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Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems

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arxiv 2404.02758 v3 pith:I57FWHOQ submitted 2024-04-03 math.NA cs.NA

Frédéric Nataf , Emile Parolin This is my paper · ORCID
classification math.NAcs.NA
keywords coarsenon-symmetricadditiveeigenproblemsgeneralizedmethodpreconditionersschwarz
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Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of adaptive coarse spaces we present here is quite general since it applies to symmetric and non-symmetric problems, to symmetric preconditioners such as the additive Schwarz method (ASM) and to the non-symmetric preconditioner restricted additive Schwarz (RAS), as well as to exact or inexact subdomain solves. The coarse space is built by solving generalized eigenproblems in the subdomains and applying a well-chosen operator to the selected eigenvectors.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coarse space preconditioning for Generalized Optimized Schwarz Methods. Part I: continuous case

    math.NA 2026-08 conditional novelty 7.0 of 10

    A rank-r coarse space built from the top singular modes of the local scattering map makes the GOSM skeleton operator identity-plus-compact, giving superlinear GMRES convergence with explicit bounds.

  2. Theory of two-level Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation

    math.NA 2025-01 accept novelty 7.0 of 10

    With polynomial degree growing like log k, two-level additive and hybrid Schwarz GMRES converges in O((log k)^4) iterations for Helmholtz problems, with pollution-free piecewise-polynomial fine and coarse spaces.

  3. Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces

    math.NA 2025-09 conditional novelty 5.0 of 10

    In a large reproducible benchmark of two-level domain-decomposition solvers for the heterogeneous Helmholtz equation, harmonic and extended-harmonic spectral coarse spaces outperform DtN and Hk-GenEO in iteration coun...

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