Local absorbing boundary conditions for elliptical shaped boundaries

Authors:
M. Medvinsky;E. Turkel;U. Hetmaniuk
Affiliations:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185, United States
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an ellipse. We solve the Helmholtz equation with both finite differences and finite elements. We also introduce a new boundary condition for an ellipse based on a modal expansion.