Trefftz methods with evanescent plane waves
For researchers using Trefftz methods for Helmholtz equations, this provides a simple recipe to enhance numerical stability and accuracy.
The paper addresses numerical instabilities in classical Trefftz methods for Helmholtz problems by proposing evanescent plane wave bases, which significantly improve the Ultraweak Variational Formulation (UWVF) results.
Classical Trefftz methods approximate Helmholtz solutions using propagative plane waves and are subject to strong numerical instabilities. Evanescent plane wave bases can substantially mitigate this phenomenon. We propose a simple recipe to select such basis functions. We show that the numerical results obtained by the Ultraweak Variational Formulation (UWVF) greatly improve thanks to this choice. More details and examples will soon be available in [Galante, Moiola, Parolin 2026].