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Biorthogonal wavelet bases for the boundary element method
Author(s) -
Harbrecht Helmut,
Schneiderd Reinhold
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310171
Subject(s) - biorthogonal system , wavelet , mathematics , biorthogonal wavelet , galerkin method , basis (linear algebra) , mathematical analysis , boundary (topology) , scheme (mathematics) , basis function , finite element method , wavelet transform , geometry , computer science , artificial intelligence , physics , thermodynamics
As shown by Dahmen, Harbrecht and Schneider [7, 23, 32], the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate wavelet bases on manifolds based on the biorthogonal spline wavelets of A. Cohen, I. Daubechies and J.‐C. Feauveau [4]. By numerical experiments we demonstrate that it is worthwhile to spent effort on their construction to increase the performance of the wavelet Galerkin scheme considerably. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)