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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.

Callihan , Robert S. and Wood , Aihua W.. (2012). 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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