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NESTED KRYLOV METHODS FOR SHIFTED LINEAR SYSTEMS
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DOI：10.1137/140979927.png)
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摘要
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We consider Krylov subspace methods that are designed for sequences of shifted linear systems. For the efficient numerical solution of shifted problems, the shift-invariance property of the corresponding Krylov subspaces is used such that a Krylov basis is computed only once for all shifted systems. Preconditioners in general destroy this shift-invariance property. Known preconditioners that preserve the shift-invariance are the shift-and-invert preconditioner as well as polynomial preconditioners. In this work, we introduce a new approach to the preconditioning of multi-shift Krylov methods. In our new nested framework, we use an inner multi-shift Krylov method as a flexible preconditioner within an outer multi-shift Krylov method. In order to preserve the shift-invariance of the underlying Krylov subspaces, we require collinear residuals for the inner Krylov method. This new approach has been implemented for two possible combinations, namely, FOM-FGMRES and IDR-FQMRIDR, and has been tested for various numerical examples arising from geophysical applications.
Keyword:
Krylov subspace methods
shifted linear systems
flexible preconditioning
inner-outer Krylov methods
induced dimension reduction (IDR) method
time-harmonic wave equation
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2.6
论文数:
5.1K
被引数:
1.8W
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