated forseveral common methods.

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Hybrid Numerical Techniques for Efficient Determination of stochastic Nonlin-ear Dynamic Responses via harmonic WaveletsP.D. Spanos, Rice University, USAAbstract. Responses of dynamical systems exposed to stochastic excitations described byharmonic wavelets are considered. A surrogate optimal linear system is introduced which fa-cilitates the nonlinear system response. The surrogate system is determined by satisfying anappropriate error minimization criterion. Subsequently the convenient spectral input/outputrelationship of the surrogate system are utilized to compute the spectrum of the stochasticresponse of the nonlinear system.Results from extensive numerical studies demonstrate thereliability and efficiency of the proposed method.

Computational Methods for Analyzing Fluid Flow Dynamics from Digital Im-ageryAaron Luttman, National Security Technologies LLC, USAAbstract. Optical flow is the term used to describe the inverse problem of extractingphysical flow information from time-dependent image data. The classical variational meth-ods are based on the assumption of conservation of intensity, which is only appropriate fordivergence-free and non-advective flows. We present a method for analyzing fluid flows fromdigital imagery, by adapting the classical variational approach for computing dense flows,which incorporates the physics of fluid flows into the data fidelity and allows for a varietyof prior assumptions on the flow, through the regularization. The computed flow fields arethen used to analyze the flow dynamics, using methods from computational dynamical sys-tems. The method is demonstrated on synthetic data as well as on data-assimilated, modelimagery of sea surface temperature of the Columbia River delta in Oregon, USA.

This is a joint work with Erik Bollt, Ranil Basnayake, and Sean Kramer.

Application of Random Field TheoryA.V. Balakkrishnan, University of California, Los Angeles, USAAbstract. 2D and 3D random field models: Turbulence-the Kolmogorov Theory: Aeroe-lastic Flutter; Monitoring Wind Flow by Laser Foreward Scattering; NonLinear Noise Func-tionals.

Analysis and Methods for Time Resolved Neutron DetectionNeveen Shlayan, Singapore-MIT Alliance for Research & Technology, USAAbstract. Various aspects of the neutron spectroscopy problem have been studied. The-oretically, the neutron emission problem is parallel to the limited angle radon transformproblem. In order to solve this ill posed problem, various algorithms were developed span-ning two different techniques; algebraic reconstruction as well as Monte-Carlo methods. Thedeveloped algorithms are the Stochastic Gradient Approximation (SGA) method, Simulta-neous Perturbation Stochastic Approximation (SPSA) method, and Time of Flight (TOF)method. Enhanced adaptive techniques were developed as well in order to improve thecurrent methods.

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Stochastic Spectral Approximation with Redundant Multiresolution Dictionar-ies for Uncertainty QuantificationDaniele Schiavazzi∗ and Gianluca Iaccarino, Stanford University, USAAbstract. The possibilities related to the quantification of the aleatoric uncertainty of phys-ical systems have greatly increased in recent years. Many reliable methodologies are alreadyavailable in the literature to efficiently propagate the uncertainty from input quantities tosystem responses. The present work focuses on non intrusive methodologies in which onedeterministic simulation is required for every realization. As a consequence, all propagationschemes aim at reducing the total number of samples, while preserving the maximum possibleaccuracy in the response statistics. While various methods have been recently proposed, twomain challenges remain to be tackled. One is related to problems in which a large numberof random parameters or a small correlation length of stochastic processes involved lead tovery high dimensions in random space. The second challenge is the presence of discontinu-ities in stochastic space commonly observed in problems involving instability or bifurcationphenomena. The present work proposes a novel framework assembled with the above chal-lenges in mind. Responses are represented in a multiresolution Alpert multiwavelet basisdictionary, where piecewise smooth responses exhibit a sparse structure. Furthermore, thisnon intrusive framework offers a straightforward generalization of Legendre and Haar chaostechniques, allowing both polynomial fitting in large domain areas together with the abilityof capturing discontinuous responses. Stochastic spectral coefficients are evaluated usinggreedy methodologies within the Compressed Sensing paradigm, in an attempt to unveilthe intrinsic redundancy in the response, of special interest for increasing dimensionality.In particular, a sparse tree representation in the Alpert multiwavelet domain is assumed,to improve the reconstruction of the stochastic response. The effect of various samplingstrategies is also investigated to provide better reconstruction performances.

Conservation Law Methods for Uncertainty Propagation in Dynamic SystemsLillian Ratliff, UC Berkeley, USAAbstract. We present methods of propagating uncertainty in the initial condition throughvarious types of dynamical systems with the goal of gaining insights into the geometricrepresentation of the uncertainty as it evolves under the dynamics. In particular, we providea review of uncertainty propagation in systems of ordinary differential equations. Using thisas motivation, we present a method for propagating uncertainty in systems with parametricuncertainty. We construct probability spaces at each time step and define an evolutionoperator which is preserves the probability measure. We also propose a method to extendthese result to dynamical systems characterized by differential inclusions.

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High Order Finite Difference Methods for Maxwell’s Equations in DispersiveMediaVrushali Bokil, Oregon State University, USAAbstract. We consider models for electromagnetic wave propagation in linear dispersivemedia which include ordinary differential equations for the electric polarization coupled toMaxwell’s equations. We discretize these models using high order finite difference methodsand study the properties of the corresponding discrete models. In this talk we will presentthe stability, dispersion and convergence analysis for a class of finite difference methodsthat are second order accurate in time and have arbitrary (even) order accuracy in space.Using representative numerical values for the physical parameters, we validate the stabilitycriterion while quantifying numerical dissipation. Lastly, we demonstrate the effect that thespatial discretization order and the corresponding stability condition has on the dispersionerror.

HDG methods for Reissner-Mindlin platesFatih Celiker, Wayne State University, USAAbstract. We introduce a family of hybridizable discontinuous Galerkin (HDG) methodsfor solving the Reissner-Mindlin plate equations. The method is based on rewriting the equa-tions a system of first-order partial differential equations. We then introduce the hybridizedmethod which results in the elimination of all the unknowns except for those associated withthe transverse displacement and rotations of the vertical fibers at the edges of the mesh.Therefore, the methods are efficiently implementable. We prove that the methods are well-defined and display numerical results to ascertain their convergence behavior. We also shownumerically that a simple element-by-element post-processing of the transverse displacementprovides an approximation which converges faster than the original approximation.

Spectral Collocation Methods for Volterra Integro-Differential EquationsYanping Chen, South China Normal University, ChinaAbstract. This talk presents Legendre spectral collocation methods for pantograph Volterradelay-integro-differential equations and Jacobi spectral collocation methods for weakly sin-gular Volterra integro-differential equations with smooth solutions and with nonsmooth so-lutions in some special case. We provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximatederivatives of the solutions decay exponentially in L∞-norm and weighted L2-norm. Thenumerical examples are given to illustrate the theoretical results.

Multi-frequency methods for an inverse source problemS. Acosta, Rice University, USAS. Chow∗, Brigham Young University, USAV. Villamizar, Brigham Young University, USAAbstract. We study an inverse source problem in acoustics, where an unknown source is tobe identified from the knowledge of its radiated wave. The existence of non-radiating sourcesat a given frequency leads to the lack of uniqueness for the inverse source problem. In our

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previous work we prove that data obtained from finitely many frequencies is not sufficient.On the other hand, if the frequency varies within an open interval of the positive real line,then the source is determined uniquely. We will discuss two algorithms for the reconstructionof the source using multi-frequency data. One algorithm is based on an incomplete Fouriertransform of the measured data and we establish an error estimate under certain regularityassumptions on the source function. The other algorithm involves the solution of an adjointproblem. Some numerical result will be presented.

