Boundary element solution of a scattering problem involving a generalized impedance boundary condition

A boundary element method is introduced to approximate the solution of a sc attering problem for the Helmholtz equation with a generalized Fourier-Robi n-type boundary condition given by a second-order elliptic differential ope rator. The formulation involves three unknown fields, but is free from any hypersingular integral. Existence and uniqueness of the solution are establ ished using a Babuska inf-sup condition. When implementing the method, a lu mping process allows to remove two fields from the formulation. The numeric al solution has thus the same cost as the one of a problem relative to a us ual Neumann boundary condition. Numerical tests confirm the ability of the method for solving this type of non-standard boundary value problems. Copyr ight (C) 1999 John Wiley & Sons, Ltd.