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Local absorbing boundary conditions for elliptical shaped boundaries

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
227
Issue
18
Identifiers
DOI: 10.1016/j.jcp.2008.05.010
Keywords
  • Helmholtz Equation
  • Absorbing Boundary Conditions
  • Mathieu Functions
Disciplines
  • Computer Science

Abstract

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.

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