Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II

Details Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations, II

2011-05-16

arxiv.org/abs/1105.3217v1

Mathematics

Numerical Analysis

36 pages, 5 figures

Scientific paper

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 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 Muller 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.

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