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

Date

2001

Authors

Tran, T
Stephan, E

Journal Title

Journal ISSN

Volume Title

Publisher

Springer

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 + logp)2 maxi(1 + 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(1 + logH/δ)2(1 + logp)2 where δ is the size of the overlap and H = maxiHi. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that case is b ounded by c log2 M, where M is the degrees of freedom.

Description

Keywords

Keywords: Boundary element method; Galerkin methods; Integral equations; Laplace transforms; Polynomials; Schwarz preconditioners; Matrix algebra Additive Schwarz; Boundary element; Geometric mesh; h-p version Galerkin; Preconditioned conjugate gradient

Citation

Source

Computing

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1007/s006070170016

Restricted until

2037-12-31