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Conference Papers Year : 2017

Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD

Abstract

Krylov methods such as GMRES are efficient iterative methods to solve large sparse linear systems, with only a few key kernel operations: the matrix-vector product, solving a preconditioning system, and building the orthonormal Krylov basis. Domain Decomposition methods allow parallel computations for both the matrix-vector products and preconditioning by using a Schwarz approach combined with deflation (similar to a coarse-grid correction). However, building the orthonormal Krylov basis involves scalar products, which in turn have a communication overhead. In order to avoid this communication, it is possible to build the basis by a block of vectors at a time, sometimes at the price of a loss of orthogonality. We define a sequence of such blocks with a variable size. We show through some theoretical results and some numerical experiments that increasing the block size as a Fibonacci sequence improves stability and convergence.
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Dates and versions

hal-01528636 , version 1 (23-11-2017)

Identifiers

  • HAL Id : hal-01528636 , version 1

Cite

David Imberti, Jocelyne Erhel. Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD. DD24 - International Conference on Domain Decomposition Methods, Feb 2017, Longyearbyen, Norway. ⟨hal-01528636⟩
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