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Two-Grid Deflated Krylov Methods for Linear Equations

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arxiv 2005.03070 v1 pith:5IVJXEMV submitted 2020-05-06 math.NA cs.NAhep-lat

Ronald B. Morgan , Travis Whyte , Walter Wilcox , Zhao Yang This is my paper · ORCID
classification math.NAcs.NAhep-lat
keywords gridapproachfinelinearmethodsbicgstabcoarseequations
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An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are first used on both the coarse and fine grids. Then another approach is given that has a restarted BiCGStab (or IDR) method on the fine grid. While BiCGStab is generally considered to be a non-restarted method, it works well in this context with deflating and restarting. Tests show this new approach can be very efficient for difficult linear equations problems.

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    hep-lat 2025-02 conditional novelty 5.0 of 10

    An SVD-based rank-k truncation of chirally split test vectors reduces Wilson fermion multigrid solve times on HSC and MILC ensembles.

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