2011/05/16 by Charles L. Epstein, Leslie Greengard, Epstein, Charles L. +3
Engineering · Mathematics · Physics and Astronomy · #31B10 #35Q61 #65N80 #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1105.3217
openalex publication_date 2011/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 R3. 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.