Generalized image charge solvation model for electrostatic interactions in molec-ular dynamics simulations of aqueous solutionsShaozhong Deng, UNC Charlotte, USAAbstract. I will discuss the extension of the image charge solvation model (ICSM) [J. Chem.Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interac-tions in computer simulations of bio- molecules formulated for spherical cavities, to prolatespheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-sphericalsolutes in molecular dynamics (MD) simulations. In addition to the utilization of a generaltruncated octahedron as the MD simulation box, central to the proposed extension is thecomputation of reaction fields in an one-image approximation for non-spherical objects. Theresulting generalized image charge solvation model (GICSM) is tested in simulations of liq-uid water, and the results are analyzed in comparison with those obtained from the ICSMsimulations as a reference.

L2 Projected C0 Elements for non H1 Very Weak Solution of curl and div Oper-atorsHuoyuan Duan, Nankai University, ChinaAbstract. Most partial differential equations either are governed by curl and div op-erators or can be recast into the ones governed by curl and div operators. Note that−∆u = curlcurlu − ∇divu. In general, a well-known fact for curl and div operators thesolution is non H1 very weak solution, although curl and div operators are closely related togradient operator. The non H1 solution may be caused by many reasons, such as interfacialcorners, cross-points, reentrant corners, reentrant edges, irregular boundary points, singularright-hand side and boundary data (e.g., Dirac, L1 data), and so on. An intractable diffi-culty has been well-known for more than half a century that the classical continuous C0 finiteelement method fails in seeking a correct convergent finite element solution for the non H1

space very weak solution. In particular, more badly, the classical continuous C0 finite ele-ment method of the relevant eigenproblem is seriously polluted by spurious solutions. Whatis pessimistically worse, when applied to the classical continuous C0 finite element method,the adaptive finite element method is useless for non H1 very weak solution of curl and divoperators, although the adaptive method has been pervasively well-known to be so strongand so powerful in dealing singularities in scientific and engineering computations. In thistalk we shall report our work [1] on how to generalize and adapt and apply our L2 projectedC0 finite element method (continuous/H1-conforming) [2] for a vectorial second-order ellipticeigenvalue problem in the form of the curlcurl-grad div operator, where the eigenfunctionsmay be very weak and may not be in H1 space. Such eigenproblems usually arise fromcomputational electromagnetism and computational fluid-structure interaction problem. In

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[1] we show that optimal error bounds O(h2r) are obtained for eigenvalues for the non H1

space eigenfunctions with the Hr regularity for some 0 < r < 1, and that our L2 projectedC0 finite element method is spectrally correct.

Acknowledgements This work was supported in part by the National Natural ScienceFoundation of CHINA under the grants 11071132 and 11171168 and the Research Fund forthe Doctoral Program of Higher Education of China under grant 20100031110002.

References

[1] H. Y. Duan, P. Lin and R.C.E Tan: Error estimates for a vectorial second-order ellipticeigenproblem by the local L2 projected C0 finite element method, research report.

[2] H. Y. Duan, F. Jia, P. Lin, and R.C.E. Tan: The local L2 projected C0 finite elementmethod for Maxwell problem, SIAM J. Numer. Anal., 47(2009), pp. 1274–1303.

On A Family of Models in X-ray Dark-field TomographyWeimin Han, University of Iowa, USAAbstract. X-ray mammography is currently the most prevalent imaging modality for screen-ing and diagnosis of breast cancers. However, its success is limited by the poor contrastbetween healthy and diseased tissues in the mammogram. A potentially prominent imagingmodality is based on the significant difference of x-ray scattering behaviors between tumorand normal tissues. Driven by major practical needs for better x-ray imaging, explorationinto contrast mechanisms other than attenuation has been active for decades, e.g., in termsof scattering, which is also known as dark-field tomography. In this talk, a theoretical studyis provided for the x-ray dark-field tomography (XDT) assuming the spectral x-ray detectiontechnology.

The radiative transfer equation (RTE) is usually employed to describe the light propagationwithin biological medium. It is challenging to solve RTE numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even moredifficult to solve RTE since accurate numerical solutions require a high resolution of thedirection variable, leading to prohibitively large amount of computations. For this reason,various approximations of RTE have been proposed in the literature. For XDT, a familyof differential approximations of the RTE is employed to describe the light propagation forhighly forward-peaked medium with small but sufficient amount of large-angle scattering.The forward and inverse parameter problems are studied theoretically and approximatednumerically.

Instant System AvailabilityKai Huang∗ and Jie Mi, Florida International University, USAAbstract. In this work, we study the instant availability A(t) of a repairable system throughintegral equation. We proved initial monotonicity of availability, and derived lower boundsto A(t) and average availability. The availabilities of two systems are compared. Numericalalgorithm for computing A(t) is proposed. Examples show high accuracy and efficiency ofthis algorithm.

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Optimization Under Uncertainty: Models and Computational TechniquesRalph Baker Kearfott, University of Louisiana at Lafayette, USAAbstract. In various situations, some quantities or model parameters are not known pre-cisely, but may be known to lie within certain bounds, while other quantities that affectoutcomes are under our control. We wish to compute the best possible outcome under theseconditions. Mathematically, we have an objective function φ, a set of controllable parametersx, and a set of unknown parameters u, and we wish to solve the problem

minxφ(x, u) (2)

where x ∈ x ∈ Rn, u ∈ u ∈ Rp, where we may choose the values x, but where the values uare unknown and out of our control. Here, we may assume x and u are hyperrectangles, andwe may also have additional equality or inequality constraints involving both the x’s and u’s.There are several interpretations of what solutions to such an imprecisely known problemare, and each interpretation leads to its own computational issues. In this talk, we give anoverview of common ways of defining the solution to (2), mention the appropriateness ofeach in real-world situations, and discuss computational difficulties and advantages of each.

A Scalable Non-Conformal Domain Decomposition Method For Solving Time-Harmonic Maxwell Equations In 3DZ. Peng∗ and J. F. Lee, Ohio State University, USAAbstract. We present a non-overlapping and non-conformal domain decomposition method(DDM) for solving the time-harmonic Maxwell equations in R3. There are three major tech-nical ingredients in the proposed non-conformal DDM: a. A true second order transmissioncondition (SOTC) to enforce fields continuities across domain interfaces; b. A corner edgepenalty term to account for corner edges between neighboring sub-domains; and, c. A globalplane wave deflation technique to further improve the convergence of DDM for electricallylarge problems. It is shown previously that a SOTC, which involves two second-order trans-verse derivatives, facilitates convergence in the conformal domain decomposition method forboth propagating and evanescent electromagnetic waves across domain interfaces. However,the discontinuous nature of the cement variables across the corner edges between neigh-boring sub-domains remains troublesome. To mitigate the technical difficulty encounteredand to enforce the needed divergence-free condition, we introduced a corner edge penaltyterm into the interior penalty formulation for the non-conformal DDM. The introduction ofthe corner edge penalty term successfully restored the superior performance of the SOTC.Finally, through an analysis of the DDM with the SOTC, we show that there still exists aweakly convergent region where the convergence in the DDM can still be unbearably slowfor electrically large problems. Furthermore, it is found that the weakly convergent region iscentered at the cutoff modes, or electromagnetic waves propagate in parallel to the domaininterfaces. Subsequently, a global plane wave deflation technique is utilized to derive aneffective global-coarse-grid preconditioner to promote fast convergence of the cutoff or nearcutoff modes in the vicinity of domain interfaces.

