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On generalized solutions of the problems of electromagnetic wave diffraction in the open space. (English) Zbl 1469.78009

Summary: In this article we construct a special class of the generalized functions for the rigorous justification of joining method of solving some diffraction problems of electromagnetic waves by thin conducting screens. Linear functionals on a set of linear combinations of Hermite functions are considered as the generalized functions. The traces of the solutions of Helmholtz equation on the plane are interpreted in the generalized sense. The infinite sets of linear algebraic equations are derived directly from the generalized boundary conditions. The results of the computing experiment are presented.

MSC:

78A45 Diffraction, scattering
78A50 Antennas, waveguides in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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