Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source

Ke Sun, Shuang Ding, Junli Zhang and Yan-Cheng Liu
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Ke Sun: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Shuang Ding: Shanghai Tongyan Civil Engineering Technology Co., Ltd., Shanghai 200092, China
Junli Zhang: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Yan-Cheng Liu: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China

Mathematics, 2022, vol. 10, issue 7, 1-24

Abstract: The localized method of fundamental solutions (LMFS) is a domain-type, meshless numerical method. Compared with numerical methods that have a high grid dependence, it does not require grid generation and numerical integration, so it can effectively improve computational efficiency and avoid complex integration processes. Moreover, it is formed using the traditional method of fundamental solutions (MFS) and the localization approach. Previous studies have shown that the MFS may produce a dense and ill-conditioned matrix. However, the proposed LMFS can yield a sparse system of linear algebraic equations, so it is more suitable and effective in solving complicated engineering problems. In this article, LMFS was used to solve eigenfrequency problems in electromagnetic waves, which were controlled using two-dimensional Helmholtz equations. Additionally, the resonant frequencies of the eigenproblem were determined by the response amplitudes. In order to determine the eigenfrequencies, LMFS was applied for solving a sequence of inhomogeneous problems by introducing an external source. Waveguides with different shapes were analyzed to prove the stability of the present LMFS in this paper.

Keywords: Helmholtz equation; waveguides; eigenfrequencies problem; external source; localized methods of fundamental solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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