Trefftz methods with evanescent plane waves

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].