A course space construction based on local Dirichlet-to-Neumann maps

Frédéric Nataf; Hua Xiang; Victorita Dolean Maini; Nicole Spillane

doi:10.1137/100796376

A course space construction based on local Dirichlet-to-Neumann maps

Frédéric Nataf, Hua Xiang, Victorita Dolean Maini, Nicole Spillane

Mathematics And Statistics

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Abstract

Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings.

Original language	English
Pages (from-to)	1623-1642
Number of pages	20
Journal	SIAM Journal on Scientific Computing
Volume	33
Issue number	4
Early online date	21 Jul 2011
DOIs	https://doi.org/10.1137/100796376
Publication status	E-pub ahead of print - 21 Jul 2011

Keywords

domain decomposition
coarse grid deflation
heterogeneous coefficients
course space
construction based
Dirichlet-to-Neumann maps

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N2 - Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings.

AB - Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings.

KW - domain decomposition

KW - coarse grid deflation

KW - heterogeneous coefficients

KW - course space

KW - construction based

KW - Dirichlet-to-Neumann maps

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ER -

A course space construction based on local Dirichlet-to-Neumann maps

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