Experiments with Krylov subspace methods on a massively parallel computer

@article{Hanke1993,
abstract = {In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total computing time than on the basis of number of iterations required to achieve a given accuracy. Our limited numerical experiments here suggest that, in terms of total computing time, semiiterative and hybrid methods are very attractive for such MASPAR implementations.},
author = {Hanke, Martin, Hochbruck, Marlis, Niethammer, Wilhelm},
journal = {Applications of Mathematics},
keywords = {massively parallel computers; iterative methods; nonsymmetric linear systems; Krylov subspace methods; preconditionings; parallel computation; Krylov subspace iterative methods; conjugate gradient type methods; BiCGStab; semiiterative methods; GMRES-Richardson method; successive overrelaxation; red-black ordering; parallel computation; Krylov subspace iterative methods; conjugate gradient type methods; BiCGStab; semiiterative methods; GMRES-Richardson method; preconditioning; successive overrelaxation; red-black ordering},
language = {eng},
number = {6},
pages = {440-451},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Experiments with Krylov subspace methods on a massively parallel computer},
url = {http://eudml.org/doc/15764},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Hanke, Martin
AU - Hochbruck, Marlis
AU - Niethammer, Wilhelm
TI - Experiments with Krylov subspace methods on a massively parallel computer
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 440
EP - 451
AB - In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total computing time than on the basis of number of iterations required to achieve a given accuracy. Our limited numerical experiments here suggest that, in terms of total computing time, semiiterative and hybrid methods are very attractive for such MASPAR implementations.
LA - eng
KW - massively parallel computers; iterative methods; nonsymmetric linear systems; Krylov subspace methods; preconditionings; parallel computation; Krylov subspace iterative methods; conjugate gradient type methods; BiCGStab; semiiterative methods; GMRES-Richardson method; successive overrelaxation; red-black ordering; parallel computation; Krylov subspace iterative methods; conjugate gradient type methods; BiCGStab; semiiterative methods; GMRES-Richardson method; preconditioning; successive overrelaxation; red-black ordering
UR - http://eudml.org/doc/15764
ER -