Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations II. Issue 5 (28th August 2012)

• Record Type: Journal Article
• Authors: Epstein, Charles L.; Greengard, Leslie; O'Neil, Michael
• Is Part Of: Communications on pure and applied mathematics. Volume 66:Issue 5(2013:May)
• Page Start: 753
• Page End: 789
• Publication Date: 2012-08-28
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21420
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 <tex-math notation="tex"><![CDATA[$\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}\R^3$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg1rtwsrxn" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />. 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.</p> </abstract>