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

✍ Scribed by Laurent Vernhet

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
149 KB
Volume
22
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by J. C. NeΒ΄deΒ΄lec

A boundary element method is introduced to approximate the solution of a scattering problem for the Helmholtz equation with a generalized Fourier-Robin-type boundary condition given by a second-order elliptic differential operator. The formulation involves three unknown fields, but is free from any hypersingular integral. Existence and uniqueness of the solution are established using a Babus\ ka inf-sup condition. When implementing the method, a lumping process allows to remove two fields from the formulation. The numerical solution has thus the same cost as the one of a problem relative to a usual Neumann boundary condition. Numerical tests confirm the ability of the method for solving this type of non-standard boundary value problems.

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