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A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids

Published online by Cambridge University Press:  03 June 2015

Hualong Feng ,
Amlan Barua ,
Shuwang Li  and
Xiaofan Li
Hualong Feng*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, P.R. China
Amlan Barua*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
Shuwang Li*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
Xiaofan Li*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
*
Email:hfeng8@iit.edu
Email:abarua@hawk.iit.edu
Email:sli@math.iit.edu
Corresponding author.Email:lix@iit.edu
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Abstract

The evolution of precipitates in stressed solids is modeled by coupling a quasi-steady diffusion equation and a linear elasticity equation with dynamic boundary conditions. The governing equations are solved numerically using a boundary integral method (BIM). A critical step in applying BIM is to develop fast algorithms to reduce the arithmetic operation count of matrix-vector multiplications. In this paper, we develop a fast adaptive treecode algorithm for the diffusion and elasticity problems in two dimensions (2D). We present a novel source dividing strategy to parallelize the treecode. Numerical results show that the speedup factor is nearly perfect up to a moderate number of processors. This approach of parallelization can be readily implemented in other treecodes using either uniform or non-uniform point distribution. We demonstrate the effectiveness of the treecode by computing the long-time evolution of a complicated microstructure in elastic media, which would be extremely difficult with a direct summation method due to CPU time constraint. The treecode speeds up computations dramatically while fulfilling the stringent precision requirement dictated by the spectrally accurate BIM.

Keywords

65D3065N3574B05Treecodeparallelelasticityboundary integral method
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014 , pp. 365 - 387
Copyright
Copyright © Global Science Press Limited 2014

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