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Generalized Foldy-Lax Formulation and its Application to the Inverse ScatteringPeijun Li, Purdue University, USAAbstract. We consider the scattering of a time-harmonic plane wave incident on a two-scale hetero-geneous medium, which consists of scatterers that are much smaller than thewavelength and extended scatterers that are comparable to the wavelength. A generalizedFoldy-Lax formulation is proposed to capture multiple scattering among point scatterersand extended scatterers. Our formulation is given as a coupled system, which combines theoriginal Foldy–Lax formulation for the point scatterers and the regular boundary integralequation for the extended obstacle scatterers. An efficient physically motivated Gauss-Seideliterative method is proposed to solve the coupled system, where only a linear system ofalgebraic equations for point scatterers or a boundary integral equation for a single extendedobstacle scatterer is required to solve at each step of iteration. In contrast to the standardinverse obstacle scattering problem, the proposed inverse scattering problem is not only todetermine the shape of the extended obstacle scatterer but also to locate the point scatterers.Based on the generalized Foldy–Lax formulation and the singular value decomposition of theresponse matrix constructed from the far-field pattern, an imaging function is developed tovisualize the location of the point scatterers and the shape of the extended obstacle scatterer.

A Multiple-Endpoints Chebysheve Collocation Method For High Order Prob-lemsShan Wang and Zhiping Li∗, Peking University, ChinaAbstract. Pseudospectral methods as meshless methods are successfully used for widelydiverse applications. The Chebyshev type collocation methods are among the most popu-lar spectral methods because of computational convenience. A typical choice of collocationpoints for solving boundary value problems of second order differential equations with aChebyshev method is to use the Chebyshev-Gauss-Lobatto collocation points, which in-clude certain inner collocation points and two end points. Chebyshev-Gauss collocationmethod, which has no endpoints, is also a popular choice. However, difficulties, such as over-determined system or ill-conditioned differential matrix, often arise when pseudospectralmethod is applied to higher order differential equations, especially in high dimensions.

In this paper, following the idea of establishing the Gauss-Lobatto collocation points, wedesign a new type of collocation points, named multiple-endpoints collocation points forhigh order differential equations. Simply speaking, for problems with K boundary conditionson each boundary points, a sequence of orthogonal polynomials is established in such away that each polynomial in the sequence has, other than the separated inner zeros, theboundary points as its K-zeros, and the collocation points are then determined in a standardway. Numerical examples on 1D 6th-order and 2D 4th-order linear differential equations,with both hard clamped boundary condition and reciprocally periodic connection boundaryconditions, are presented to show the improved condition numbers of the differential matricesand accuracy of the new method as compared with the method using Gauss and Gauss-Lobatto collocation points. In particular, we present an example on an elastic thin filmbuckling problem governed by a nonlinear von Karman equation, for which the standardChebyshev methods failed to produce physically consistent solutions

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Hybrid weighted essentially non-oscillatory schemes with different indicatorsJianxian Qiu∗, Xiamen University, ChinaGang Li, Qingdao University, ChinaAbstract. A key idea in finite difference weighted essentially non-oscillatory (WENO)schemes is a combination of lower order fluxes to obtain a higher order approximation. Thechoice of the weight to each candidate stencil, which is a nonlinear function of the grid values,is crucial to the success of WENO. For the system case, WENO schemes are based on localcharacteristic decompositions and flux splitting to avoid spurious oscillatory. But the cost ofcomputation of nonlinear weights and local characteristic decompositions is very expensive.

In the presentation, we investigate hybrid schemes of WENO schemes with high order up-wind linear schemes using different discontinuity indicators and explore the possibility inavoiding the local characteristic decompositions and the nonlinear weights for part of theprocedure, hence reducing the cost but still maintaining non-oscillatory properties for prob-lems with strong shocks. The idea is to identify discontinuity by an discontinuity indicator,then reconstruct numerical flux by WENO approximation at discontinuity and up-wind lin-ear approximation at smoothness. These indicators are mainly based on the troubled-cellindicators for discontinuous Galerkin (DG) method which are listed in the paper by Qiuand Shu SIAM J. Sci. Comput. 27 (2005) 995-1013. The emphasis of the paper is oncomparison of the performance of hybrid scheme using different indicators, with an objectiveof obtaining efficient and reliable indicators to obtain better performance of hybrid schemeto save computational cost. Detail numerical studies in one- and two-dimensional cases areperformed, addressing the issues of efficiency (less CPU time and more accurate numericalsolution), non-oscillatory property.

A High-Order Transport Scheme for Unstructured Atmosphere and Ocean Cli-mate ModelsTodd Ringler∗ and Robert Lowrie, Los Alamos National Laboratory, USAAbstract. Traditional climate models of the atmosphere and ocean have utilized latitude-longitude meshes or, more recently, quasi-uniform, structured meshes. A joint project be-tween NCAR and LANL has recently resulted in global atmosphere and ocean climate modelsthat are able to utilize variable resolution, unstructured, conforming meshes. These modelsallow for the placement of enhanced resolution in specific areas of interest, such as over NorthAmerica for the atmosphere and in the North Atlantic for the ocean. Tessellating the surfaceof the sphere with an arbitrary set of conforming, convex polygons presents many numericalchallenges, not the least of which is the development of high-order transport schemes.

To start, we will briefly summarize this new modeling system, called Model for PredictionAcross Scales, and present global atmosphere and ocean simulations that have been con-ducted to date. We will then turn quickly to the topic of transport. First, we will motivatethe importance of accurate and conservative transport in climate system models. We willthen present an extension of the Characteristic Discontinuous Galerkin transport methodsuitable for arbitrary convex polygon meshes. The method retains an arbitrary number ofbasis functions per element (i.e. per convex polygon). Fluxes across element faces are com-puted by tracking fluid velocities backward in time to determine the volume swept acrosseach face during the time step. The flux of tracer constituents is computed by integrating

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the swept region with high-order quadrature. Boundedness of tracer values is insured duringthe computation of the fluxes across each face.

Examples of the impact of this high-order transport scheme will be presented for an idealizedconfiguration of the Antarctic Circumpolar Current.

A mixed finite element method with exactly divergence-free velocities for incom-pressible magnetohydrodynamicsDominik Schoetzau, University of British Columbia, CanadaAbstract. We propose and analyze a mixed finite element method for the numerical dis-cretization of a stationary incompressible magnetohydrodynamics problem, in two and threedimensions. The velocity field is discretized using divergence-conforming Brezzi-Douglas-Marini (BDM) elements and the magnetic field is approximated by curl-conforming Nedelecelements. The conformity of the velocity field is enforced by a discontinuous Galerkin ap-proach. A central feature of the method is that it produces exactly divergence-free velocityapproximations, and captures the strongest magnetic singularities. We prove that the en-ergy norm error is convergent in the mesh size in general Lipschitz polyhedra under minimalregularity assumptions, and derive nearly optimal a-priori error estimates. We present a com-prehensive set of numerical experiments, which indicate optimal convergence of the proposedmethod for two-dimensional as well as three-dimensional problems.

