modeling, adaptive discretizations and solvers for fluid...
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Modeling, Adaptive Discretizations and Solvers for Fluid-Structure InteractionInternational Symposium and Winter-School
boo k oF AbStr Ac tS
January 11–15, 2016 RICAM, Linz, Austriawww.uni-heidelberg.de/numerik/~modiso-fsi
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organizer
Stefan Frei (Heidelberg University)
Bärbel Janssen (KTH Stockholm)
Thomas Richter (University of Erlangen-Nuremberg)
Thomas Wick (RICAM Linz)
Huidong Yang (RICAM Linz)
Heidelberg Graduate School of Mathematical and computational Methods for the Sciences
Prof. Dr. Peter BastianInterdisciplinary Center for Scientific Computing (IWR)Im Neuenheimer Feld 36869120 Heidelberg
Dr. Michael J. WincklerInterdisciplinary Center for Scientific Computing (IWR)Im Neuenheimer Feld 36869120 Heidelberg
Phone: +49 (0) 6221 54 4981Email: [email protected]
HGS MathCompIm Neuenheimer Feld 368, Room 507 69120 Heidelberg
phone: +49 (0) 6221 54 4944Email: [email protected]
Opening HoursMonday & Thursday: 09:00h – 12:00h / 14:00h – 16:00hWednesday: 10:00h – 12:00h / 14:00h – 16:00h
Tuesday & Friday: closed
Chairman
AdministrativeDirector
Office
Welcome 1
Welcome
We welcome everybody to the
International Symposium and Winter-School on Modeling, Adaptive Discretizations andSolvers for Fluid-Structure Interaction at RICAM Linz in Austria.
This meeting aims at bringing together experts and junior scientists in the fields of mod-eling, adaptive discretizations and solvers for fluid-structure interaction. To provide aplatform in order to teach and learn state-of-the art formulations for fluid-structure inter-action, this workshop consists of a two-day-school and a subsequent three-day-symposium.The latter one will consist of invited and contributed presentations of junior scientists andexperts whereas the school lectures will be given by three young experts in their field cover-ing each of the three topics of our symposium. Our program reflects the idea of workshopswithin a RICAM special semester, which has a long and very successful tradition at thisinstitute.
On the following pages, more information on the location, the schedule, the participantsand details on presentations including their abstracts are provided. We have assembled 28interesting talks and there are about 60 participants from over 15 countries.
Finally, we are very grateful to Annette Weihs who helped us a lot with the administrationand we wish to thank our main sponsors
• Austrian Academy of Sciences
• Johann Radon Institute for Computational and Applied Mathematics (RICAM)
• HGS MathComp Heidelberg
• DK W1214 Computational Mathematics
who provided the basic funding of this event.
We look very much forward to meeting all participants and wish everybody an enjoyableand stimulating conference.
The organizers:Stefan Frei, Barbel Janssen, Thomas Richter, Thomas Wick, Huidong Yang
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
2 Conference Location
1. Harry’s Home Linz
2. Sommerhaus Hotel
3. RICAM Linz (4th floor)
4. Mensa (lunch/conference dinner)
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
Time table 3
Time table
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
Monday Tuesday
09:30
Registration10:15
10:15 Welcome10:30
10:30
Thomas Richter
12:00
12:00
Lunch break
14:00
14:00
Thomas Richter
15:30
15:30
Coffee break16:00
16:00
Simone Deparis
17:30
18:00
School snack/dinner
19:30
08:30
Simone Deparis
10:00
10:00 Coffee break10:30
10:30
David A. Nordsletten
12:00
12:00
Lunch break
14:00
14:00
David A. Nordsletten
15:30
15:30
Coffee break16:00
16:00
Common event/free time
19:30
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
4 Time table
Wednesday Thursday Friday
08:30
Registration
09:00
09:00
Miriam Mehl (1)
10:00
10:00
Coffee break10:30
10:30
Simone Deparis (2)
11:00
11:00
Christoph M. Augustin (3)11:30
11:30
Elias Karabelas (4)
12:00
12:00
Alfonso Santiago (5)12:30
12:30
Lunch break
14:00
14:00
Laurent Monasse (6)14:30
14:30
Meriem Jedouaa (7)
15:00
15:00
Stefan Frei (8)15:30
15:30
Coffee break
16:00
16:00
M.Shokrpour-Roudbari (9)16:30
16:30
Felix Brinkmann (10)
17:00
17:00
Tobias Elbinger (11)17:20
09:00
Annalisa Quaini (12)
10:00
10:00
Coffee break10:30
10:30
Giorgio Bornia (13)
11:00
11:00
Florian Sonner (14)11:30
11:30
Philipp Birken (15)
12:00
12:00
Azahar Monge (16)12:30
12:30
Lunch break
14:00
14:00
Ina Schussler (17)14:30
14:30
Ioannis Toulopoulos (18)
15:00
15:00
Andreas Rupp (19)15:20
15:20
Coffee break15:50
15:50
Angelos Mantzaflaris (20)
16:20
16:20
Andreas Hessenthaler (21)16:50
16:50
Nam-Seok Kim (22)17:10
17:10
Sabine Upnere (23)17:30
19:00
Conference dinner
19:59
09:00
Wim van Rees (24)
10:00
10:00
Coffee break10:30
10:30
Michael Lahnert 25)
11:00
11:00
Florian Lindner(26)11:30
11:30
B.S.M. Ebna Hai (27)
12:00
12:00
Lukas Failer (28)12:30
12:30
Closing12:45
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
General remarks 5
General remarks
General information sheet
For any kind of information we provide you in your welcome package a ‘General InformationSheet’ on which you find important information for your stay in Linz.
Talk lengths
As there are no parallel sessions, we have some flexibility in the schedule. The scheduledtimes have to be seen as maximal speaking slots. Please leave at least 5 minutes fordiscussion. Furthermore, we encourage everybody to talk rather shorter than to fill thewhole time. In this way, there is more time for discussion, either immediately after thetalk or during the coffee break.
Common event (winter school)
For Tuesday afternoon, we plan a common event to close the Winter School. If the weatheris nice, an option could be to hike around Linz or through the old town with a restaurantor bar as final destination.
School snack/dinner and conference dinner
On Monday evening (6 pm), we have a small school dinner providing snacks and drinks.The conference dinner will take place on Thursday evening (7 pm) at the mensa of theJohannes-Kepler-Universitat (see the map on page 2).
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
6 School speakers
School speakers
Our school speakers are distinguished young researchers who are briefly introduced here:
Simone Deparis
Simone Deparis is Maitre d’Enseignement et de Recherche at EPF Lausanne and deputydirector of the Section of mathematics. He obtained a PhD degree in Mathematics at EPFLin 2004, from 2004 to 2006 he has been a post-doctoral Fellow at MIT. His research interestsare in modeling and applications of vascular flows, including fluid-structure interactionsolvers and parallel algorithms, and in reduced order modeling for parametrized partialdifferential equations by the reduced basis method.
