Volume 15, Issue 2
A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids

Hualong Feng, Amlan Barua, Shuwang Li & Xiaofan Li

Commun. Comput. Phys., 15 (2014), pp. 365-387.

Published online: 2014-02

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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.

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@Article{CiCP-15-365, author = {}, title = {A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {2}, pages = {365--387}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220812.220513a}, url = {http://global-sci.org/intro/article_detail/cicp/7098.html} }
TY - JOUR T1 - A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids JO - Communications in Computational Physics VL - 2 SP - 365 EP - 387 PY - 2014 DA - 2014/02 SN - 15 DO - http://dor.org/10.4208/cicp.220812.220513a UR - https://global-sci.org/intro/article_detail/cicp/7098.html KW - AB -

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.

Hualong Feng, Amlan Barua, Shuwang Li & Xiaofan Li. (2020). A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids. Communications in Computational Physics. 15 (2). 365-387. doi:10.4208/cicp.220812.220513a
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