Networked Computing Laboratory (NCLab)Pavel Solin∗ and Lukas Korous, University of Nevada – Reno, USAAcademy of Sciences of the Czech Republic, Czech RepublicCharles University, Prague, Czech RepublicPetr Mach, Czech Technical University, Czech RepublicAbstract. The Networked Computing Laboratory (NCLab) is a pioneering web frameworkfor collaborative scientific computing, as well as a new vehicle for the transfer of knowledgebetween academia and the public. NCLab has different objectives from commercial softwaressuch as Matlab, Maple, MathCAD, Comsol, Ansys and others. As part of its objectives itprovides a mechanism for researchers to develop interactive graphical applications basedon their own computational methods, and make them instantly available to vast amountsof users. NCLab is powered by cloud computers and it works entirely in the web browserwindow. It uses advanced networking technologies to provide a highly creative atmosphere ofsharing and real-time collaboration. Users can (obviously) access their accounts on anytime-anywhere basis, including from mobile devices, meet in NCLab and work there together. Theonly requirement is a working Internet connection. The framework is still in development,but it already has around 1000 regular users. In this presentation we will describe basicfeatures of NCLab and focus on modules for geometrical modeling, mesh generation, andpostprocessing that can be attached to any finite element code that complies with theirsimple APIs. We will also mention directions for NCLab’s future development.

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A balanced finite element method for singularly perturbed reaction-diffusionproblemsM. Stynes∗, National University of Ireland, IrelandRunchang Lin, Texas A&M International University, USAAbstract. An introduction is given to the properties of the singularly perturbed linearreaction-diffusion problem −ε2∆u+bu = f posed in Ω ⊂ Rd, with the homogeneous Dirichletcondition u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitz-continuous boundary ∂Ω, and the parameter ε satisfies 0 < ε 1. These properties revealthat for this type of problem, the standard associated energy norm v 7→ [ε2|v|21 + ‖v‖20]1/2 istoo weak a norm to measure adequately the errors in solutions computed by finite elementmethods because the exponent of ε in this norm is too large so that the norm is essentiallyequivalent to the L2 norm.

This failure is because the norm is unbalanced: its different components have different ordersof magnitude. A balanced and stronger norm is introduced, then for d ≥ 2 a mixed finiteelement method is constructed whose solution is quasi-optimal in this new norm. By aduality argument it is shown that this solution attains a higher order of convergence in theL2 norm. Error bounds derived from these analyses are presented for the cases d = 2, 3. Fora problem posed on the unit square in R2, an error bound that is uniform in ε is derivedwhen the new method is implemented on a Shishkin mesh.

Pricing Options under Jump-diffusion ModelsJari Toivanen, Stanford University, Stanford, USAAbstract. The value of assets like stocks usually have more complicated behavior than ageometric Brownian motion assumed by the Black-Scholes model. For example, sometimesthe value has jump-like rapid change. European options can be exercised only when theyexpire while American options can be exercised any time during their life. Often it is possibleto derive a formula for the price of a European option while usually American options needto be priced using numerical methods.

When jumps are included in the model, a parabolic partial integro-differential equation canbe derived for the price of a European option. For the price of an American option, a linearcomplementarity problem with the same operator can be derived. We design and analyzeefficient numerical methods for pricing options using finite difference discretizations. Partic-ularly, we consider the treatment of the integral terms due to the jumps. We demonstratethat sufficiently accurate prices for most practical purposes can be computed in a smallfraction of a second on a PC.

Multiphase complex fluid models and their applications to complex biologicalsystemsQi Wang, University of South Carolina, USAAbstract. I will present a multiphase complex fluid models for a number of complex fluidphases along with their interfacial boundaries. Interfacial elasticity in some interfaces can beenforced and so can the long range molecular interaction within some phases. The model isthen applied to study cell cluster aggregate fusion and cytoskeletal dynamics and buffer-cellinteraction leading to cell migration.

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Topics on electromagnetic scattering from cavitiesAihua W. Wood, Air Force Institute of Technology, USAAbstract. The analysis of the electromagnetic scattering phenomenon induced by cavitiesembedded in an infinite ground plane is of high interest to the engineering community.Applications include the design of cavity-backed conformal antennas for civil and militaryuse, the characterization of radar cross section (RCS) of vehicles with grooves, and theadvancement of automatic target recognition. Due to the wide range of applications andthe challenge of solutions, the problem has been the focus of much mathematical research inrecent years.

This talk will provide a survey of mathematical research in this area. In addition I willdescribe the underlining mathematical formulation for this framework. Specifically, oneseeks to determine the fields scattered by a cavity upon a given incident wave. The generalway of approach involves decomposing the entire solution domain to two subdomains via anartificial boundary enclosing the cavity: the infinite upper half plane over the infinite groundplane exterior to the boundary, and the cavity plus the interior region. The problem is solvedexactly in the infinite sub-domain, while the other is solved numerically. The two regionsare then coupled over the artificial boundary via the introduction of a boundary operatorexploiting the field continuity over material interfaces. We will touch on both the PerfectElectric Conducting and Impedance ground planes. Results of numerical implementationswill be presented.

Most Likely Paths of Shortfalls in Long-Term Hedging with Short-Term FuturesZhijian Wu, University of Alabama, USAAbstract. With or without the constraint of the terminal risk, an optimal strategy tominimize the running risk in hedging a long-term commitment with short-term futures canbe solved explicitly if the underline stock follows the simple stochastic differential equation

dSt = µdt+ σdBt

where Bt is the standard Brownian motion. In this talk, the most likely paths of shortfallsassociated with the hedging are discussed. We typically focus on the shortfalls correspond-ing to the optimal strategies established to minimize the running risk with or without theterminal constraint. These paths give information about how risky events occur and not justtheir probability of occurrence.

Mortar multiscale methods for Stokes-Darcy flows in irregular domainsIvan Yotov, University of Pittsburgh, USAAbstract. We study multiscale numerical approximations for the coupled Stokes-Darcy flowsystem. The equations in the coarse Darcy elements (or subdomains) are discretized on a finegrid scale by a multipoint flux mixed finite element method that reduces to cell-centered finitedifferences on irregular grids. The Stokes subdomains can be discretized by any stable Stokesfinite elements. The subdomain grids do not have to match across the interfaces. Continuityconditions between coarse elements are imposed via a mortar finite element space on a coarsegrid scale. With an appropriate choice of polynomial degree of the mortar space, we deriveoptimal order convergence on the fine scale for the multiscale pressure and velocity. The

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algebraic system is reduced via a non-overlapping domain decomposition to a coarse scalemortar interface problem that is solved using a multiscale flux basis. Numerical experimentsare presented to confirm the theory and illustrate the efficiency and flexibility of the method.