David Alexander Nordsletten
David Nordsletten is a Senior Lecturer in Biomedical Engineering at King’s College Lon-don. Previously, he has worked as a post-doctoral fellow at the Massachusetts Instituteof Technology and University of Oxford. His research team focuses on the integration ofbiomechanical modeling and advanced numerical techniques with clinical imaging. Thismerger of disparate - yet mutually complementary – fields provides a new paradigm for ana-lyzing and assessing health and disease, moving toward personalized patient care. Throughthe development of patient-specific mathematical models, we construct novel analysis toolsto improve diagnosis, treatment and therapy planning in the heart. A key area of empha-sis in our lab is the biomechanics of both healthy and failing hearts. Using biomechanicalanalysis software, we aim to characterize alterations in cardiac structure and function indisease.
Thomas Richter
Thomas Richter is Professor for Scientific Computing and Numerical Analysis at the Uni-versity Erlangen-Nuernberg. His research focus is on adaptive finite elements for continuummechanics with applications in biology and medicine. He holds a PhD degree in appliedmathematics from Heidelberg University in Germany. He spend one year as Post-Doc atthe Massachusetts Institute of Technology. Prior to his position in Erlangen, Richter wasAssistant Professor for Numerics of Partial Differential equations at Heidelberg University.
International Symposium and Winter-School onModeling, Adaptive Discretizations and Solvers for Fluid-Structure Interaction
at RICAM, Linz, January 11 – 15, 2016
7
Abstracts
1. Partitioned Approaches for Multi-Physics Simulations – From First Ideasto Today’s Robust Approaches
Miriam Mehl, University of Stuttgart
Partitioned approaches for multi-phsics simulations have been estalished for fluid-structure interactions already in the late 90s (Park, Felippa et al.). The idea was toestablish this new class of simulation without the time-consuming process of re-implementing a whole simulation code from scratch. Instead, sophisticated andtrusted simulation software for fluid flow and structural dynamics were re-used andcoupled in an as tight as neccessary fashion.These first approaches allowed for aneasy and fast realization of fluid-structure simulation environments but still had is-sues in terms of stability and convergence speed of coupling iterations. In addition,they were not designed to efficiently make use of parallel compute architectures. Dueto these issues and with this type of simulation becoming an important and widelyused application, more and more monolithic codes setting up and solving the coupledsystem as a whole were developed. Obviously, they allow for highly optimized solverimplementations for the underlying ill-conditioned systems of equations. At the sametime also the partitioned coupling approach has developed into a robust class of iter-ative solvers for multi-physics problems and still has the great advantage of provingfull flexibility in exchanging involved models, solvers, coupling methods, or addingfurther physical fields in a very short development time. The presentation givesan overview of the past and current developments in partitioned multi-physics sim-ulations including inter-code communication, data mapping between non-matchingmeshes, iterative equation coupling, and software tools.
2. Reduced order modeling and simulation of vascular flows
Simone Deparis, EPFL Lausanne
We are interested in numerical simulations of vascular flows which can run on alaptop in real time. To reduce the complexity of the model, the fluid computationaldomain is assumed fixed and the structure is considered as a thin membrane. Thestructure is integrated in the fluid equations, yielding the Navier-Stokes equationswith a generalized Robin boundary condition on the fluid-structure interface. ProperOrthogonal Decomposition (POD) and the Reduced Basis Method (RBM) allows fornumerical reduction. Their combination allows to split the computational effort intoan offline and an online parts. The offline part runs on a HPC system and takesabout 5 hours on 1000 processors, while the online part can be run in real time, i.e.1 second of simulations in less than 1 second of CPU time, on a notebook. The real
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gain of such an approach is that after offline computations, the parameters of thepatient specific simulation, like flow rate, heart pace, stiffness of the artery, can bechanged online.
3. Simulating patient-specific whole heart electromechanics with efficient al-gebraic multigrid preconditioners
Christoph M. Augustin, Institute of Biophysics, Medical University of Graz
Developing efficient frameworks for multiscale-multiphysics models of cardiac elec-tromechanics is a challenging task due to the vast computational costs and the nu-merical complexities involved in coupling different physics.
Due to preferential orientations of fibers, such as collagen and myocytes, the pas-sive mechanical behavior of myocardial tissue is anisotropic and highly nonlinear.Moreover, an active contraction is driven by electrical processes, which is modeledby an additional active stress contribution. This additive term is computed using aparticular cell model and a cardiac electrophysiology model, based on the bidomainequations. To specify prescribed displacements or tractions Dirichlet and Neumannboundary conditions are incorporated. Windkessel models of the circulatory sys-tem are fitted to match pressure-volume relations during ejection and diastolic fillingphases. In order to obtain a numerical solution we apply variational and finite ele-ment techniques and the nonlinear system is linearized using Newton’s method.
However, such detailed multiphysics simulations are computationally vastly demand-ing, since the resulting discretized systems of equations are large, with several millionsof degrees of freedom. While current trends in high performance computing (HPC)hardware promise to alleviate this problem, exploiting the potential of such archi-tectures remains challenging for various reasons. On one hand, strongly scalablealgorithms are necessitated to achieve a sufficient reduction in execution time byengaging a large number of cores, and, on the other hand, alternative accelerationtechnologies such as graphics processing units (GPUs) are playing an increasinglyimportant role which imposes further constraints on design and implementation ofsolver codes.
We present a domain decomposition algebraic multigrid (AMG) preconditioner foran iterative Krylov solver (CG, GMRES) which is custom-tailored for the specificproblem. Benchmarking studies were performed and strong scalability results up to8192 cores for electromechanical simulations will be shown.
The next (future) step is to enhance this cardiac electromechanics framework withFSI; a central building block, computational hemodynamics, is already at an ad-vanced state (see the talk of Elias Karabelas). This will enable bidirectionally cou-pled electro-mechano-fluidic simulations of total heart function at an anatomicallyaccurate and biophysically adequate level of detail.
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1. CM Augustin, A Neic, M Liebmann, AJ Prassl, SA Niederer, G Haase, and GPlank. ”Anatomically accurate high resolution modeling of cardiac electrome-chanics: a strongly scalable algebraic multigrid solver method for non-lineardeformation”. Journal of Computational Physics 305 (2016), pp. 622–646.
4. Parallel Simulation of Aortic Blood Flow
Elias Karabelas, Institute of Biophysics, Medical University of Graz
The development of multi-physics simulation frameworks for cardiac function is chal-lenging. Mostly due to the vast computational costs coming from the different phys-ical models for electrics, mechanics and blood flow.
