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Generalized combined field integral equations for the iterative solution of the three-dimensional Maxwell equations. (English) Zbl 1135.78012

The paper is devoted to the construction of second kind Fredholm integral equations for the numerical solution of problems of high-frequency electromagnetic scattering by a perfect conductor. The main goal is to provide integral equations with a condition number independent of the mesh refinement and the high-frequency parameters. In view of this, the authors propose two families of integral equations which can be seen as generalizations of the Brakhage-Werner approach and of the combined field integral equations. A corresponding spectral study is presented for the spherical geometry case.

MSC:

78M15 Boundary element methods applied to problems in optics and electromagnetic theory
65R20 Numerical methods for integral equations
35C15 Integral representations of solutions to PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
47G30 Pseudodifferential operators
65F10 Iterative numerical methods for linear systems
78A25 Electromagnetic theory (general)
78A45 Diffraction, scattering
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