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The construction of some efficient preconditioners in the boundary element method

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Abstract

The discretization of first kind boundary integral equations leads in general to a dense system of linear equations, whose spectral condition number depends on the discretization used. Here we describe a general preconditioning technique based on a boundary integral operator of opposite order. The corresponding spectral equivalence inequalities are independent of the special discretization used, i.e., independent of the triangulations and of the trial functions. Since the proposed preconditioning form involves a (pseudo)inverse operator, one needs for its discretization only a stability condition for obtaining a spectrally equivalent approximation.

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Steinbach, O., Wendland, W. The construction of some efficient preconditioners in the boundary element method. Advances in Computational Mathematics 9, 191–216 (1998). https://doi.org/10.1023/A:1018937506719

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