Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems
Numerical Analysis
2025-02-04 v1 Numerical Analysis
Abstract
In this paper, we discuss the stable discretisation of the double layer boundary integral operator for the wave equation in . For this, we show that the boundary integral formulation is -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.
Keywords
Cite
@article{arxiv.2502.01374,
title = {Towards Stable Second-Kind Boundary Integral Equations for Transient Wave Problems},
author = {Daniel Hoonhout and Carolina Urzúa-Torres},
journal= {arXiv preprint arXiv:2502.01374},
year = {2025}
}