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

A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids

Hualong Feng 1, Amlan Barua 2, Shuwang Li 2, Xiaofan Li 2*

1 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.
2 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.

Received 22 August 2012; Accepted (in revised version) 22 May 2013
Available online 10 September 2013


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.

AMS subject classifications: 65D30, 65N35, 74B05

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Key words: Treecode, parallel, elasticity, boundary integral method.

*Corresponding author.
Email: (H. Feng), (A. Barua), (S. Li), (X. Li)

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