Exact Non-reflecting Boundary Conditions on General Domains

The authors present a new method for the realization of exact non-reflecting (transparent) boundary conditions in two dimensional direct scattering problems. This work is an extension of Keller, Givoli, and Grote's work on such conditions which required that the shape of the boundary be quite specific, i.e. circular or elliptical. The condition is enforced via the Dirichlet-Neumann operator (DNO) which, on general boundaries, presents the main difficulty in the method. The implementation is performed by one of two perturbative methods (where the perturbation parameter measures the deformation of the general geometry from a canonical one). A rigorous proof of the analyticity for the DNO with respect to this perturbation parameter is presented. Numerical results show both perturbative methods are fast and accurate, and can enable significant computational savings.

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