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://doi.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.