Multiplicative Schwarz Algorithms for the Galerkin Boundary Element Method

Authors:
Matthias Maischak
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 6

Two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method for 2-d problems

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Multiplicative Schwarz algorithms for the p-version Galerkin boundary element method in 3D

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An efficient algebraic multigrid preconditioner for a fast multipole boundary element method

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A multilevel additive Schwarz method for a hypersingular integral equation on an open curve with graded meshes

Applied Numerical Mathematics
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Schwarz preconditioned CG algorithm for the mortar finite element

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Abstract

We study the multiplicative Schwarz method for the h- and the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the first kind. For both integral equations we prove that the contraction rate of the multiplicative Schwarz operator is strictly less than 1 for the h-version for the two level and the multilevel methods, whereas for the p-version we show that the contraction rate approaches one only logarithmically in p for the 2-level method. Computational results are presented for both the h-version and the p-version which support our theory.