Boundary element preconditioners for a hypersingular integral equation on an interval Article DOI:
Cite this article as: McLean, W. & Steinbach, O. Advances in Computational Mathematics (1999) 11: 271. doi:10.1023/A:1018944530343 Abstract
We propose an almost optimal preconditioner for the iterative solution of the Galerkin equations arising from a hypersingular integral equation on an interval. This preconditioning technique, which is based on the single layer potential, was already studied for closed curves [11,14]. For a boundary element trial space, we show that the condition number is of order (1 + | log
h min|) 2, where h min is the length of the smallest element. The proof requires only a mild assumption on the mesh, easily satisfied by adaptive refinement algorithms. preconditioning techniques boundary element methods 65F35 65N22 65N38 References
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