While the talk of Christoph Augustin (see schedule) is focused on cardiac electrome-chanics, the emphasis of this presentation is on hemodynamics. The physics aredescribed with the Navier-Stokes equations, closed with suitable boundary condi-tions.
In order to obtain a numerical solution we apply variational and finite element tech-niques paired with time-stepping methods. The resulting nonlinear systems are lin-earized using Newton’s method. To resolve possible turbulence and to representanatomical models correctly it is necessary to work with very fine unstructuredmeshes. This results in linear systems with a huge amount of degrees of freedom.
We aim at tackling this problem with the help of high performance computing (HPC).The solution strategy is based on a domain decomposition algebraic multigrid (AMG)preconditioned iterative GMRES solver custom-tailored to the specific problem. Wewill present first results making use of this parallel solution strategy.
5. Fluid Structure interaction applied to a cardiovascular model
Alfonso Santiago, Barcelona Supercomputing Center.
Fluid Structure interaction applied to a cardiovascular model Alfonso Santiago, BarcelonaSupercomputing Center. In this work a model for an electro-fluid-mechanic compu-tational heart is presented, focus- ing in the Fluid structure interaction problem. Theproblem is solved with Alya, the BSC in-house tool for Finite Element modelling.This is a 3D, multiscale, multiphysics, HPC code, that allows modelling and solv-ing the heartbeat electromechanic problem [4, 5]. The cardiovascular system can bedecomposed as a coupled electromechanical system: the propagation of the actionpotential induces the mechanical deformation of the myocardium, which reduces theinner cavity inducing the pumping action against the blood through the arteries. In
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this way, three problems have to be solved: the propagation of the electric poten-tial[5, 2, 3], the deformation of the solid[4, 1] due to the electrophisologic stimuli andouter forces, and the fluid dynamics inside the ventricle[6, 7].
But apart from the physical problems, the coupling problems must be solved. In onehand there is the electric-solid coupling and in the other hand there is the solid-fluidcoupling. In the former coupling, the Hunter-Nash [8] formulation is used.
To approach the Fluid Structure Interaction problem, the whole domain is split intwo meshes: one in which the physics of in the solid are solved, and the other in whichthe problems of the fluid are computed. In this way, we work with two independentmeshes, and two independent instances of the software that are run in parallel, butconnected with MPI subroutines.
With the current strategy also come a great flexibility in the coupling schemes. TheJacobi approach allows running the simulations in less time, but also difficult theconvergence. The Gauss-Seidel method facilitates the convergence but leads to longerduration of the simulations. As the densities of the solid and the fluid are similar,the added mass inesta- bility frequently appears. To deal with this fixed and Aitkenrelaxation in both ways of the communication is used.
It is important to notice that this work is part of a bigger project where two of themost complex biomechanical models of the heart and the arterial vascular networkare being coupled to create the first non-lumped cardiovascular model.
6. Three-dimensional fluid structure interaction between a compressible fluidand a fragmenting structure with a conservative immersed boundary method
Laurent Monasse, Ecole des Ponts ParisTech
In this work, we present a conservative method for three-dimensional inviscid fluid-structure interaction problems.
On the fluid side, we consider an inviscid Euler fluid in conservative form. The FiniteVolume method uses the OSMP high-order flux with a Strang operator directionalsplitting [1].
On the solid side, we consider an elastic deformable solid with possible fragmenta-tion. We use a Discrete Element method (particles connected with springs) for thediscretization of the solid [2].
Body-fitted methods are not well-suited for large displacements or fragmentation ofthe structure, since they involve possibly costly remeshing of the fluid domain. Weuse instead an immersed boundary technique through the modification of the finitevolume fluxes in the vicinity of the solid. The method is tailored to yield the exact
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conservation of mass, momentum and energy of the system and exhibits consistencyproperties [3, 4]. In the event of fragmentation, void can appear due to the velocityof crack opening. Since the high-order OSMP numerical flux is not stable in thepresence of void, we resort locally to the Lax-Friedrichs flux near cracks [5].
Since both fluid and solid methods are explicit, the coupling scheme is designed tobe explicit too. The computational cost of the fluid and solid methods lies mainly inthe evaluation of fluxes on the fluid side and of forces and torques on the solid side.It should be noted that the coupling algorithm evaluates these only once every timestep, ensuring the computational efficiency of the coupling.
We will present numerical results showing the robustness of the method in the caseof a fragmenting solid coupled with a compressible fluid flow.
[1] C. Tenaud and V. Daru. High-order one-step monotonicity-preserving schemesfor unsteady compressible flow calculations. Journal of Computational Physics,193:563–594, 2004.
[2] L. Monasse and C. Mariotti. An energy-preserving Discrete Element Methodfor elastodynamics. ESAIM: Mathematical Modelling and Numerical Analysis,46:1527–1553, 2012.
[3] M. A. Puscas, L. Monasse. A three-dimensional conservative coupling methodbetween an inviscid compressible flow and a moving rigid solid body. SIAMJournal on Scientific Computing, accepted, 2015.
[4] M. A. Puscas, L. Monasse, A. Ern, C. Tenaud, C. Mariotti, V. Daru. A timesemi-implicit scheme for the energy-balanced coupling of a shocked fluid flowwith a deformable structure. Journal of Computational Physics, 296:241–262,2015.
[5] M. A. Puscas, L. Monasse, A. Ern, C. Tenaud, C. Mariotti. A conservativeembedded boundary method for an inviscid compressible flow coupled with afragmenting structure. International Journal for Numerical methods in Engi-neering, 103:970–995, 2015.
7. An efficient interface capturing method for a large collection of interactingimmersed rigid bodies
Meriem Jedouaa, Laboratoire Jean Kuntzmann, Grenoble Alpes University and CNRS
A method to efficiently capture an arbitrary number of fluid/solid or fluid/fluid in-terfaces, in a level-set framework, is presented. This technique, borrowed from imageanalysis [1] is introduced in the context of the interaction of several bodies immersedin a fluid. The main idea is to consider the whole fluid/structure system as a set of
FSI at RICAM Linz, Jan 11 – 15, 2016
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objects, one for each immersed structure, and one for the fluid.A configuration of these objects is described by three label maps giving at each pointthe first and second neighbours, and their associated distance functions. Only onelevel set function captures the union of all interfaces and is transported with thefluid velocity. Then a local fast marching algorithm is performed at each time stepto evolve the label and distance functions.Using the distance to the first closest structures we introduce a short range repulsiveforce, inspired by [3], to avoid contacts between bodies. The main advantage of thismethod is that only five field functions are required to capture any number of struc-tures, and at the same time to deal with collisions, which reduces the computationalcost.The method is applied to the simulation of a dense suspension of rigid bodies im-mersed in an incompressible fluid. A global penalization model uses the label mapsto follow the solid bodies altogether without a separate computation of each bodyvelocity as usually [2]. Consequently, the method is very efficient when dealing witha large number of cells. Numerical simulations are performed in dimensions two andthree, under gravity force.
