A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

Y. Boubendir; X. Antoine; C. Geuzaine

doi:10.1016/j.jcp.2011.08.007

A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

Y. Boubendir, X. Antoine, C. Geuzaine

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

102 Scopus citations

Abstract

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.

Original language	English (US)
Pages (from-to)	262-280
Number of pages	19
Journal	Journal of Computational Physics
Volume	231
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2011.08.007
State	Published - Jan 20 2012

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Keywords

Domain decomposition methods
Finite elements
Helmholtz equation
Padé approximants

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10.1016/j.jcp.2011.08.007

Cite this

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title = "A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation",

abstract = "This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.",

keywords = "Domain decomposition methods, Finite elements, Helmholtz equation, Pad{\'e} approximants",

author = "Y. Boubendir and X. Antoine and C. Geuzaine",

note = "Funding Information: Y. Boubendir gratefully acknowledges support from NSF through grant No. DMS-1016405 . X. Antoine gratefully acknowledges support from the Agence Nationale pour la Recherche (Ref : ANR-09-BLAN-0057-01) ( http://www.microwave.math.cnrs.fr/ ) and the Fondation de Recherche pour l{\textquoteright}A{\'e}ronautique et l{\textquoteright}Espace (IPPON Project). C. Geuzaine gratefully acknowledges support from the Belgian Science Policy ( IAP P6/21 ), Belgian French Community ( ARC 09/14-02 ) and Walloon Region (WIST3 No 1017086 “ONELAB”).",

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AU - Antoine, X.

AU - Geuzaine, C.

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AB - This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.

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KW - Finite elements

KW - Helmholtz equation

KW - Padé approximants

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A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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