Title: Comparative study of point matching method with spectral method on numerical solution electromagnetic problems

Authors: Mahmoud Behroozifar

Addresses: Faculty of Mathematics, Babol Noshirvani University of Technology, Babol, Iran

Abstract: The present study focuses on comparing the point matching method and spectral method for solving the integral equations arising in the electromagnetic domain. The point matching method, which is a traditional method, was based on basis functions which most of the time result in a singular and ill-posed system of nonlinear equations. In order to prevent these inconveniences, the physical structure of the object must be altered in some cases, which yields a high error in the results and requires high CPU time and memory usage. Also in most cases, this method converges slowly and leads to a singular and ill-posed system. Consequently, applying the point matching method for this problem leads to an approximate solution with low accuracy and high computation volume. As an alternative, we present the spectral method based on Bernstein polynomials (BPs) as a robust nominee. Employing the BPs reduces the problem to an algebraic equations system. The other merits of the presented method are faster convergence and avoidance of occurring a singular system.

Keywords: Bernstein polynomials; electrostatic; microstrip; point matching method; spectral method.

DOI: 10.1504/IJCSE.2023.135279

International Journal of Computational Science and Engineering, 2023 Vol.26 No.6, pp.665 - 672

Received: 14 Dec 2021
Received in revised form: 06 May 2022
Accepted: 10 May 2022
Published online: 04 Dec 2023 *

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