1) J. A. Bogovic, J. L. Prince and P.-L. Bazin, A multiple object geometricdeformable model for image segmentation, Computer Vision and ImageUnderstanding, vol 117, 2, pp 145-157, 2013.
2) C. Bost, G.-H. Cottet , and E. Maitre, Convergence analysis of a pe-nalization method for the three-dimensional motion of a rigid body in an incom-pressible viscous fluid. SIAM Journal on Numerical Analysis, 48(4),pp 1313-1337, 2010.
3) M. Coquerelle and G.-H. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, Journal ofComputational Physics, 227(21), 9121-9137, 2008.
4) M. Jedouaa, C.-H. Bruneau and E. Maitre, An efficient interface cap-turing method for a large collection of interacting cells immersed in a fluid, inpreparation.
8. Accurate spatial and temporal discretization techniques for interface prob-lems and fluid-structure interactions in Eulerian coordinates
Stefan Frei, Heidelberg University and Thomas Richter, University of Erlangen-Nurnberg
Interface problems pose several challenges for discretization, especially in the casewhen the interface is moving. If the interface is not resolved by the discretization,we typically obtain a reduced order of convergence and possibly stability issues.
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In this talk, we present discretization schemes in both space and time in order to avoidthese issues. The proposed finite element discretization in space corresponds to afitted finite element method that uses a fixed patch mesh independent of the interfacelocations in combination with an interiour refinement to resolve the interface. Fortime discretization, we use a modified time-stepping scheme that is based on a space-time cG(1) approach. Instead of using linear polynomials in direction of time acrossthe interface, however, we define an ansatz space that is linear on trajectories thatstay within each subdomain. The resulting time-stepping scheme is similar to thefixed-mesh ALE method proposed by Codina and co-workers. We show second-order convergence for both discretization in space and time and give a bound on thecondition of the system matrix. Finally, we illustrate the capability of our approachin the context of fluid-structure interaction problems.
9. Elasto-Capillary Simulations based on a Phase-Field Model
E.Harald van Brummelen, Mahnaz Shokrpour-Roudbari and Gertjan J. van Zwieten,Multi-scale Engineering Fluid Dynamics, Mechanical Engineering Department, Eind-hoven University of technology
This study focouses on a computational model for a complex-fluid-solid-interactionproblem based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The fluid flow is described by the incompressibleNavier-Stokes-Cahn-Hilliard equations with preferential-wetting boundary conditionsat the contact-line. The numerical simulation of the aggregated complex-fluid-solid-interaction problem, are conducted based on an Arbitrary-Lagrangian-Eulerian for-mulation of the Navier-Stokes-Cahn-Hilliard equations and a proper reformulation ofthe complex-fluid traction and the fluid-solid surface tension. The presented complex-fluid-solid-interaction model, is then compared with experimental data for a dropleton a soft substrate.
10. Finite Elements for Mechanochemical Pattern Formation
Felix Brinkmann, Institute of Applied Mathematics, Heidelberg University
In this talk a finite element method for mechanochemical pattern formation will bepresented. A biological application of this prototypic model is embryonic developmente.g. early development stages of the fruit fly.
We model biological tissues using the hyperelastic Saint Venant-Kirchhoff model.The growth processes are modeled by splitting the deformation gradient into anactive part and an elastic response. The active part depends on the concentration ofsignaling molecules, which are modeled by an reaction-diffusion equation.
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Evolving patterns are reinforced by a feedback mechanism since experimental obser-vations show that biological cells react to stress, compression or strain. I will presentmechanisms using compression and strain as feedback which are stable under differ-ent initial conditions and different scales of diffusion. Also, a mechanism using stresswill be presented.
Finally, implementation details such as oscillating growth and rotating solutions willbe addressed. Large problems, in particular in 3D, are solved with a parallel multigridsolver of the software library Gascoigne 3D.
11. Simulation of metabolic processes including surface reactions in cells
Tobias Elbinger, Chair of Applied Mathematics 1, FAU Erlangen-Nurnberg
The interior of living cells can be considered as a porous medium consisting of threecompartments: cytosol, chloroplasts and mitochondria. Diffusion and reactions takeplace inside the cytosol, inside the chloroplasts and on the surface of the mitochon-dria. A two-scale homogenized model is used for the mathematical description ofthe cells. The particular numerical challenge lies in the treatment of the complexinter-scale dependencies, the large number of biochemical species and the rate termsresulting from the enzyme kinetics. Suitable discretizations and methods that reducecomputation time by reduction of the problem size and parallelization are presented.Finally, the role of the enzyme localization on the mitochondria surfaces is investi-gated.
12. Simulation of fluid-structure interaction problems arising in hemodynam-ics
Annalisa Quaini, University of Houston
We focus on the interaction of an incompressible fluid and an elastic structure. Twocases are considered: 1. the elastic structure covers part of the fluid boundary andundergoes small displacement and 2. the elastic structure is immersed in the fluid andit features large displacement. For the first case, we propose an Arbitrary Lagrangian-Eulerian (ALE) method based on Lie’s operator splitting. The resulting algorithmis unconditionally stable and weakly coupled: it requires the solution of one fluidsubproblem and one structure subproblem, both endowed with Robin type boundaryconditions, per time step. This algorithm is applied to blood flow in a healthy straightartery and in a diseased artery with implanted stent. Standard ALE methods failwhen the structural displacement is large. Thus, for the second case we propose anextended ALE method that avoids remeshing. The extended ALE approach relies ona variational mesh optimization technique, combined with an additional constraintwhich is imposed to enforce the alignment of the structure with certain edges of
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the fluid triangulation without changing connectivity. This method is applied to a2D benchmark problem modeling valves: a thin elastic 1D leaflet, modeled by aninextensible beam equation, is immersed in a 2D incompressible, viscous fluid drivenby the time-dependent inlet and outlet data.
13. Geometric multigrid and domain decomposition methods for incompress-ible FSI problems
Giorgio Bornia, Department of Mathematics and Statistics, Texas Tech University
We investigate the numerical performance of a Newton-Krylov geometric multigridsolver with domain decomposition smoothing for the solution of a class of incompress-ible FSI problems. The mathematical formulation is based on a monolithic approach,where mass and stress balance are automatically satisfied across the fluid-solid in-terface. The numerical solution of these problems poses several challenges, such asthe solution on a moving domain, the treatment of the nonlinearities and the en-forcement of the incompressibility condition. Additional challenges are encounteredin the steady-state case, due to a worse conditioning of the stiffness matrix. The so-lution of steady-state cases is typically dealt with by using time stepping strategies.In this work we propose a solver which does not require time iterations in order tocompute a steady-state configuration. This solver is characterized by a geometricmultigrid algorithm with additive Schwarz smoothing. The deformation of the fluiddomain in the steady-state nonlinear iterations is taken into account according to anArbitrary Lagrangian Eulerian (ALE) scheme. The domain decomposition is drivenby the natural split between the fluid and solid domains. Due to the complexity ofthe operators, the implementation of the Jacobian matrix in the Newton iterationsis a non-trivial task. To this purpose, we consider the use of automatic differentia-tion tools. The numerical results of some benchmark tests show agreement with theliterature and robustness of the computational procedure.
