A parallel DSDADI method for solution of the steady state diffusion equation |
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| Affiliation: | 1. Department of Applied Science, University of California at Davis, Davis, CA, USA;2. Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551, USA;1. Dept. of Mechanical Engineering, Osaka University, 2-1 Yamada-oka, Suita-city, Osaka, 565-0871, Japan;2. Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi, 980-8577, Japan;3. Dept. of Mechanical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK |
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| Abstract: | A parallel diagonally scaled dynamic alternating-direction-implicit (DSDADI) method is shown to be an effective algorithm for solving the 2D and 3D steady-state diffusion equation on large uniform Cartesian grids. Empirical evidence from the parallel solution of large gridsize problems suggests that the computational work done by DSDADI to converge over an Nd grid with continuous diffusivity is of lower order than O(Nd+α) for any fixed α > 0. This is in contrast to the method of diagonally scaled conjugate gradients (DSCG), for which the computational work necessary for convergence is O(Nd+1). Furthermore, the combination of diagonal scaling, spatial domain decomposition (SDD), and distributed tridiagonal system solution gives the DSDADI algorithm reasonable scalability on distributed-memory multiprocessors such as the CRAY T3D. Finally, an approximate parallel tridiagonal system solver with diminished interprocessor communication exhibits additional utility for DSDADI. |
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