Adaptive Mesh Modification in Parallel Framework

Application of parFUMSandhya Mangala (MIE)

Prof. Philippe H. Geubelle (AE)

University of Illinois, Urbana-Champaign

October 18, 2005

4th Annual Workshop on Charm++ and its Applications

Overview

• Motivation

• Objective

• Adaptive Mesh Modification

• Results

• Conclusions

• Future work

Motivation

http://www.uni-stuttgart.de/ibs/research/adaptive/

http://www.tp1.ruhr-uni-bochum.de/~dreher/racoon/example.html

Adaptive mesh modification

– Optimum mesh spacing cannot be determined a priori

– Mesh repair in Lagrangian formulation

– Problems of strain localization

high velocity impact problems

Parallel programming

– Reduction in

computational time

Objective – Current work

• Trade-off between solution accuracy and cost of computation

• Capture solution with Mesh Adaptivity

– Refine in areas of interest

– Coarsen elsewhere

– Ability to do so in parallel

• ParFUM: provides adaptivity on parallel unstructured meshes

– Support high-level refinement and coarsening algorithms

– Straightforward interface

– Parallelism built in at primitive level

1-D Wave Propagation Problem• Simulating 1D wave propagation

problem• Bottom end fixed• Top end pulled with constant velocity• Side edges on rollers• Shock wave propagating from top to

bottom at the dilatational wave speed• GOAL: To accurately capture shock

with fine mesh• Dynamically modify mesh based on the

normalized velocity gradient

v

Mesh Adaptivity - Criterion

• Based on normalized velocity gradient

v B v B v B v

v B v B v B v

v v v

x x x x

y y y y

x y

1 1 3 2 5 3

2 1 4 2 6 3

2 2

v3x,v3y

v1x,v1y

v2x,v2y

N orm alized velocity grad ien tv

v

m ax ( )

G.T. Camacho and M. Ortiz, 1997

Initial Serial Code

• F90 code

• Explicit time-stepping scheme

• 2 D dynamic code

C

B

A

D

OldNew

Find Longest edge and add new node at mid point

Refinement Strategy

C

B

AOld Triangle

For the triangle to be refined

Adjacent Triangle

Coarsening Strategy

Region of mesh to be coarsened

Triangles being squashed

Nodes merge

Parallel Code Organization• Init

– Read input mesh – Read material properties, boundary conditions and loading– Register data with parFUM– Set up ghost layer– Partition the mesh

• Driver– Access data registered in init– Time loop

– Compute solution on each chunk– Update shared/ghost data– Find regions for refinement and coarsening– Resize arrays when needed– parFUM refinement/coarsening calls– Solution transfer after mesh adaptivity

– End of time loop

parFUM - Features

• Handles – Mesh partitioning– Resizing the arrays– Solution transfer– Communication across chunks

• Mesh quality measures built in – Refinement

• Does not degrade the quality of mesh– Coarsening

• Targets “not” so good elements– Adaptive mesh

• Preserves the quality of mesh

Sequential Refinement and Coarsening Results

Shock propagation and reflection down the length of the bar

Adaptive mesh modification to capture the shock propagation

Solution Comparison

Initial Mesh

Adaptive Mesh

Fine Mesh

Initial Adaptive Fine

# nodes 278 400 1666

# elements 467 650 3092

Parallel Refinement and Coarsening

Conclusions

1. Adaptive refinement - parallel

2. Adaptive coarsening - parallel

3. Adaptive mesh modification – Refinement and coarsening

• Parallel adaptive mesh modification tested

Future Work

• 3D parallel refinement and coarsening

• 3D adaptive cohesive finite element code

Crack propagation with adaptive mesh modification in parallel framework• Parallel cohesive code• Refining and coarsening of cohesive elements

http://www.zaczek.com/research/uiuc_thesis/node56.html#fig:ch5_adaptcrack

AcknowledgementsParallel Programming Group

• Terry L Wilmarth – Refinement and Coarsening Algorithms and Implementation

• Sayantan Chakravorty – FEM interface• Nilesh Choudhury, Isaac Dooley – Parallel implementation • Orion Sky Lawlor – Charm ++ and Parallel Implementation

Support

• NSF

Questions?