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On the performance of some rapid elliptic solvers on a vector processor. (English) Zbl 0661.65100
The authors present a comparative numerical study of several different solvers of two-dimensional elliptic partial differential equations on a CRAY-1S in vector mode. The solvers included:
1. The vectorized multigrid routines MGD1V and MGD5V [cf. P. Wesseling, Lect. Notes Math. 960, 614-630 (1982; Zbl 0505.65052); and P. W. Hemker, R. Kettler, P. Wesseling and P. M. de Zeeuw, Appl. Math. Comput. 13, 311-326 (1983; Zbl 0527.65070)], which use incomplete factorization as smoothers.
2. The code MG00 [cf. H. Foerster and K. Witsch, GMD-Stud. 70 (1982; Zbl 0488.65046)] based on red-black Gauss-Seidel.
3. A preconditioned conjugate gradient code developed by the authors.
4. Two direct methods HWSCRT and BLKTRI from FISHPAK [cf. P. N. Swarztrauber and R. A. Sweet, ACM Trans. Math. Software 5, 352-364 (1979; Zbl 0419.35043)] based on cyclic reduction.
Reviewer: S.F.McCormick
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y05 Parallel numerical computation
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