Volume 6, Issue 2
A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems

Chao Jin & Xiao-Chuan Cai

DOI:

Commun. Comput. Phys., 6 (2009), pp. 342-353.

Published online: 2009-06

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  • Abstract

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loève expansions are used to represent the stochastic variables and the stochastic Galerkin method with double orthogonal polynomials is used to derive a sequence of uncoupled deterministic equations. We show numerically that the Schwarz preconditioned recycling GMRES method is an effective technique for solving the entire family of linear systems and, in particular, the use of recycled Krylov subspaces is the key element of this successful approach.

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@Article{CiCP-6-342, author = {}, title = {A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {2}, pages = {342--353}, abstract = {

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loève expansions are used to represent the stochastic variables and the stochastic Galerkin method with double orthogonal polynomials is used to derive a sequence of uncoupled deterministic equations. We show numerically that the Schwarz preconditioned recycling GMRES method is an effective technique for solving the entire family of linear systems and, in particular, the use of recycled Krylov subspaces is the key element of this successful approach.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7683.html} }
TY - JOUR T1 - A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems JO - Communications in Computational Physics VL - 2 SP - 342 EP - 353 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7683.html KW - AB -

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loève expansions are used to represent the stochastic variables and the stochastic Galerkin method with double orthogonal polynomials is used to derive a sequence of uncoupled deterministic equations. We show numerically that the Schwarz preconditioned recycling GMRES method is an effective technique for solving the entire family of linear systems and, in particular, the use of recycled Krylov subspaces is the key element of this successful approach.

Chao Jin & Xiao-Chuan Cai. (2020). A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems. Communications in Computational Physics. 6 (2). 342-353. doi:
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