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 - <p style="text-align: justify;">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. &nbsp;A Green&#39;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.</p>