A comparison of some standard elliptic solvers: CM-5 vs. Cray C-90 (Q2564861)

The Laplace equation on the unit square and on an \(L\)-shaped region is solved on the parallel computer using the domain decomposition method, the successive overrelaxation (SOR) method, the multigrid method and the conjugate gradient method. The implementations of these problems on CM-5 and Cray C-90 computers are described end evaluated. The domain decomposition method uses the Schwarz alternating direction method. In each domain the one-dimensional fast Fourier transform is taken to convert the problem into the tridiagonal systems which are solved by the scientific libraries installed in the CM-5 and Cray-90. On the CM-5 the \(V\)-cycle multigrid method 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. Natural order SOR is used on Cray C-90, while \(R/B\) SOR on CM-5. The main result is that multigrid is the fasted method on CM-5 and three methods except for SOR give similar performances on Cray C-90.