Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hoonhout, Daniel, Urzúa-Torres, Carolina
Institution: Delft University of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407170302