Quasi-Trefftz spaces for a first-order formulation of the Helmholtz equation

Abstract

This work is concerned with the development of quasi-Trefftz methods for first-order differential systems. It focuses on discrete quasi-Trefftz spaces, starting from their definition and including the construction of corresponding bases together with their computational aspect. This is the first attempt at constructing quasi-Trefftz bases for a problem governed by a first-order system without relying on an auxiliary scalar equation. A decoupling approach, with a second order scalar equation for the one unknown, is proposed here simply as a point of comparison to this new approach.