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Improved interface conditions for 2D domain decomposition with corners: a theoretical determination

Content Provider	Springer Nature Link
Author	Chniti, Chokri Nataf, Frédéric Nier, Francis
Copyright Year	2008
Abstract	This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. The problem amounts to determining the coefficients of interface boundary conditions so that the domain decomposition algorithm has rapid convergence. Specific problems occur in the presence of conical singularities. Starting from the method used for regular interfaces, we derive a local improvement by matching the singularities, that is, the initial terms of the asymptotic expansion arond the corner, provided by Kondratiev theory. This theoretical approach leads to the explicit computation of coefficients in the interface boundary conditions, which have been tested numerically. This final numerical step is presented in a companion article [4]. This article focuses on the method used to compute these coefficients and provides detailed examples for a model problem.
Starting Page	111
Ending Page	147
Page Count	37
File Format	PDF
ISSN	00080624
Journal	CALCOLO
Volume Number	45
Issue Number	2
e-ISSN	11265434
Language	English
Publisher	Springer Milan
Publisher Date	2008-10-08
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Corner singularity domain decomposition method Kodratiev theory Theory of Computation Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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Improved Interface Conditions for 2D Domain Decomposition with Corners: Numerical Applications

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