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arXiv · 2509.08936

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

Lise-Marie Imbert-Gérard·Andréa Lagardère·Guillaume Sylvand·Sébastien Tordeux
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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.

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Lise-Marie Imbert-Gérard, Andréa Lagardère, Guillaume Sylvand, Sébastien Tordeux. 2025-09-10. Quasi-Trefftz spaces for a first-order formulation of the Helmholtz equation. https://arxiv.org/abs/2509.08936

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