A vector absorbing boundary condition for vector potential satisfying the Lorentz gauge

Author

Deeley, E.M.

Author_Institution

Dept. of Electron. & Electr. Eng., King´´s Coll., London, UK

Volume

32

Issue

3

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

858

Lastpage

861

Abstract

A vector absorbing boundary condition is derived for a vector potential which satisfies the Lorentz gauge, based on a form of the Representation theorem for field quantities having non-zero divergence. The potential is assumed to be the linear superposition of those of arbitrarily arranged Hertzian dipoles, which potentials are individually particular solutions of the Helmholtz equation. Compared with ABCs derived for fields a penalty is introduced by the non-zero divergence and for a first-order ABC the error is shown to be 0(r^-2). A second-order condition is derived, and using a Galerkin formulation both conditions can yield symmetric matrices

Keywords

Galerkin method; Helmholtz equations; electric fields; electric potential; electromagnetic wave absorption; integral equations; magnetic fields; matrix algebra; vectors; Galerkin formulation; Helmholtz equation; Hertzian dipoles; Lorentz gauge; Representation theorem; field quantities; first-order ABC; linear superposition; nonzero divergence; second-order condition; symmetric matrices; vector absorbing boundary condition; vector potential; Boundary conditions; Current density; Educational institutions; Equations; Green function; Magnetic fields; Magnetic separation; Moment methods; Symmetric matrices; Vectors;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.497376

Filename

497376