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.
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McLean, W., Steinbach, O. Boundary element preconditioners for a hypersingular integral equation on an interval. Advances in Computational Mathematics 11, 271–286 (1999). https://doi.org/10.1023/A:1018944530343
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DOI: https://doi.org/10.1023/A:1018944530343