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IMA Journal of Numerical Analysis 1997 17(4):603-619; doi:10.1093/imanum/17.4.603
© 1997 by Institute of Mathematics and its Applications
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Hierarchical basis methods for hypersingular integral equations

THANG CAO

School of Mathematics, University of New South Wales Kensington, NSW 2052, Australia

In this paper we present hierarchical basis methods for the Galerkin approximation of hypersingular integral equations on the interval {Gamma} = (–1,1). The condition number of the stiffness matrix with respect to the hierarchical basis is shown to behave like O(|logh|2). The implementations are based on the preconditioned conjugate gradient method using a hierarchical basis (HB) preconditioner. The numerical results are presented with a comparison between the HB preconditioner and the BPX (Bramble, Pasciak and Xu) preconditioner.


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