Geodesic
Experiments with Krylov subspace methods on a massively parallel computer
Applications of Mathematics, Tome 38 (1993) no. 6, pp. 440-451

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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.
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.
DOI : 10.21136/AM.1993.104566
Classification : 65F10, 65W05, 65Y05
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 
Hanke, Martin; Hochbruck, Marlis; Niethammer, Wilhelm. Experiments with Krylov subspace methods on a massively parallel computer. Applications of Mathematics, Tome 38 (1993) no. 6, pp. 440-451. doi: 10.21136/AM.1993.104566
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     zbl = {0810.65030},
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