Evaluation of singular Fourier coefficients in solving electromagnetic scattering by body of revolution

Abstract

[1] We develop an efficient evaluation scheme for the singular Fourier coefficients in solving electromagnetic scattering by body of revolution (BOR). For the singular modal Green's function (MGF), the scheme first evaluates the integrals over generating arc segments analytically and then distinguishes the singular part from the regular part for the integral over the angle in the revolution direction. This allows us to avoid the approximate calculation for the elliptical integral and the separated singular part is exactly evaluated in a closed form. For the singular MGF's derivatives generated from the gradient of the Green's function, we subtract the kernels with more similar singular integrands in the vicinity of singularity so that the kernels are better regularized. The procedure differs from the existent Glisson's method in several aspects and numerical experiments show that the scheme is simpler in implementation and more efficient for calculation.

Accurate and Efficient Computation of the Modal Green's Function Arising in the Electric-Field Integral Equation for a Body of Revolution

“…In [9], a closed-form solution for the singular elements arising in the EFIE and MFIE formulation has been constructed based on a singularity extraction technique and in [10] a closed-form solution for the MGF has been proposed for source and observation points that are close to the axis of rotation but the distance between them is large. For the case where the distance between source and observation points is small, a numerical scheme for the MGF and its derivative has been developed in [11]. Finally, in [12] it was shown that a combination of the trapezoidal rule and Gauss-Hermite quadrature along the steepest-decent contours reaches high accuracy for a low computational cost if source and observation point are not too close and for near-singular cases a similar accuracy can be obtained at slightly higher computational costs.…”

Determination of Normalized Magnetic Eigenfields in Microwave Cavities

“…Authors using the MFIE in axially symmetric domains apply it to exterior problems and the same is true for the related electric field integral equation (EFIE) and the combined field integral equation (CFIE). The method of moments (MoM) is the most common method for discretization, see [2], [14], [22], and the reference list in [28]. Only a few papers favor Nyström methods, see [12] and [29].…”

Numerical solution of hypersingular equation using recursive wavelet on invariant set

“…For solving partial differential equations and integral equations arising in various computational sciences [8][9][10], wavelet-based algorithms have shown their robustness in the past decade [11][12][13]. The wavelet-based Galerkin method has also been developed to solve the natural boundary integral equation [14][15][16].…”