A Parallel Adaptive Treecode Algorithm for Evolution of Elastically Stressed Solids (Communications in Computational Physics, 2018)
The evolution of precipitates in stressed solids is modeled by coupling aquasi-steady diffusion equation and a linear elasticity equation with dynamic boundary conditions. The governing equations are solved numerically using a boundaryintegral method (BIM). A critical step in applying BIM is to develop fast algorithms toreduce the arithmetic operation count of matrix-vector multiplications. In this paper,we develop a fast adaptive treecode algorithm for the diffusion and elasticity problemsin two dimensions (2D). We present a novel source dividing strategy to parallelize thetreecode. Numerical results show that the speedup factor is nearly perfect up to amoderate number of processors. This approach of parallelization can be readily implemented in other treecodes using either uniform or non-uniform point distribution. Wedemonstrate the effectiveness of the treecode by computing the long-time evolution ofa complicated microstructure in elastic media, which would be extremely difficult witha direct summation method due to CPU time constraint. The treecode speeds up computations dramatically while fulfilling the stringent precision requirement dictated bythe spectrally accurate BIM.