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Stability analysis of boundary element methods for the wave equation: The weakly singular operator in 1d

  • Daniel Hoonhout
  • Richard Löscher
  • Carolina Urzúa-Torres
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Abstract

We discuss the construction of stable discrete pairs of trial and test spaces for the wave equation. Building on a general abstract operator-theoretic framework, we show how optimal pairings can be derived for a one-dimensional boundary element formulation of the wave equation with prescribed Dirichlet data, based on an indirect single layer potential ansatz. In this setting, the optimal test space can be computed analytically and has a physical interpretation, reflecting the non-local nature of the underlying operator.

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Cite

BibTeXRIS
BibTeX
@misc{hoonhout2026stability,
  title = {{Stability analysis of boundary element methods for the wave equation: The weakly singular operator in $1d$}},
  author = {Daniel Hoonhout and Richard Löscher and Carolina Urzúa-Torres},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29795},
  eprint = {2610.29795},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29795},
}
RIS
TY  - UNPB
TI  - Stability analysis of boundary element methods for the wave equation: The weakly singular operator in 1d
AU  - Daniel Hoonhout
AU  - Richard Löscher
AU  - Carolina Urzúa-Torres
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29795
UR  - https://arxiv.org/abs/2610.29795
AB  - We discuss the construction of stable discrete pairs of trial and test spaces for the wave equation. Building on a general abstract operator-theoretic framework, we show how optimal pairings can be derived for a one-dimensional boundary element formulation of the wave equation with prescribed Dirichlet data, based on an indirect single layer potential ansatz. In this setting, the optimal test space can be computed analytically and has a physical interpretation, reflecting the non-local nature of the underlying operator.
ER  -