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Boundary element solution of a scattering problem involving a generalized impedance boundary condition. (Résolution par éléments finis de frontière d’un problème de diffraction d’onde comportant une condition aux limites d’impédance généralisée.) (French. Abridged English version) Zbl 0837.65130
Summary: A boundary element method is introduced to approximate the solution of a scattering problem for the Helmholtz equation involving a generalized impedance boundary condition given by an elliptic differential operator of order 2. The method is based on the reduction of the boundary value problem to an integro-differential variational system on the boundary involving three unknown fields but without hypersingular integrals. In the numerical implementation, a lumping process leaves only one unknown field in the formulation. Numerical tests confirm the ability of the method to solve efficiently this type of non standard problems.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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