Experiments with Krylov subspace methods on a massively parallel computer
Different Krylov subspace iterative methods are compared in numerical experiments on the MasPar MP-1, a massively parallel computer with 16K processors. They include the conjugate gradient type methods BiCGStab of \textit{H. A. Van der Vorst} [SIAM J. Sci. Stat. Comput. 13, No. 2, 631-644 (1992; Zbl 0761.65023)] and GMRES of \textit{Y. Saad} and \textit{M. H. Schultz} [ibid. 7, 856-869 (1986; Zbl 0599.65018)], two- and four-step semiiterative methods as they are presented in the papers of \textit{T. A. Manteuffel} [Numer. Math. 28, 307-327 (1977; Zbl 0361.65024)] and \textit{W. Niethammer} and \textit{R. S. Varga} [ibid. 41, 177-206 (1983; Zbl 0509.65016)] and the hybrid GMRES-Richardson method. The above methods are also tested with preconditioning of the algebraic system matrix by the symmetric successive overrelaxation with red-black ordering and relaxation parameter \(W = 1\). The authors conclude that within their set of examples the semiiterative and hybrid methods are more attractive. They note also that the semiiterative method achieved the required accuracy fastest, however the a priori determination of the parameters, that are required for such methods is not always practical. The results of the experiment are influenced in particular by the fact that in parallel computers the cost of multiplication of matrix by vector is less than for scalar products.
scientific article; zbMATH DE number 558557
scientific article