The talk is based on joint work with Benjamin Ganis, Vivette Girault, Pu Song, and DanailVassilev

Fractional Differential Equations: Modeling and Numerical SolutionsChuanju Xu, Xiamen University, ChinaAbstract. The fractional partial differential equations are extensions of the traditionalmodels, based on fractional calculus. They are now winning more and more scientific appli-cations cross a variety of fields including control theory, biology, electrochemical processes,viscoelastic materials, polymer, finance, and etc. In this talk, we will address the fractionalmodels using random walk process, and numerical methods to solve these models. Par-ticularly, we focus on the existence and uniqueness of the weak solution, and its spectralapproximations. Two definitions, i.e. Riemann–Liouville definition and Caputo one, of thefractional derivative are considered in parallel. We construct and analyze efficient spectralapproximations based on the weak formulations associated to these two definitions. Someinteresting applications to viscoelastic materials and molecular biology will also be discussed.

Direct Discontinuous Galerkin method and Its Variations for Diffusion ProblemsJue Yan∗ and Chad Vidden, Iowa State University, USAAbstract. In this talk, we will discuss the recent four discontinuous Galerkin methodsfor diffusion problems; 1) the Direct discontinuous Galerkin(DDG) method; 2) the DDGmethod with interface corrections; 3) the DDG method with symmetric structure; and 4) anew DG method with none symmetric structure. Major contribution of the DDG method isthe introduction of the jumps of second or higher order solution derivatives in the numericalflux formula. The symmetric version of the DDG method helps us obtain the optimal L2(L2)error analysis for the DG solution. For the non-symmetric version, we show that the schemeperforms better than the Baumann-Oden scheme or the NIPG method in the sense thatoptimal order of accurcy is recovered with even-th order polynomial approximations. Aseries of numerical examples are presented to show the high order accuracy and the capacityof the methods. At the end, we will discuss the recent studies of the maximum-principle-satisfying or the positivity preserving properties of the DDG related methods.

High order interface methods for electromagnetic systems in dispersive inhomo-geneous mediaShan Zhao, University of Alabama, USAAbstract. Across a material interface separating two dielectric media, the electromagneticfields are known to be non-smooth or even discontinuous. Moreover, if one dielectric mediumis dispersive, such a discontinuity will be frequency-dependent or time-varying. Based onthe auxiliary differential equation (ADE) approach, we will examine such a dispersive in-terface problem with the Debye dispersion model. A novel mathematical formulation willbe established to describe the regularity changes in electromagnetic fields at the dispersiveinterface. The resulting time-dependent jump conditions will then be numerically enforcedvia the matched interface and boundary (MIB) scheme. Some preliminary numerical results

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will be reported.

Sponsors: NSF (DMS-0616704, DMS-0731503, and DMS-1016579) and University of Al-abama RGC Award.

Second Order Virtual Node Algorithms for Stokes Flow Problems with Interfa-cial Forces and Irregular DomainsDiego C. Assencio∗ and Joseph M. Teran, University of California, Los Angeles, USAAbstract. We present numerical methods for the solution of the Stokes equations in ir-regular domains and with interfacial discontinuities. We handle both the continuous anddiscontinuous viscosity cases. In both of them, our method provides discretely divergencefree velocities which are second order accurate. The discretization is performed on a uniformMAC-grid employing virtual nodes at interfaces and boundaries. Interfaces and boundariesare represented with a hybrid Lagrangian/level set method. The discretizations of boththe irregular domain and the interface problem with continuous viscosity yield symmetricpositive definite linear systems, while the discretization of the interface problem with dis-continuous viscosity yields a symmetric indefinite linear system. Numerical results indicatesecond order accuracy in L∞.

A Fast Volume Integral Solver for 3-D Objects Embedded in Layered MediaMin Hyung Cho∗ and Wei Cai, The University of North Carolina at Charlotte, USAAbstract. The Helmholtz equation is solved for 3-D objects embedded in layered media.The layered media Green’s function is found in two steps. First, the spectral Green’s functionis obtained with a transfer matrix technique. Then, the Sommerfeld integral is numericallytaken to obtain the real space Green’s function. The surface pole effects and slow decay ofthe spectral Green’s function in the Sommerfeld integral are addressed with the adaptivegeneralized Gaussian quadrature rules and the window function, respectively. The efficiencyof the two numerical techniques will be presented. Next, by rewriting the Helmholtz integraloperator in layered media as a summation of 2-D cylindrical wave operators, a parallel fastsolver is developed. Here, the 2-D cylindrical wave operators are calculated independentlywith a wideband Fast Multipole Method or a local expansion tree-code in a fast manner.The fast solver is implemented with OpenMP for a shared memory machine and comparedwith the direct solver. With the layered media Green’s function, a volume integral equa-tion is derived and implemented for cube objects embedded in a layered structure by usingappropriate interface and decay conditions and Green’s 2nd identity.

Unconditionally Positive Residual Distribution Schemes for Hyperbolic Conser-vation LawsM.E.Hubbard∗ and D.Sarmany,University of Leeds, UKM.Ricchiuto, INRIA Bordeaux, FranceAbstract. The residual distribution framework was developed as an alternative to the finitevolume approach for approximating hyperbolic systems of conservation laws which would al-low a natural representation of genuinely multidimensional flow features. The resultingalgorithms are closely related to conforming finite elements, but their structure makes it farsimpler to construct nonlinear approximation schemes, and therefore to avoid unphysical

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oscillations in the numerical solution. They have been successfully applied to a wide rangeof nonlinear systems of equations, producing accurate simulations of both steady and, morerecently, time-dependent flows. When designed carefully, these schemes have the followingvery useful properties.

• They can be simultaneously second order accurate (in space and time) and free ofunphysical oscillations, even in the presence of turning points in the solution.

• The CRD (Conservative Residual Distribution) formulation [1] provides a very naturalway to approximate balance terms in a manner which automatically retains equilbriainherent in the underlying system.

• It is possible to construct residual distribution schemes which allow for a discontinuousrepresentation of the dependent variables [2]. In particular, the inclusion of discontinu-ities in time allows for the development of schemes which are unconditionally positive[3], i.e. they are free of unphysical oscillations whatever size of time-step is taken. Dis-continuities in space provide a very natural manner in which to approximate shocksand to apply weak boundary conditions.

This presentation will focus on discontinuous residual distribution and the developmentof unconditionally positive schemes for approximating multidimensional, time-dependentproblems. The combination of second order accuracy and unconditional positivity will bedemonstrated for the scalar advection equation, followed by a discussion of recent progresson their extension to nonlinear systems of equations. Numerical results will be presentedfor the Euler equations and/or the shallow water equations. For the latter, the issue ofconstructing a well-balanced scheme for the case where source terms are used to representvariable bed topography will be addressed.

References

[1] A.Csik, M.Ricchiuto, H.Deconinck, J Comput Phys, 179(2):286–312, 2002.

[2] M.E.Hubbard, J Comput Phys, 227(24):10125–10147, 2008.

[3] M.E.Hubbard, M.Ricchiuto, Comput Fluids, 46(1):263–269, 2011.

Lie Group Analysis – a microscope of physical and engineering sciencesRanis N. Ibragimov, University of Texas at Brownsville, USAAbstract. The formulation of fundamental natural laws and of technological problems inthe form of rigorous mathematical models is given frequently, even prevalently, in terms ofnonlinear differential equations. An appropriate method for tackling nonlinear differentialequations is provided by Lie group analysis.

The aim of this presentation is, from the one hand, to impart to the wide audience ofresearchers and students with the comprehensive and easy to follow introduction to Lie’sgroup analysis and, from the other hand, is to present several recent results in this areawhose discussion discloses the advantages to be gained from the use of the group theoreticapproach.

