An A-$\Phi$ Formulation Solver in Electromagnetics Based on Discrete Exterior Calculus

IF 1.8 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC IEEE Journal on Multiscale and Multiphysics Computational Techniques Pub Date : 2022-12-20 DOI:10.1109/JMMCT.2022.3230732

Boyuan Zhang;Dong-Yeop Na;Dan Jiao;Weng Cho Chew

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引用次数: 1

Abstract

An efficient numerical solver for the A -

$\Phi$

formulation in electromagnetics based on discrete exterior calculus (DEC) is proposed in this paper. The A -

$\Phi$

formulation is immune to low-frequency breakdown and ideal for broadband and multi-scale analysis. The generalized Lorenz gauge is used in this paper, which decouples the A equation and the

$\Phi$

equation. The A -

$\Phi$

formulation is discretized by using the DEC, which is the discretized version of exterior calculus in differential geometry. In general, DEC can be viewed as a generalized version of the finite difference method, where Stokes' theorem and Gauss's theorem are naturally preserved. Furthermore, compared with finite difference method, where rectangular grids are applied, DEC can be implemented with unstructured mesh schemes, such as tetrahedral meshes. Thus, the proposed DEC A -

$\Phi$

solver is inherently stable, free of spurious solutions and can capture highly complex structures efficiently. In this paper, the background knowledge about the A -

$\Phi$

formulation and DEC is introduced, as well as technical details in implementing the DEC A -

$\Phi$

solver with different boundary conditions. Numerical examples are provided for validation purposes as well.

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电磁学中基于离散外微积分的A-$\Phi$公式求解器

本文提出了一种基于离散外部微积分（DEC）的电磁学A$\Phi$公式的高效数值求解器。A$\Phi$公式不受低频击穿的影响，非常适合宽带和多尺度分析。本文采用广义洛伦兹规范对A方程和$\Phi$方程进行解耦。A$\Phi$公式通过使用DEC进行离散化，DEC是微分几何中外部微积分的离散化版本。一般来说，DEC可以被视为有限差分法的一个广义版本，其中斯托克斯定理和高斯定理自然保留。此外，与应用矩形网格的有限差分方法相比，DEC可以用非结构化网格格式来实现，例如四面体网格。因此，所提出的DEC A-$\Phi$求解器本质上是稳定的，没有伪解，并且可以有效地捕获高度复杂的结构。本文介绍了A-$\Phi$公式和DEC的背景知识，以及在不同边界条件下实现DEC A-$\Pi$求解器的技术细节。数值示例也用于验证目的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Journal on Multiscale and Multiphysics Computational Techniques Mathematics-Mathematical Physics

CiteScore

4.30

自引率

0.00%

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