A Modified Helmholtz Equation with Impedance Boundary Conditions

A Modified Helmholtz Equation with Impedance Boundary Conditions

Year:    2012

Author:    Robert S. Callihan, Aihua W. Wood

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 703–718

Abstract

Here considered is the problem of transient electromagnetic scattering from overfilled cavities embedded in an impedance ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those fields inside.  A Green's function solution is obtained for the exterior domain, while the interior problem is solved using finite element method. Well-posedness of the associated variational formulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-12S02

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 703–718

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Helmholtz equation impedance boundary conditions finite element method.

Author Details

Robert S. Callihan

Aihua W. Wood

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