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The well‐posedness of the electric field integral equation for transient scattering from a perfectly conducting body
Author(s) -
Rynne Bryan P.
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990510)22:7<619::aid-mma59>3.0.co;2-e
Subject(s) - electric field integral equation , integral equation , mathematical analysis , electric field , mathematics , scattering , field (mathematics) , scalar field , surface (topology) , scalar (mathematics) , electromagnetic field , surface integral , transient (computer programming) , physics , geometry , mathematical physics , optics , quantum mechanics , computer science , pure mathematics , operating system
We consider the scattering of a transient electromagnetic field incident on a body with a smooth, perfectly conducting surface. A standard numerical method for calculating the scattered field is to use a time dependent, surface integral equation (called the electric field integral equation) to calculate the surface currents and charges induced by the incident field—these currents and charges then yield the scattered fields by means of standard integral representations (vector and scalar potentials). In this paper we show that the time‐dependent electric field integral equation is well‐posed in a suitable function space setting. We also investigate the behaviour of the solutions at large time. Copyright © 1999 John Wiley & Sons, Ltd.