Solving large sparse linear systems with a variable s-step GMRES preconditioned by DD
International audience 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...
Main Authors: | , |
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Other Authors: | , , , , , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2017
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Subjects: | |
Online Access: | https://hal.inria.fr/hal-01528636 https://hal.inria.fr/hal-01528636/document https://hal.inria.fr/hal-01528636/file/fibgmres.pdf |
Summary: | International audience 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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