Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
Numerical Analysis
2025-09-08 v2 Numerical Analysis
Abstract
In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the length of the waveguide. These stability estimates are used for the analysis of the (ideal) ultraweak (UW) variant of the Discontinuous Petrov Galerkin (DPG) method. For this UW DPG, we show that the stability deterioration with can be countered by suitably scaling the test norm of the method. We present the ``full envelope approximation'', a UW DPG method based on non-polynomial ansatz functions that allows for treating long waveguides.
Keywords
Cite
@article{arxiv.2307.04521,
title = {Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides},
author = {Jens Markus Melenk and Leszek Demkowicz and Stefan Henneking},
journal= {arXiv preprint arXiv:2307.04521},
year = {2025}
}