Computing the electric and magnetic matrix Green’s functions in a rectangular parallelepiped with a perfect conducting boundary. (English) Zbl 1474.78003

Yakhno, V. G.; Ersoy, Ş.

Abstr. Appl. Anal. 2014, Article ID 586370, 13 p. (2014).

Summary: A method for the approximate computation of frequency-dependent magnetic and electric matrix Green’s functions in a rectangular parallelepiped with a perfect conducting boundary is suggested in the paper. This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. The elements of approximate Green’s functions are found explicitly in the form of the Fourier series with a finite number of terms. The convergence analysis for finding the number of the terms is given. The computational experiments have confirmed the robustness of the method.

MSC:

78A25	Electromagnetic theory (general)
35A08	Fundamental solutions to PDEs
35Q60	PDEs in connection with optics and electromagnetic theory
78M10	Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory

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