Dirac delta methods for Helmholtz transmission problems |
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Authors: | V Domínguez M-L Rapún F-J Sayas |
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Institution: | (1) Departamento Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain;(2) Departamento Matemática Aplicada, Universidad de Zaragoza C.P.S., 50018 Zaragoza, Spain |
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Abstract: | In this paper we use a boundary integral method with single layer potentials to solve a class of Helmholtz transmission problems
in the plane. We propose and analyze a novel and very simple quadrature method to solve numerically the equivalent system
of integral equations which provides an approximation of the solution of the original problem with linear convergence (quadratic
in some special cases). Furthermore, we also investigate a modified quadrature approximation based on the ideas of qualocation
methods. This new scheme is again extremely simple to implement and has order three in weak norms.
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Keywords: | 65R20 65N38 |
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