ISSN:
1572-9044
Keywords:
boundary integral equations
;
prewavelets
;
preconditioned conjugate gradient
;
additive Schwarz
;
hierarchical basis
;
65N55
;
65N38
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We study simple preconditioners for the conjugate gradient method when used to solve matrix systems arising from some hypersingular and weakly singular integral equations. The preconditioners, which are of the type of hierarchical basis preconditioners, are based on the decomposition of the piecewise-linear (respectively piecewise-constant) functions as the sum of prewavelets (respectively derivatives of prewavelets). We prove that with these preconditioners the preconditioned systems have condition numbers uniformly bounded with respect to the degrees of freedom. Numerical experiments support our analysis.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018993624466
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