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

We study a 2-level multiplicative Schwarz method for the p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the p version grows only logarithmically in p and is i...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 56; no. 10; pp. 1370 - 1382
Main Author: Maischak, Matthias
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.10.2006
Elsevier
Subjects:
Exact sciences and technology
Mathematics
Multiplicative Schwarz operator
Numerical analysis
Numerical analysis. Scientific computation
p-version boundary integral equation method
Partial differential equations, boundary value problems
Preconditioned conjugate gradient algorithm
Sciences and techniques of general use
Multiplicative Schwarz operator
Preconditioned conjugate gradient algorithm
65N55
p-version boundary integral equation method
65N38
Conjugate gradient method
Convergence acceleration
Singular equation
Schwarz method
Numerical analysis
Applied mathematics
First integral
Convergence rate
Galerkin method
Preconditioning
Boundary element method
Boundary integral equations
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary:We study a 2-level multiplicative Schwarz method for the p version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3D. We prove that the rate of convergence of the multiplicative Schwarz operator for the p version grows only logarithmically in p and is independent of h.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2006.03.019