The emphasis will be on an application of Lie group analysis to fully nonlinear Navier-Stokesequations modelling the large-scale atmospheric motion around the rotating Earth. The

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inquiry is motivated by dynamically significant Coriolis forces in meteorology and oceano-graphic applications such as a climate variability models and the general atmospheric cir-culation. This project is aimed to contribute to a better observational knowledge of thespatial and temporal distribution of mixing in the atmosphere and the ocean than achievedto date. Application of Lie group analysis allows to perform the complete integration of themodel by quadratures and thus to write the exact solutions of the Navier-Stokes equations interms of elementary functions and visualize them. One of the impacts of the project is, fromone hand, to learn more about the influences of large scale fluid flows on the environment,highlighted by fundamental issues such as global warming and long term climate change and,from the other hands, is to illustrate the advantages of mathematical modeling of e.g., oilspill associated with the Deepwater Horizon incident.

Partially, the presentation is based on the research projects that also involve a graduatestudent:

References

Ibragimov, R.N., Dameron, M., 2011: Spinning phenomena and energetics of sphericallypulsating patterns in stratified fluids. Physica Scripta, 84, 015402.

Ibragimov, R.N., Pelinovsky, D.E., 2010: Effects of rotation on stability of viscous stationaryflows on a spherical surface. Physics of Fluids, 22, 126-602

On Generalized Bell Numbers for Complex ArgumentRoberto B. Corcino∗, Maribeth B. Montero, Mindanao State University, PhilippinesCristina B. Corcino, De La Salle University, PhilippinesAbstract. In this talk, more properties of the generalized Bell numbers and polynomialsfor integral arguments are obtained. Moreover, the generalized Stirling numbers of thesecond kind for complex arguments are defined using Hankel contour and some propertiesnecessary in defining and investigating the generalized Bell numbers for complex argumentare established.

Asymptotic Formulas for the Generalized Stirling Numbers of the Second Kindwith Integer ParametersCristina B. Corcino∗, De La Salle University, PhilippinesNestor G. Acala and Jay M. Ontolan, Mindanao State University, PhilippinesAbstract. Asymptotic formulas of the classical Stirling numbers have been done by manyauthors like Temme [Studies in Applied Math., Vol.89 (1993)] and Moser and Wyman [DukeMath, Vol.25, 29-43, (1958)] due to the importance of the formulas in computing values ofthe numbers under consideration when parameters become large. The generalized Stirlingnumbers on the other hand, are important due to their statistical applications [MatimyasMatematika Vol.25(1) 19–29 (2002) ]. The generalization of Stirling numbers consideredhere are generalizations along the lines of Hsu and Shuie’s unified generalization [Advancesin Appl. Math. Vol.20 366-384 (1998)] and R. B. Corcino’s generalization [Mindanao Forum,Vol. XIV, no.2, 91-99 (1999)]. In this paper two asymptotic formulas for the generalizedStirling numbers of the second kind with integer parameters are obtained and the range ofvalidity of each formula is established.

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A Potential-based Finite Element Scheme with CGM for Eddy Current Prob-lemsTong Kang, Communication University of China, ChinaAbstract. An improved potential-based nodal finite element scheme combining with Com-posite Grid Method (CGM) is used to solve 3D eddy current problems. In our scheme,introducing a magnetic vector potential and an electric scalar potential is justified as abetter way of dealing with possible discontinuities of coefficients. By appending a penaltyfunction to the potential-based formulation, the existence and uniqueness of approximatingsolutions are ensured. Some computer simulations of the magnetic flux density and eddy cur-rent density for two eddy current benchmark models (TEAM Workshop Problem 7 and IEEJmodel) are demonstrated to verify the feasibility and efficiency of the proposed algorithms.

Discontinuous-in-Space Explicit Runge-Kutta Residual Distribution Schemes forHyperbolic Conservation LawsM. E. Hubbard, University of Leeds, UKM. Ricchiuto, Inria Bordeaux, FranceA. Warzynski∗, University of Leeds, UKA¯

bstract. The Residual Distribution (RD) framework for multidimensional hyperbolic con-servation laws can be illustrated by considering the scalar conservation law given by

∇ · f = 0 (3)

on a domain Ω, with appropriate boundary conditions. The residual associated with a meshcell E is defined to be

φE =

∫E

∇ · fdΩ, (4)

and this is then distributed among the vertices of E. Assuming a piecewise linear represen-tation of the approximate solution leads to the discrete system∑

E∈Di

βEi φE = 0 ∀i (5)

where the βEi signify the proportion of the residual in cell E assigned to node i and Didenotes the subset of triangles containing i. System (5) is solved to find the approximatesolution values at the mesh nodes, typically using a pseudo-time-stepping approach.

In the case of steady state problems, where f in (3) only has a spatial dependence, the RDconcept has already proven to be very successful. The RD approach, in a relatively naturalmanner, enables construction of positive, linearity preserving and conservative schemes ableto carry out a truly multidimensional upwinding for both scalar and systems of hyperbolicconservation laws.

Extension to time-dependent problems is currently a subject of intensive ongoing research.It is possible to develop schemes of the form (5), as derived when the divergence in (3)includes the time variation, but solving the system (5) at each time-step is typically verycpu-intensive. To overcome this Abgrall and Ricchiuto in [1] proposed a framework forexplicit, second order residual distribution schemes for transient problems. In this talk I will

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present their approach in conjunction with discontinuous-in-space data representation. Thisextends previous work on discontinuous residual distribution schemes for steady problemsinitiated in [2, 3]. It also extends work of Abgrall and Shu [4] in the sense that it reformulatesthe Runge-Kutta Discontinuous Galerkin (DG) method in the framework of Runge-KuttaRD schemes. This is, briefly speaking, done by considering flux differences (edge residualsin the RD framework) instead of the fluxes themselves.

Different types of cell– and edge–based distribution strategies can be applied and we willdiscuss the most interesting choices characteristic for either RD [2, 3] or DG type approaches[4, 5]. Relevant numerical results for two-dimensional hyperbolic conservation laws will bepresented and available analytical results discussed. We will also briefly comment on otherrecent developments in the discontinuous RD framework, i.e. discontinuous-in-time schemes[6], and compare our approach with possible alternatives like DG schemes [5].

References

[1] R. Abgrall, M. Ricchiuto Explicit Runge–Kutta residual distribution schemes fortime dependent problems: second order case. J. Comput. Phys. 229(16), 5653–5691, 2010.

[2] M. E. Hubbard A framework for discontinuous fluctuation distribution. Internat. J.Numer. Methods Fluids 56(8), 1305–1311, 2008.

[3] M. E. Hubbard Discontinuous fluctuation distribution. J. Comput. Phys. 227(24),10125–10147, 2008.

[4] R. Abgrall, C.-W. Shu Development of Residual Distribution Schemes for the Dis-continuous Galerkin Method: The Scalar Case with Linear Elements. Commun. in Comp.Phys. 5(2), 376-390, 2009.

[5] B. Cockburn, S.-C. Hou, C.-W. Shu The Runge–Kutta local projection discontin-uous Galerkin finite-element method for conservation laws. 4 The Multidimensional Case.Mathematics of Computation 54(190), 545-581, 1990.

[6] M. E. Hubbard, M. Ricchiuto Discontinuous upwind residual distribution: A routeto unconditional positivity and high order accuracy. Comput. Fluids, Volume 46, Issue 1,2011.

