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Volume 4, Issue 6
A Modified Helmholtz Equation with Impedance Boundary Conditions

Robert S. Callihan & Aihua W. Wood

DOI: 10.4208/aamm.12-12S02

Adv. Appl. Math. Mech., 4 (2012), pp. 703-718.

Published online: 2012-12

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  • 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.

  • Keywords

Helmholtz equation, impedance boundary conditions, finite element method.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-703, author = {Callihan , Robert S. and Wood , Aihua W.}, title = {A Modified Helmholtz Equation with Impedance Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-12S02}, url = {http://global-sci.org/intro/article_detail/aamm/144.html} }
TY - JOUR T1 - A Modified Helmholtz Equation with Impedance Boundary Conditions AU - Callihan , Robert S. AU - Wood , Aihua W. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 703 EP - 718 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S02 UR - https://global-sci.org/intro/article_detail/aamm/144.html KW - Helmholtz equation, impedance boundary conditions, finite element method. AB -

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.

Robert S. Callihan & Aihua W. Wood. (1970). A Modified Helmholtz Equation with Impedance Boundary Conditions. Advances in Applied Mathematics and Mechanics. 4 (6). 703-718. doi:10.4208/aamm.12-12S02
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