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Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations II
Author(s) -
Epstein Charles L.,
Greengard Leslie,
O'Neil Michael
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21420
Subject(s) - mathematics , piecewise , maxwell's equations , integral equation , spurious relationship , mathematical analysis , debye , representation (politics) , scalar (mathematics) , fredholm integral equation , permittivity , dielectric , physics , quantum mechanics , geometry , statistics , politics , political science , law
In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}\R^3$ . This representation leads to a coupled system of Fredholm integral equations of the second kind for four scalar densities supported on the material interface. Like the classical Müller equation, it has no spurious resonances. Unlike the classical approach, however, the representation does not suffer from low‐frequency breakdown. We illustrate the performance of the method with numerical examples. © 2012 Wiley Periodicals, Inc.