14. Monolithic and Partitioned Solvers for a Linear Model Problem
Florian Sonner, FAU Erlangen-Nurnberg
We consider a linearized fluid-structure interaction problem consisting of a coupledStokes and Navier-Lame system without domain deformation. For this model prob-lem we compare a partitioned Dirichlet-Neumann iteration with a monolithic multi-grid solver.
Using domain decomposition techniques we show that the partitioned iteration con-verges to the monolithic solution. The speed of convergence is independent of themesh cell size but deteriorates for small time steps, in agreement with numericalresults.
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To solve the monolithic system we use a multigrid algorithm with a smoother basedon partitioned solvers. Through numerical experiments we verify that a smoothingproperty is satisfied.
A numerical investigation on the influence of the physical parameters on the solversis done with special focus on the added-mass effect. We see that the monolithic solverwith partitioned smoothing is more robust than the partitioned iteration itself.
15. Inexact fixed point schemes in fluid structure interaction
Philipp Birken, Numerical Analysis, Centre for the Mathematical Sciences, LundUniversity
Recently, a fast time adaptive methods for fluid structure interaction has been pro-posed [2,3]. In order to get a good estimate of the time integration error, it isnecessary to have an iteration error that is smaller than that one. In turn, thisrequires the ability to control the iteration error by a suitable choice of tolerances.
The standard iterative solver for fluid structure interaction within a partitioned set-ting is the Dirichlet-Neumann iteration. This can be written as a fixed point iterationfor the unknowns on the interface, where the iteration consists of solving the sub-problems. In practice, this requires another iterative solver, leading to the situationof an outer iteration (Dirichlet-Neumann) and an inner iteration for the subproblems,similar to inexact Newton methods. This gives rise to the question on accurate theinner solves need to be.
Whereas this problem has been analyzed satisfactorily for inexact Newton methods[4], it has not been answered for fixed point methods. We present theory for thelinear case on how to choose the tolerance in inner and outer solvers for these inexactfixed point schemes and relate this to the type of tolerance criterion for the innersolves used [1]. Besides fluid structure interaction, this can also be applied to thePicard iteration.
[1] P. Birken. Termination criteria for inexact fixed point schemes. Numer. LinearAlgebra Appl., 2015.
[2] P. Birken, T. Gleim, D. Kuhl, and A. Meister. Fast solvers for unsteady thermalfluid structure interaction. Int. J. Num. Meth. Fluids, 79:16–29, 2015.
[3] P. Birken, K. J. Quint, S. Hartmann, and A. Meister. A Time-Adaptive Fluid-Structure Interaction Method for Thermal Coupling. Comp. Vis. in Science,13(7):331–340, 2010.
[4] S. C. Eisenstat and H. F. Walker. Choosing the forcing terms in an inexactnewton method. SIAM J. Sci. Comput., 17(1):16–32, 1996.
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16. Convergence analysis of coupling iterations for the unsteady transmissionproblem
Azahar Monge and Philipp Birken, Centre for Mathematical Sciences, Lund Univer-sity
Unsteady thermal fluid structure interaction is modelled using two partial differen-tial equations describing a fluid and a structure on different domains. The standardalgorithm to find solutions of the coupled problem is the Dirichlet-Neumann itera-tion, where the PDEs are solved separately using Dirichlet-, respectively Neumannboundary conditions with data given from the solution of the other problem. Previousnumerical experiments [1] show that this iteration is fast, and although the iterationhas been analyzed and a convergence condition is given by [4], the convergence rateshave not been computed.
Henshaw and Chad provided in [2] a method to analyse stability and convergencespeed of the Dirichlet-Neumann iteration for the semi-discretized equations of thethermal transmission problem. However, our numerical results for the fully-discretizedcase are not completely covered by this analysis, and therefore, we propose a com-plementary analysis for this case. We consider the transmission problem because itis a basic building block in fluid structure interaction. In particular, we consider thecoupling of two heat equations on two identical non overlapping domains. These arediscretized using the finite element method. Besides, the implicit Euler method isused for the time discretization.
In this context, the exact iteration matrix of the Dirichlet-Neumann coupling canbe written down and using the eigendecomposition of the discretization matrices wefind a formula for the spectral radius, i.e, a formula that gives the exact convergencerates. Moreover, if we restrict ourselves to the 1D version, we can also estimate theasymptotic behaviour of the convergence rates when both the spatial mesh size andthe stepsize tend to 0. The resulting asymptotics when the spatial mesh size tendsto zero are consistent with a previous work using finite differences instead of finiteelement for the discretization of the Laplacian [3]. Numerical results are presentedto illustrate the analysis.
REFERENCES
1) P. Birken, T. Gleim, A. Meister and D. Kuhl. Fast solvers for unsteady thermalfluid structure interaction. Int. J. Numer. Meth. Fluids, 79(1):pp. 16-29, 2015.
2) W.D. Henshaw and K.K. Chand. A composite grid solver for conjugate heattranfer in fluid-structure systems. J. Comp. Phys., 228:pp. 2708-3741, 2009.
3) A. Monge and P. Birken. Convergence speed of coupling iterations for the un-steady transmission problem, in B. Schrefler, E. Onate and M. Papadrakakis
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(Eds), VI International Conference on Computational Methods for CoupledProblems in Science and Engineering, COUPLED PROBLEMS 2015.
4) A. Quarteroni and A. Valli. Domain decomposition methods for partial differ-ential equations, Oxford Science Publications, 1999.
17. Simulation of the temporal effects in high performance ball-bearings
Ina Schussler, FAU Erlangen-Nurnberg
Topic of the presentation will be the simulation of the lubricant film in high per-formance ball bearings. Focus is on the temporal dynamics of ball bearings and inparticular on the effects of complex rheology with pressure dependent viscosities. Weconsider the lubricant flow around one ball, modeled as a free and rotational rigidbody.
The extreme characteristics of this setting, for example the high velocity of the balland the small distance between ball and housing, are very challenging. To discretizethe Navier Stokes equations on this difficult domain, grids with cells with a highaspect ratio are used. In this presentation the focus will be on the implementationof weak boundary data on highly anisotropic domains. Here the dependence of thepenalty parameter on the shape of the domain -measured by its inf-sup constant- isshown.
