Abstract
The implementations of the domain decomposition, SOR, multigrid and conjugate gradient method on CM-5 and Cray C-90 are described for the Laplace's equation on the unit square and L-shaped region. Domain decomposition method uses the Schwarz alternating method. In each domain we take the one-dimensional FFT to convert the problem into the tridiagonal systems which are solved by the scientific libraries installed in the CM-5 and the Cray C-90. On the CM-5 the V-cycle multigrid with symmetric smoothings on P-1 finite element spaces is run with red/black Gauss-Seidel relaxation. Multigrid with natural order Gauss-Seidel relaxation is used on the Cray C-90. While natural order SOR is used in the Cray C-90, R/B SOR is performed on the CM-5. Multigrid is the fastest method on the CM-5 and three methods except SOR give similar performances on Cray C-90.
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This research was partially supported by the National Science Foundation under Grant No. CDA-9024618.
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Lee, CO. A comparison of some standard elliptic solvers: CM-5 vs. Cray C-90. J Sci Comput 11, 99–126 (1996). https://doi.org/10.1007/BF02088819
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DOI: https://doi.org/10.1007/BF02088819