Effects of Rotation on Energy Stabilization of Internal Gravity Waves Confinedin a Cylindrical BasinMichael Dameron, University of Texas at Brownsville, USA.Abstract. A linear, uniformly stratified ocean model is used to investigate propagation oflarge scale internal gravity waves confined in a cylindrical basin. Because of the inclusion ofsignificant Coriolis acceleration and stable stratification, the presence of vertical boundariesallows one to associate the wave motion under question with baroclinic Kelvin waves. Aparticular question of interest was to investigate the effects of rotation on energetics of Kelvinwaves. It was found that the Earth’s rotation stabilizes the energy density fluctuation as wellas pressure perturbation of Kelvin waves. We also observe the existence of the rotationallypersistent oceanic region where the energy density changes relatively rapidly with the depth.The time series of the equipotential curves for the energy density were visualized as spinningpatterns that look rotating in an anticlockwise sense when looking from above the North

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Pole. Such spinning patterns were compared with the flow around a low-pressure area thatis usually being linked with a modeling of hurricanes. Discussion of nonlinear modeling isalso presented.

Dispersion and Dissipation Analysis of Two Fully Discrete Discontinuous GalerkinMethodsHe Yang∗, Rensselaer Polytechnic Institute, USAFengyan Li, Rensselaer Polytechnic Institute, USAJianqian Qiu, Nanjing University, ChinaAbstract. The dispersion and dissipation properties of numerical methods are very impor-tant in wave simulations. In this talk, such properties will be analyzed for Runge-Kuttaand Lax-Wendroff discontinuous Galerkin methods when solving the linear advection equa-tion. With the standard method of calculating discrete dispersion relation, it will be shownthat the dispersion and dissipation errors of these two numerical schemes are of the sameorder of accuracy, but with different leading coefficients. For Lax-Wendroff discontinuousGalerkin methods, an alternative approach is introduced and shown to have some advantagein computing discrete dispersion relation. By making use of this approach, how to constructbetter numerical flux is also discussed. Small time step limit is considered for both Runge-Kutta and Lax-Wendroff discontinuous Galerkin methods. The role of temporal and spatialdiscretization in discrete dispersion relation is eventually clarified.

Higher and Approximate Symmetries of Differential Equations Using MAPLEGrace Jefferson, Deakin University, AustraliaAbstract. One method of finding special exact solutions of differential equations is affordedby the work of nineteenth century mathematician Sophus Lie (1842-1899) and the use of con-tinuous transformation groups. In recent times, there has been an ever increasing interest inhigher symmetries, that is, symmetries which have a dependence on derivatives of dependentvariables. The automated determination of these higher symmetries, through the generationand solution of a determining system of equations using computer algebra systems, leadsus to describe the MAPLE computer algebra package DESOLVII (Vu, Jefferson and Carmi-nati 2011), which is a major upgrade of DESOLV (Vu and Carminati 2003). DESOLVIInow includes new routines allowing the determination of higher symmetries (contact andLie-Bcklund) for systems of both ordinary and partial differential equations. In the briefcomparative study carried out, DESOLVII was found to be the only package (of three) tofind all full solution sets for both point and higher symmetries in fast times.

Moreover, extensions to the basic Lie group theory have also been proposed. Of particularinterest here is the theory of approximate symmetries which deals fundamentally with a com-bination of perturbation theory and classical Lie group analysis. A recent paper comparedthree methods of determining approximate symmetries of differential equations. Two of thesemethods are well known and involve either a perturbation of the classical Lie symmetry gen-erator of the differential system (Baikov, Gazizov and Ibragimov 1988) or a perturbation ofthe dependent variable/s and subsequent determination of the classical Lie symmetries ofthe resulting coupled system (Fushchich and Shtelen 1989), both up to a specified order inthe perturbation parameter. The third method, proposed by Pakdemirli, Yrsoy and Dolapi(2004), simplifies the calculations required by Fushchich and Shtelen’s method through the

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assignment of arbitrary functions to the non-linear components prior to computing symme-tries.

All three methods have been implemented in the new MAPLE package ASP (AutomatedSymmetry Package), an add-on to DESOLVII. The algorithms for each of the three methodshave been implemented and tested, allowing the efficient computation of approximate sym-metries for differential systems. In addition, the results obtained from this study highlightedthe ability of ASP to find more generalised functions which extend approximate algebrasusing a classification routine and an altered PDE solution routine. To our knowledge, itis now the only package currently available in MAPLE which is able to find approximatesymmetries by all three methods.

Immerse Finite Element Methods for Solving Parabolic Type Moving InterfaceProblemsXu Zhang, Virginia Tech, USAAbstract. In science and engineering, many simulations are carried out over domains con-sisting of multiple materials separated by curves/surfaces. This often leads to the so-calledinterface problems of partial differential equations whose coefficients are piecewise constants.Using conventional finite element methods, convergence cannot be guaranteed unless meshesare constructed according to the material interfaces. Due to this reason the mesh in a con-ventional finite element method for solving an interface problem has to be unstructured tohandle non- trivial interface configurations. This restriction usually causes many negativeimpacts on the simulations if material interfaces evolve. In this presentation, we will discusshow the recently developed immersed finite elements (IFE) can alleviate this limitation ofconventional finite element methods. We will present both semi-discrete and full discrete IFEmethods for solving parabolic equations whose diffusion coefficient is discontinuous across atime dependent interface. We will also use IFEs in method of lines (MoL) to obtain anotherclass of flexible, efficient, and reliable methods for solving parabolic moving interface prob-lems. These methods can use a fixed structured mesh even the interface moves. Numericalexamples will be provided to demonstrate features of these IFE methods.

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List of Participants

Name InstitutionWalter Allegretto University of Alberta, CanadaTodd Arbogast University of Texas at Austin, USAXylar Asay-Davis Los Alamos National Laboratory, USADiego C. Assencio University of California, Los Angeles, USAA.V. Balakkrishnan University of California, Los Angeles, USARandolph E. Bank University of California at San Diego, USAJeff Banks Lawrence Livermore National Laboratory, USAGang Bao Zhejiang University, China and

Michigan State University, USATim Barth NASA Ames Research Center Moffett Field, USAJohn Berger Colorado School of Mines, USAB. Bialecki Colorado School of Mines, USAJerome Blair Keystone International and NSTec, USAPavel Bochev Sandia National Laboratories, USAVrushali Bokil Oregon State University, USAYassine Boubendir New Jersey Institute of Technology, USAAbigail Bowers Clemson University, USAJames Brannick The Pennsylvania State University, USASean Breckling University of Nevada, Las Vegas, USAJed Brown Argonne National Laboratory, USAJiacheng Cai University of Nevada, Las Vegas, USAXiao-Chuan Cai University of Colorado at Boulder, USADaniela Calvetti Case Western Reserve University, USALiqun Cao Chinese Academy of Sciences, ChinaFatih Celiker Wayne State University, USARaymond Chan The Chinese University of Hong Kong, Hong KongQingshan Chen Los Alamos National Laboratory, USAZhangxin Chen University of Calgary, CanadaC.S. Chen University of Southern Mississippi, USALong Chen University of California at Irvine, USAYanping Chen South China Normal University, ChinaYitung Chen University of Nevada, Las Vegas, USAMin Hyung Cho The University of North Carolina at Charlotte, USASum Chow Brigham Young University, USACristina B. Corcino De La Salle University, PhilippinesRoberto B. Corcino Mindanao State University, PhilippinesMichael Dameron University of Texas at Brownsville, USALeszek Demkowicz ICES, UT Austin, USA

