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PRECONDITIONED INFINITE GMRES FOR PARAMETERIZED LINEAR SYSTEMS
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DOI：10.1137/22M1502380.png)
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摘要
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We are interested in obtaining solutions to parameterized linear systems of the form A(mu)x(mu) = b for many values of the parameter mu. Here A(mu) is large, sparse, and nonsingular with a nonlinear, analytic dependence on mu. Our approach approximates the solution to a linearized system linearization is based on a companion matrix similar to the operator in the infinite Arnoldi method novel approach applies the action of a preconditioner inexactly, providing performance improvement pp. 1382-1405] without a loss of accuracy in general. The method returns a function (x) over tilde(mu) which is cheap to evaluate for different mu. We show that the error of our method is estimated based on the magnitude of the parameter mu, the inexactness of the preconditioning, and the spectrum of the companion matrix. Numerical examples from a finite element discretization of a Helmholtz equation with a parameterized material coefficient illustrate the competitiveness of our approach. The software used in the simulations is publicly available online, and all the experiments are reproducible.
Keyword:
inexact preconditioning
parameterized linear systems
Krylov methods
companion linearization
shifted linear systems
infinite Arnoldi
inner stopping criteria
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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