18. Numerical solutions for p-Laplace type problems
Ioannis Toulopoulos and Thomas Thomas Wick,Johann Radon Institute for Computational and Applied Mathematics (RICAM),Austrian Academy of Sciences
In this work, we present finite element methods for solving nonlinear elliptic problems,which have the form −div(ε2 + |∇u|2) p−2
2 ∇u = f . This type of problems appear asmathematical models for describing several physical phenomena, as for example,non-Newtonian flow motions. The whole approach includes two parts, (i) the finiteelement discretization and (ii) the iterative procedure for solving the resulting non-linear algebraic system.
In the first part, we discuss the discretization of the problem using tensor productfinite elements, and we present a priory error estimates by following the ideas pre-sented in [1]. It is known that for this type of problems, the developing of efficientiterative methods for the solution of the resulting finite element system is not aneasy task. Specially, when ε is very small and p < 2, the classical iterative meth-ods, e.g., Newton-like methods, can exhibit an unstable behavior for the case where
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|∇u| → 0. In the second part, among others iterative methods for solving the non-linear algebraic system, we give a clear presentation of the construction of AugmentedLangrangian Methods, that have been proposed in [2]. At the last part, we presentsome numerical examples which validate the derived error estimates and highlightthe efficiency of the proposed iterative methods.
[1] Diening L. and Ruzicka M., Interpolation operators in Orliz-Sobolev spaces, Nu-mer. Math. (2007) 107, 107-129.
[2] R. Glowinski and P. L. Tallec, Augmented Lagrangian and Operator-SplittingMethods in Nonlinear Mechanics, (1989) Society for Industrial and AppliedMathematics, Philadelphia, USA.
19. A Non-Symmetric Discontinuous Galerkin Approach to Couple 2D Verti-cal Shallow Water Equations and Darcy-Equation
Andreas Rupp, Friedrich-Alexander-University Erlangen-Nurnberg
In this talk we will discuss the discretization of water flowing through a saturatedporous medium using the Local Discontinuous Galerkin (LDG) method. Hence wewill talk about convergence analysis of the LDG scheme and efficiently implementingit using MATLAB. Moreover we will discuss the discretization of the two-dimensionalvertical shallow water equations and briefly look at the Riemann problems arisingfrom our LDG method.Afterwards we will see an approach of coupling both equations and resolving theproblem of different time-scales. Therefore we will use an interface that has somekind of memory.
20. Adaptive isogeometric discretizations by means of hierarchical splines
Angelos Mantzaflaris, RICAM, Austrian Academy of Sciences
The introduction of isogeometric analysis in the recent years revealed that the useof compatible representations between geometric modeling and numerical simulationhas significant advantages. Indeed, on the one hand this allows the integration offinite element analysis into conventional computer-aided design tools and, on theother hand, provides highly accurate simulation results with increased smoothness,whenever possible. However, standard geometric design representations are based ontensor-product B-splines, which preclude the possibility for adaptive mesh refinement.This has triggered the introduction of hierarchical and truncated hierarchical B-splinebases as a means to overcome the limitation. We shall demonstrate the potential ofthis machinery using illustrative 2D and 3D numerical examples.
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21. 3D Fluid-Structure Interaction Benchmark Experiment
Andreas Hessenthaler, Institute of Applied Mechanics (CE), Stuttgart, Germany
In the field of fluid-structure interaction (FSI), a wide range of numerical methodsand algorithms have been proposed to date, differing in aspects like fluid-structurecoupling, discretization of underlying meshes, numerical solution schemes, etc. Pos-sible fields of application vary as much and where one method might be particularlywell-suited for a given application, another method might give more accurate resultsfor a different application. Nowadays, numerical tools are increasingly developed toassist clinical medicine to address biomedical engineering problems. Within theseframeworks, imaging techniques, such as magnetic resonance imaging (MRI), com-puter tomography and ultrasound, are often used for data acquisition, e.g. to obtaininput geometries and boundary conditions.
In order to understand the power, applicability to specific problems and possiblelimitations of numerical FSI techniques, validation and benchmarking are key. Re-searchers have proposed both numerical and experimental FSI benchmark test casesin two and three dimensions, e.g. [1, 2, 3, 4, 5], providing an invaluable testbed.
Based on these works, a benchmark experiment was developed with interaction ofan incompressible non-linear solid and a moderately viscous Newtonian fluid in afully three-dimensional setting [6] in order to extend currently available benchmarktest cases. Precise geometry definition was achieved using CAD tools and materialparameters of the fluid and the solid were determined. Two test cases were defined,resulting in a steady-state and periodic steady-state with flow in the laminar regime.A 3T MRI scanner was used for data acquisition to obtain a rich and comprehensivedata set in a format that is used in typical biomedical applications. Acquired time-resolved MRI data includes inflow boundary condition data as well as geometry andflow images.
In this talk, the 3D FSI benchmark experiment is presented, the benchmark problemdefined and experimental data compared with numerical results.
[1] Wall W, Ramm E. Fluid-structure interaction based upon a stabilized (ALE)finite element method. 4th World Congress on Computational Mechanics: NewTrends and Applications, CIMNE, Barcelona 1998.
[2] Wall W. Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen.Ph.D. Thesis, Institut fur Baustatik, Universitat Stuttgart 1999.
[3] Turek S, Hron J. Proposal for numerical benchmarking of fluid-structure interac-tion between an elastic object and laminar incompressible flow. Springer BerlinHeidelberg 2006.
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[4] Gomes JP, Yigit S, Lienhart H, Schafer M. Experimental and numerical studyon a laminar fluid-structure interaction reference test case. Journal of Fluids andStructures 2011; 27:43–61.
[5] Kalmbach A, De Nayer G, Breuer M. A new turbulent three-dimensional FSIBenchmark FSI-PFS-3A: Definition and measurements. V International Confer-ence on Computational Methods in Marine Engineering 2013.
[6] Gaddum N, Holub O, Hessenthaler A, Sinkus R, Nordsletten D. Benchmark ex-periment for validation of fluid-structure interaction algorithms. Proceedings ofthe 4th International Conference on Computational and Mathematical BiomedicalEngineering 2015.
22. A Comparison of Dynamic Mesh Methods to Describe a Check ValveClosure
Nam-Seok Kim, Korea Institute of Nuclear Safety
The present study aims at drawing up recommendations for choosing the appropriatemoving mesh techniques to describe the dynamic behavior of the flow field withincheck valve and to calculate a pressure build-up response to the adjacent equip-ment due to check valve closure. Two different dynamic mesh techniques of ANSYSCFX, the immersed boundary and the remeshing methods, were used to describethe disc movement of the valve. The sensitivity of grid levels and momentum sourcescaling factors were evaluated to optimize the immersed boundary mehtod, and theinterpolation performances of the remeshing method were investigated. The resultsof calculations made by means of the immersed boundary method and remeshingmethod have been compared. The comparisons of results were similar in the as-pect of pressure and velocity distribution as the check valve is closing. However,as the valve disc is almost closed, the immersed boundary method can’t describethe inflowing behavior of fluid. And the build-up pressure caused by compressionof fluid is underestimated. With these evaluation results, the remeshing method ismore suitable to predict an accurate build-up pressure due to the check valve clo-sure. Additionally, the dependency of disc’s angular velocities was evaluated withthe remeshing method.
