电磁波导的稳定性分析。第 2 部分：非均质波导

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-04-29 DOI:10.1007/s10444-024-10130-x

Leszek Demkowicz, Jens M. Melenk, Jacob Badger, Stefan Henneking

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引用次数: 0

摘要

本文是 Melenk 等人 "电磁波导稳定性分析"（2023 年）[5] 的延续。第一部分：声波和同质电磁波导"（2023 年）[5]，将同质电磁波导的稳定性结果扩展到非同质情况。分析采用了自联合算子特征问题的扰动技术。我们证明，非均质电磁波导问题的稳定性常数与波导长度 L 成线性缩放关系。这些结果为证明基于全包络解析的非连续彼得洛夫-加勒金（DPG）离散化的收敛性，以及由此产生的修正麦克斯韦方程组的超弱变分公式提供了基础，见第 1 部分。

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Stability analysis for electromagnetic waveguides. Part 2: non-homogeneous waveguides

This paper is a continuation of Melenk et al., “Stability analysis for electromagnetic waveguides. Part 1: acoustic and homogeneous electromagnetic waveguides” (2023) [5], extending the stability results for homogeneous electromagnetic (EM) waveguides to the non-homogeneous case. The analysis is done using perturbation techniques for self-adjoint operators eigenproblems. We show that the non-homogeneous EM waveguide problem is well-posed with the stability constant scaling linearly with waveguide length L. The results provide a basis for proving convergence of a Discontinuous Petrov-Galerkin (DPG) discretization based on a full envelope ansatz, and the ultraweak variational formulation for the resulting modified system of Maxwell equations, see Part 1.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.