Stability analysis of boundary element methods for the wave equation: The weakly singular operator in $1d$
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Delft University of Technology, Graz 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: W7223245551