23. Modeling of Cross-Flow Induced Vibrations on Circular Cylinder at HighReynolds Number
Sabine Upnere, Riga Technical University and Ventspils University College
This work presents the study of modeling of fluid flow and circular cylinder interactionin order to investigate cross-flow induced vibrations. The flow around cylinder has
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been extensively investigated because of its wide applications in civil engineering,such as offshore structures, tall towers or stacks or nuclear reactors. The high velocityfluid flow interaction with structural components can induces self-excited vibrationsof the components. The instability can lead to the maintenance and operationalproblems.
In order to analyzed flow induced vibration two-dimensional Finite Element Mod-els have been developed using commercial software. Comparison of numerical andanalytical results have been done.
24. Multiresolution simulations of optimal self-propelled swimmers in 2D and3D: results and challenges
Wim van Rees, Harvard University
Simulations of fluid-structure interactions have applications in a wide range of fields,such as cardiovascular fluid mechanics, energy harvesting and biolocomotion. This inturn has spurred a large research effort resulting in a variety of numerical algorithmsto solve such problems, spanning an entire spectrum from intricate, accurate methodsto straightforward, low-order techniques. For solvers to be of practical use, they addi-tionally require robustness, flexibility, ease of integration with existing software, andhigh performance on modern compute architectures. These conflicting requirementsimply there is no globally optimal approach to numerically tackling the FSI problem.In this talk, I will present a perspective derived from my experience with optimal bio-logical swimming applications, achieved through combining reverse-engineering toolswith 2D/3D, CPU/GPU multiresolution remeshed vortex methods. Furthermore, Iwill provide some examples of other software algorithms that are being consistentlyused for applications in the above fields, and where they fall within this spectrum ofpossible solution techniques.
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25. Extending Simulation Domains with Minimal-Invasiveness by Using Tree-Based Dynamically-Adaptive Grids
Michael Lahnert, University of Stuttgart
Nowadays in academia there are lots of existing simulation codes, written by re-searchers from various fields, around. Each of these codes may contain expertise frommany man-years from various scientific fields like physics, chemistry or mechanicalengineering. For reasons of simplicity lots of these codes use regular discretizationsfor applying their various grid-based methods to simulate their respecitve systems.However, this approach limits the capability of increasing the domain size of a systemwhile keeping the computational costs at a feasible level. To mitigate this problem,we show a way of integrating dynamically-adaptive tree-structured grids into exist-ing applications with minimal-invasiveness. We show our results for a dynamically-adaptive implementation of the Lattice Boltzmann Method. We base our work onp4est, a well-known application for such grids, which we intergrated into ESPResSo,a well-known molecular dynamics code that uses a D3Q19 implementation of theLBM to simulate background flows.
26. preCICE – A flexible black-box coupling library
Florian Lindner, University of Stuttgart
Flexible and extensible partitioned multi-physics simulation environments requireefficient and modular tools with a broad and customizable coupling functionality.preCICE is a library for flexible numerical coupling of single-physics solvers. It usesa partitioned black-box coupling approach, thus requiring only minimal modificationsto existing solvers. This fact and the clean API foster quick and effortless integrationinto existing codes. Software packages currently coupled with preCICE compriseboth commercial and academic solvers, with a particular focus on fluid-structureinteraction. preCICE is written in C++ and features a clean and modern softwaredesign with extensive unit and integration testing while maintaining minimal externaldependencies. Inter-solver parallelism, parallel communication and data mappingtechniques will help to max out future exa-scale computers.
The resulting fixed-point problem can be solved by various pluggable coupling schemes.Selectable schemes include parallel as well as serial ones using implicit or explicit cou-pling. Communication and data mapping between coupling participants is done ina decentralized fashion by a peer to peer approach thus minimising blocking barri-ers in the process. This distributed data approach is reflected in areas such as thesimulation steering, e.g. setting of timestep lengths where one client acts as primusinter pares. Coupling schemes and mapping methods have also been adapted to workon distributed data. Data mapping between non-conformal meshes can be done bymethods ranging from nearest-neighbor to radial-basis-function interpolation.
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We will present scale-up tests involving distinct fluid and structure solvers, show-ing strong scalability in a real-world scenario. Tests have been conducted on theSuperMUC HPC system.
REFERENCES
B. Gatzhammer, Efficient and Flexible Partitioned Simulation of Fluid-StructureInteractions, PhD Thesis, Technische Universitat Munchen, Institut fur Informatik,2014.
http://www.precice.org
27. Finite Element Model-Based on-line Structural Health Monitoring (SHM)Systems with Fluid-Structure Interaction (FSI) Optimization
Bhuiyan Shameem Mahmood Ebna Hai, Helmut Schmidt University, Germany.
This research focuses on the newly developed mathematical model of a new fluid-structure interaction (FSI) problem, which is referred to as extended Fluid-StructureInteraction (eXFSI) problem in the well established Arbitrary Lagrangian Eulerian(ALE) framework framework. This model is used to design an on-live structuralhealth monitoring (SHM) system in order to determine the coupled acoustic andelastic wave propagation in moving domains and optimum locations for SHM sen-sors. The eXFSI is a strongly coupled problem of typical FSI with a wave propa-gation problem on the fluid-structure interface, where wave propagation problemsautomatically adopted the boundary conditions from of the typical FSI problem ateach time step. The ALE approach provides a simple, but powerful procedure tocouple solid deformations with fluid flows by a monolithic solution algorithm. Insuch a setting, the fluid problems are transformed to a fixed reference configurationby the ALE mapping. The goal of this work is the development of concepts for theefficient numerical solution of eXFSI problem, the analysis of various fluid-solid meshmotion techniques and comparison of different second-order time-stepping schemes.This work consists of the investigation of different time stepping scheme formulationsfor a nonlinear FSI problem coupling the acoustic/elastic wave propagation on thefluid-structure interface. Temporal discretization is based on finite differences andis formulated as an one step-θ scheme, from which we can consider the followingparticular cases: the implicit Euler, Crank-Nicolson, shifted Crank-Nicolson and theFractional-Step-θ schemes. The nonlinear problem is solved with Newton’s methodwhere the discretization is done with a Galerkin finite element scheme. The imple-mentation is accomplished via the software library package DOpElib and deal.II
for the computation of different eXFSI configurations.
