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arXiv · 2502.01374

Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems

Daniel Hoonhout·Carolina Urzúa-Torres
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Abstract

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.

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Daniel Hoonhout, Carolina Urzúa-Torres. 2025-02-03. Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems. https://arxiv.org/abs/2502.01374

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