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Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems
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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 2 Pith papers
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Theory of two-level Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation
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.
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Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces
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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