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On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
Abstract

Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
A Finite Element Method For Approximating ElectroMagnetic Scattering From A Conducting Object
 Numerische Mathematik
"... . Here we provide an error analysis of a fully discrete nite element { Fourier series method for approximating Maxwell's equations. The problem is to approximate the electromagnetic eld scattered by a bounded, inhomogeneous and anisotropic body. The method is to truncate the calculation domain ..."
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Cited by 7 (0 self)
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. Here we provide an error analysis of a fully discrete nite element { Fourier series method for approximating Maxwell's equations. The problem is to approximate the electromagnetic eld scattered by a bounded, inhomogeneous and anisotropic body. The method is to truncate the calculation domain using a series solution of the eld away from this domain. We rst prove a decomposition for the PoincareSteklov operator on this boundary into an isomorphism and a compact perturbation. This is proved using a novel argument in which the scattering problem is viewed as a perturbation of the free space problem. Using this decomposition, and edge elements to discretize the interior problem we prove an optimal error estimate for the overall problem. 1. Introduction. Motivated by the problem of computing the interaction of microwave radiation with biological tissue, we shall analyze a nite element method for approximating Maxwell's equations in an innite domain. We suppose that there is a bounde...