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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.

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