Abstract

In this work, a wave-equation-based discontinuous Galerkin (DG) method hybridized with the Robin transmission condition (DG-RTC) is developed to solve the frequency-domain electromagnetic (EM) problems. The proposed DG method directly discretizes the vector electric field wave equation in each subdomain, and subsequently, a term named numerical flux is introduced at the subdomain interfaces to connect the solutions between neighboring subdomains. However, the numerical flux depends not only on the electric field E but also on the magnetic field H residing over the interface. Thereby, another equation is essential for solving E and H simultaneously. Realizing that H only situates at the interface of adjacent subdomains, it is thus desired that the auxiliary equation also merely involves H at the interfaces. To reach this aim, at the subdomain interfaces, a Robin transmission condition (RTC) based on the tangential continuity of EM fields across the interface is introduced as the second equation. With this proposed DG-RTC algorithm, only E is a volume variable, while H is a two-dimensional (2-D) one, and the degrees of freedom (DoFs) are thus greatly reduced compared with the traditional DG method. On the other hand, in the frequency domain, the established subdomain matrix equations are implicitly coupled with each other, resulting in a global matrix system. Directly solving it is not yet cheap. To alleviate the computational cost, a finite-element tearing and interconnecting (FETI)-like approach resorts. With the block-diagonal preconditioner and a restriction operator, the global matrix is decomposed into a surface matrix equation and several local matrix equations pertinent to each subdomain. In this way, a direct solver can be applied to solve these small matrix equations efficiently. To validate the proposed DG method in solving various EM problems, several representative examples are presented.

Department(s)

Electrical and Computer Engineering

Comments

National Natural Science Foundation of China, Grant 61771311

Keywords and Phrases

Discontinuous Galerkin (DG) method; domain decomposition method (DDM); finite-element tearing and interconnecting (FETI); Robin transmission condition (RTC); wave equations

International Standard Serial Number (ISSN)

1557-9670; 0018-9480

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Apr 2023

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