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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

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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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