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28. Optimal Control of an unsteady Fluid-Structure Interaction Problem
Lukas Failer, Technische Universitat Munchen
Fluid-structure interaction (FSI) problems have been extensively studied from the-oretical and numerical point of view in the last decade. However, especially in thecontext of optimal control problems for unsteady FSI problems no optimality systemsbased on rigorous analysis are available in the literature.
In this talk, we regard a model optimal control problem governed by a linear FSIproblem, establish necessary optimality conditions, and analyze the regularity of theoptimal solutions. To this end, we propose a novel symmetric monolithic formulationfor the linear FSI problem. This formulation leads to an adjoint equation withthe same structure as the considered linear FSI problem, which allows for a unifiedanalytical and numerical treatment of the state and the adjoint systems.
In the framework suggested in this talk, the coupling conditions in the adjoint systemshave exactly the same structure as for the state system. This is advantageous not onlyfrom the theoretical point of view but especially allows to use the same discretizationschemes and the same practical solution algorithms for both the state and the adjointsystems. The fact that the coupling conditions are directly incorporated in the varia-tional formulation allows for a natural usage of Galerkin finite element discretizationsis space and time. This is advantageous particularly for optimal control problems,since the two approaches optimize-then-discretize and discretize-then-optimize leadto the same discretization scheme.
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List of Participants
Augustin, Christoph p. 8
Medical University Graz
Graz, Austria
Birken, Philipp p. 16
Lund University
Lund, Sweden
Bornia, Giorgio p. 15
Texas Tech University
Lubbock, USA
Brinkmann, Felix
Heidelberg University
Heidelberg, Germany
Corsi, Giovanni
International School for Advanced Studies
Via Bonomea, Italia
DANG, Hong Lam
Orleans University
Orleans, France
Deparis, Simone p. 7
EPFL Lausanne
Lausanne, Switzerland
Ebna Hai, Bhuiyan
Helmut Schmidt University
Hamburg, Germany
Elbinger, Tobias p. 14
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Erlangen, Germany
RICAM Linz, Jan 11 – 15, 2016
List of Participants 27
Esser, Patrick
IWR Heidelberg
Heidelberg, Germany
Faghfori, Sahar
JKU Linz
Linz, Austria
Failer, Lukas p. 25
Technische Universitat Munchen
Munchen, Germany
Fontana, Nicola
Technische Universitat Munchen
Munchen, Germany
Fratrovic, Tomislav
University of Zagreb
Zagreb, Croatia
Frei, Stefan p. 12
Heidelberg University
Heidelberg, Germany
Galic, Marija
University of Zagreb
Zagreb, Croatia
Gangl, Peter
JKU Linz
Linz, Austria
Ghasemi, Ali
Technische Universitat Munchen
Munchen, Germany
Guglielmi, Roberto
RICAM
Linz, Austria
RICAM Linz, Jan 11 – 15, 2016
28 List of Participants
Gupta, Bineet Kumar
SRM University
Tamil Nadu, India
Hagmeyer, Nora
Technische Universitat Munchen
Munchen, Germany
Hessenthaler, Andreas p. 20
Universitat Stuttgart
Stuttgart, Germany
Hoang, Tuong
IUSS Pavia
Pavia, Italia
Hochsteger, Matthias
TU Wien
Vienna, Austria
Hofer, Christoph
RICAM
Linz, Austria
Janssen, Baerbel
KTH Stockholm
Stockholm, Sweden
Joshi, Saumitra
Technische Universitat Munchen
Munchen, Germany
Karabelas, Elias p. 9
Medical University Graz
Graz, Austria
RICAM Linz, Jan 11 – 15, 2016
List of Participants 29
Khodayari-Samghabadi,
Samaneh
Shahed University
Tehran, Iran
Klingebiel, Martin
IWR Heidelberg
Heidelberg, Germany
Kumar, Yajuvindra
M.K. Government, Degree College Ninowa Farrukhabad
Uttar Pradesh, India
yaju [email protected]
Lahnert, Michael p. 23
Universitat Stuttgart
Stuttgart, Germany
Langer, Ulrich
JKU Linz / RICAM
Linz, Austria
Lederer, Philipp
TU Wien
Vienna, Austria
Lijoka, Oluwaseun
Heriot Watt University Edinburgh
Edinburgh, UK
Lindner, Florian p. 23
Universitat Stuttgart
Stuttgart, Germany
Mang, Katrin
Heidelberg University
Heidelberg, Germany
RICAM Linz, Jan 11 – 15, 2016
30 List of Participants
Mantzaflaris, Angelos p. 19
RICAM
Linz, Austria
Mehl, Miriam p. 7
Universitat Stuttgart
Stuttgart, Germany
Meriem, Jedouaa
Grenoble Universite
Grenoble, France
Monasse, Laurent p. 10
CERMICS Paris
Paris, France
Monge, Azahar p. 17
Lund University
Lund, Sweden
Moore, Stephen E.
RICAM
Linz, Austria
Nakov, Svetoslaw
RICAM
Linz, Austria
Namseok, Kim
Korea Institute for Nuclear Safety
Seoul, South Korea
Nordsletten, David
King’s College London
London, UK
Quaini, Annalisa p. 14
University of Houston
Houston, USA
RICAM Linz, Jan 11 – 15, 2016
List of Participants 31
Rafetseder, Katharina
JKU Linz
Linz, Austria
Randrianasolo, Tsiry
Montannuniveritat Leoben
Leoben, Austria
Richter, Thomas
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Erlangen, Germany
Rudrusamy, Gobithaasan
University Malaysia Terengganu
Terengganu, Malaysia
Rupp, Andreas p. 19
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Erlangen, Germany
Rusch, Alexander
Technische Universitat Munchen
Munchen, Germany
Sajavicius, Svajunas
JKU Linz
Linz, Austria
Santiago, Alfonso p. 9
Barcelona University
Barcelona, Spain
Schuessler, Ina p. 18
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Erlangen, Germany
Shokrpour-Roudbari, Mahnaz p. 13
Eindhoven University of Technology
Eindhoven, Netherlands
RICAM Linz, Jan 11 – 15, 2016
32 List of Participants
Singhammer, Korbinian
Technische Universitat Munchen
Munchen, Germany
Sonner, Florian p. 15
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Erlangen, Germany
Toulopoulos, Ioannis p. 18
RICAM
Linz, Austria
Upnere, Sabine p. 21
Riga TU, Ventspils University College
Ventspils, Latvia
van Rees, Wim p. 22
Harvard University
MA, USA
Wick, Thomas
RICAM
Linz, Austria
Wolfmayr, Monika
RICAM
Linz, Austria
Yang, Huidong
RICAM
Linz, Austria
Zhang, Qinghui
University of Trento
Trento, Italia
RICAM Linz, Jan 11 – 15, 2016