A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids  

作　　者：Hualong Feng Amlan Barua Shuwang Li Xiaofan Li 

机构地区：[1]Department of Applied Mathematics,Illinois Institute of Technology,Chicago,IL 60616,USA. [2]School of Science,Nanjing University of Science and Technology,Nanjing,Jiangsu 210094,P.R.China.

出　　处：《Communications in Computational Physics》2014年第2期365-387,共23页计算物理通讯（英文）

基　　金：supported by the NSF through Grant DMS-0923111,DMS-0914923;an Illinois Institute of Technology post-doctoral traveling allowance.

摘　　要：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.

关 键 词：Treecode PARALLEL ELASTICITY boundary integral method. 

分 类 号：O17[理学—数学]