Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915134856757248 |
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| author | Hoonhout, Daniel Urzúa-Torres, Carolina |
| author_facet | Hoonhout, Daniel Urzúa-Torres, Carolina |
| contents | In this paper, we discuss the stable discretisation of the double layer boundary integral operator for the wave equation in $1d$. For this, we show that the boundary integral formulation is $L^2$-elliptic and also inf-sup stable in standard energy spaces. This turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation and contributes to its further understanding. Moreover, we present the first BEM discretisations of second-kind operators for the wave equation for which stability is guaranteed and a complete numerical analysis is offered. We validate our theoretical findings with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems Hoonhout, Daniel Urzúa-Torres, Carolina Numerical Analysis 35L05, 45P05, 47G10 In this paper, we discuss the stable discretisation of the double layer boundary integral operator for the wave equation in $1d$. For this, we show that the boundary integral formulation is $L^2$-elliptic and also inf-sup stable in standard energy spaces. This turns out to be a particular case of a recent result on the inf-sup stability of boundary integral operators for the wave equation and contributes to its further understanding. Moreover, we present the first BEM discretisations of second-kind operators for the wave equation for which stability is guaranteed and a complete numerical analysis is offered. We validate our theoretical findings with numerical experiments. |
| title | Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems |
| topic | Numerical Analysis 35L05, 45P05, 47G10 |
| url | https://arxiv.org/abs/2502.01374 |