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

Authors:
T. Tran;E. P. Stephan
Affiliations:
-;-
Venue:
Computing
Year:
2001

Citing 14
Cited 2

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Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method

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Iterative Substructuring for Hypersingular Integral Equations in $\Bbb R^3$

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hp-adaptive two-level methods for boundary integral equations on curves

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Additive Schwarz preconditioners for the h-p version boundary-element approximation to the hypersingular operator in three dimensions

International Journal of Computer Mathematics

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Abstract

We study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind, which arise from the Neumann problems for the Laplacian in two dimensions. Overlapping and non-overlapping methods are considered. We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by c(1 + log p)2 maxi + logHi/hi) where Hi is the length of the i-th subdomain, hi is the maximum length of the elements in this subdomain, and p is the maximum polynomial degree used. For the overlapping method, we prove that the condition number is bounded by c(l + log H/z (I + logp)2 where z is the size of the overlap and H = maxi Hi. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that case is bounded by c log2 M, where M is the degrees of freedom.