3 papers
math.NA2026
Trefftz methods with evanescent plane waves
Andrea Moiola, Nicola Galante, Emile Parolin
Classical Trefftz methods approximate Helmholtz solutions using propagative plane waves and are subject to strong numerical instabilities. Evanescent plane wave bases can substanti…
math.NA2025
A Trefftz Continuous Galerkin method for Helmholtz problems
Nicola Galante, Bruno Després, Emile Parolin
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discr…
math.NA2024
Stable approximation of Helmholtz solutions in the 3D ball using evanescent plane waves
Nicola Galante, Andrea Moiola, Emile Parolin
The goal of this paper is to show that evanescent plane waves are much better at numerically approximating Helmholtz solutions than classical propagative plane waves. By generalizi…