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Open AccessFeature PaperArticle

Efficient Evaluation of Slowly Converging Integrals Arising from MAP Application to a Spectral-Domain Integral Equation

1
Department of Electrical and Information Engineering “Maurizio Scarano” (DIEI), University of Cassino and Southern Lazio, 03043 Cassino, Italy
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ELEDIA Research Center ([email protected]), University of Cassino and Southern Lazio, 03043 Cassino, Italy
3
Laboratory of Micro and Nano Optics, Institute of Radio-Physics and Electronics of the National Academy of Sciences of Ukraine (IRE-NASU), 61085 Kharkiv, Ukraine
*
Author to whom correspondence should be addressed.
Electronics 2019, 8(12), 1500; https://doi.org/10.3390/electronics8121500
Received: 31 October 2019 / Revised: 24 November 2019 / Accepted: 5 December 2019 / Published: 8 December 2019
(This article belongs to the Special Issue Computational Electromagnetics and Its Applications)
In this paper, we devised an analytical technique to efficiently evaluate the improper integrals of oscillating and slowly decaying functions arising from the application of the method of analytical preconditioning (MAP) to a spectral-domain integral equation. The reasoning behind the method’s application may consistently remain the same, but such a procedure can significantly differ from problem to problem. An exhaustive and understandable description of such a technique is provided in this paper, where we applied MAP for the first time to analysis of electromagnetic scattering from a zero-thickness perfectly electrically conducting (PEC) disk in a planarly layered medium. Our problem was formulated in the vector Hankel transform domain and discretized via the Galerkin method, with expansion functions reconstructing the physical behavior of the surface current density. This ensured fast convergence in terms of the truncation order, but involved numerical evaluation of slowly converging integrals to fill in the coefficient matrix. To overcome this problem, appropriate contributions were pulled out of the kernels of the integrals, which led to integrands transforming into exponentially decaying functions. Subsequently, integrals of the extracted contributions were expressed as linear combinations of fast-converging integrals via the Cauchy integral theorem. As shown in the numerical results section, the proposed technique drastically outperformed the classical analytical asymptotic-acceleration technique. View Full-Text
Keywords: analytical technique; method of analytical preconditioning; spectral-domain integral equation analytical technique; method of analytical preconditioning; spectral-domain integral equation
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Lucido, M.; Migliore, M.D.; Nosich, A.I.; Panariello, G.; Pinchera, D.; Schettino, F. Efficient Evaluation of Slowly Converging Integrals Arising from MAP Application to a Spectral-Domain Integral Equation. Electronics 2019, 8, 1500.

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