Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911138558509056 |
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| author | Melenk, Jens Markus Demkowicz, Leszek Henneking, Stefan |
| author_facet | Melenk, Jens Markus Demkowicz, Leszek Henneking, Stefan |
| contents | 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 non-polynomial ansatz functions that allows for treating long waveguides. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_04521 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides Melenk, Jens Markus Demkowicz, Leszek Henneking, Stefan Numerical Analysis 35J05 %laplacian operator, reduced wave equation (Helmholtz equation) 65N30 % FEM 78A50, 35Q60, 35J05, 65N30 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 non-polynomial ansatz functions that allows for treating long waveguides. |
| title | Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides |
| topic | Numerical Analysis 35J05 %laplacian operator, reduced wave equation (Helmholtz equation) 65N30 % FEM 78A50, 35Q60, 35J05, 65N30 |
| url | https://arxiv.org/abs/2307.04521 |