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Two-Level Additive Schwarz Preconditioners for the h-p Version of the Galerkin Boundary Element Method for 2-d Problems

Two-Level Additive Schwarz Preconditioners for the h-p Version of the Galerkin Boundary Element... 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   where H i is the length of the i-th subdomain, h i 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   where δ is the size of the overlap and H=max i H i . 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 clog2 M, where M is the degrees of freedom. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computing Springer Journals

Two-Level Additive Schwarz Preconditioners for the h-p Version of the Galerkin Boundary Element Method for 2-d Problems

Tran, T.; Stephan, E. P.
Computing , Volume 67 (1) – Jul 1, 2001
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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Springer-Verlag Wien
Subject
Computer Science; Computer Science, general; Information Systems Applications (incl.Internet); Computer Communication Networks; Software Engineering; Artificial Intelligence (incl. Robotics); Computer Appl. in Administrative Data Processing
ISSN
0010-485X
eISSN
1436-5057
DOI
10.1007/s006070170016
Publisher site
See Article on Publisher Site

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   where H i is the length of the i-th subdomain, h i 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   where δ is the size of the overlap and H=max i H i . 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 clog2 M, where M is the degrees of freedom.

Journal

Computing – Springer Journals

Published: Jul 1, 2001

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