Record link: 
http://hdl.handle.net/20.500.12708/215634
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Title: 
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
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Citation: 
Melenk, J. M., Demkowicz, L., & Henneking, S. (2025). Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides. SIAM Journal on Mathematical Analysis, 57(3), 2559–2595. https://doi.org/10.1137/23M1599239
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Publisher DOI: 
10.1137/23M1599239
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Melenk, Jens M. 
Demkowicz, Leszek 
Henneking, Stefan 
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Organisational Unit: 
E101-02-1 - Forschungsgruppe Computational Mathematics 
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Journal: 
SIAM Journal on Mathematical Analysis 
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ISSN: 
0036-1410
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Date (published): 
2025
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Number of Pages: 
37
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Publisher: 
SIAM PUBLICATIONS
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Peer reviewed: 
Yes
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Keywords: 
waveguide; Helmholtz equation; Maxwell’s equation; nonreflecting boundary conditions; stability
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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 L 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 L can be countered by suitably scaling the test norm of the method. We present the “full envelope approximation,” a UW DPG method based on nonpolynomial ansatz functions that allows for treating long waveguides.
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Research Areas: 
Mathematical and Algorithmic Foundations: 80%
Modeling and Simulation: 20%
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Science Branch: 
1010 - Mathematik: 100%
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