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Name InstitutionShaozhong Deng UNC Charlotte, USAHuoyuan Duan Nankai University, ChinaDerrick Dubose University of Nevada, Las Vegas, USAKatherine J. Evans Oak Ridge National Laboratory, USAGraeme Fairweather American Mathematical Society, USAHualong Feng Illinois Institute of Technology, USAR. I. Fernandes The Petroleum Institute, UAECarl Gladish New York University, USAMax Gunzburger Florida State University, USAWeimin Han University of Iowa, USAYing He Purdue University, USAJan S Hesthaven Brown University, USARobert L. Higdon Oregon State University, USAPaul Houston University of Nottingham, UKJason Howell Clarkson University, USAXiaozhe Hu The Pennsylvania State University, USAJun Hu Peking University, ChinaKai Huang Florida International University, USAMatthew Hubbard University of Leeds, UKRanis N. Ibragimov University of Texas at Brownsville, USATraian Iliescu Virginia Tech, USATobin Isaac The University of Texas at Austin, USAhline Grace Jefferson Deakin University, AustraliaE.W. Jenkins Clemson University, USAXia Ji Chinese Academy of Sciences, ChinaAugust Johansson University of California, Berkeley, USAGuillaume Jouvet Free University of Berlin, GermanyLili Ju University of South Carolina, USATong Kang Communication University of China, ChinaAndreas Karageorghis University of Cyprus, CyprusRalph Baker Kearfott University of Louisiana at Lafayette, USAPushkin Kachroo University of Nevada, Las Vegas, USATaufiquar Rahman Khan Clemson University, USALukas Korous Charles University, PragueAlexander Labovsky Michigan Technological University, USAMats Larson University of Umea, SwedenWilliam Layton University of Pittsburgh, USAHyesuk Lee Clemson University, USAWei Leng Chinese Academy of Sciences, ChinaPeijun Li Purdue University, USAHengguang Li Wayne State University, USAZhiping Li Peking University, ChinaJichun Li University of Nevada, Las Vegas, USA

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Name InstitutionWenyuan Liao University of Calgary, CanadaYanping Lin The Hong Kong Polytechnic University, Hong KongXingfeng Liu University of South Carolina, USAWing-Cheong (Jon) Lo The Ohio State University, USAAaron Luttman National Security Technologies LLC, USAEric Machorro National Security Technologies, LLC, USACarolina Manica Universidade Federal do Rio Grande do Sul, BrasilDaniel Martin Lawrence Berkeley National Lab, USAMichael McCourt Cornell University, USAPeter Minev University of Alberta, Edmonton, CanadaChiara Mocenni University of Siena, ItalyPaul Muir Saint Marys University, CanadaRam Nair National Center for Atmospheric Research, USAMurtazo Nazarov Texas A&M University, USAMonika Neda University of Nevada, Las Vegas, USANghiem V. Nguyen Utah State University, USAMaxim Olshanskii Moscow State University, RussiaJeffrey S. Ovall University of Kentucky, USADuccio Papini Universita degli Studi di Siena, ItalyZhen Peng Ohio State University, USAMauro Perego Florida State University, USAJianxian Qiu Xiamen University, ChinaLillian Ratliff UC Berkeley, USALeo Rebholz Clemson University, USATodd Ringler Los Alamos National Laboratory, USAAntoine Rousseau INRIA, FranceDaniele Schiavazzi Stanford University, USADominik Schoetzau University of British Columbia, CanadaHelene Seroussi Caltech-Jet Propulsion Laboratory, USA and

Ecole Centrale Paris, Chatenay-Malabry, FranceQin Sheng Baylor University, USANeveen Shlayan Singapore-MIT Alliance for Research & Technology, USAChi-Wang Shu Brown University, USALeslie Smith University of Wisconsin, Madison, USAPavel Solin University of Nevada, Reno, USAErkki Somersalo Case Western Reserve University, USAP.D. Spanos Rice University, USAMartin Stynes National University of Ireland, IrelandJiguang Sun Delaware State University, USAPengtao Sun University of Nevada, Las Vegas, USAWeiwei Sun City University of Hong Kong, Hong KongShuyu Sun KAUST, Kingdom of Saudi Arabia

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Name InstitutionXudong Sun University of Nevada, Las Vegas, USAYuzhou Sun University of Nevada, Las Vegas, USAMark Taylor Sandia National Laboratory, USAJari Toivanen Stanford University, Stanford, USAHoang Tran University of Pittsburgh, USAJiajia Wang University of Nevada, Las Vegas, USAQi Wang University of South Carolina, USAMing Wang UC Irvine, USA and Peking University, ChinaA. Warzynski University of Leeds, UKMary F. Wheeler The University of Texas at Austin, USANicholas Wilson Clemson University, USAYau Shu Wong University of Alberta, CanadaAihua W. Wood Air Force Institute of Technology, USAZhijian Wu University of Alabama, USAHong Xie Manulife Financial, CanadaLiwei Xu Rensselaer Polytechnic Institute, USAJinchao Xu Pennsylvania State University, USAChuanju Xu Xiamen University, ChinaGuangri Xue Shell, USAJue Yan Iowa State University, USAXiaofeng Yang University of South Carolina, USAHe Yang Rensselaer Polytechnic Institute, USAHongtao Yang University of Nevada, Las Vegas, USAIvan Yotov University of Pittsburgh, USAYanzhi Zhang Missouri University of Science and Technology, USAShuhua Zhang Tianjin University of Finance and Economics, ChinaZhimin Zhang Wayne State University, USAXu Zhang Virginia Tech, USAChensong Zhang Chinese Academy of Sciences, ChinaShangyou Zhang University of Delaware, USAShan Zhao University of Alabama, USALiuqiang Zhong South China Normal University, ChinaJiang Zhu Laboratorio Nacional de Computacao Cientıfica, BrazilWenxiang Zhu Iowa State University, USAYunrong Zhu University of California at San Diego, USA

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93

Proceedings

All participants are invited to submit a manuscript to Proceedings of the 8th InternationalConference on Scientific Computing and Applications, which will be published by the Amer-ican Mathematical Society in the Contemporary Mathematics book series. A PDF version ofyour original manuscript (prepared using the Contemporary Mathematics author package:http://www.ams.org/authors/procpackages) should be submitted to [email protected] July 4th, 2012. The reviews of all papers will be finished by Sept.1, 2012. All con-tributors will get a free copy of the book from AMS. Details can be found at our confer-ence website (http://web.unlv.edu/centers/cams/conferences/sca2012/sca2012.html) under“Proceedings”.

Since its first classes were held on campus in 1957, UNLV has transformed itself from a smallbranch college into a thriving urban research institution of more than 28,000 students and3,100 faculty and staff.

Along the way, the urban university has become an indispensable resource in one of thecountry’s fastest-growing and most enterprising cities.

The Department of Mathematical Sciences offers Ph.D degree in mathematics and statistics.The Ph.D. program has four areas of concentration: Pure Math; Appl Math; ComputationalMath and Statistics.

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