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

Summary · qwen2.5:32b

The article introduces quasi-Trefftz methods for solving first-order differential systems, specifically developing discrete quasi-Trefftz spaces and their bases without relying on auxiliary scalar equations. This method represents a novel approach compared to traditional decoupling techniques that use second-order scalar equations. A key detail is the focus on computational aspects in constructing these bases.

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arXiv:2509.08936v3 Announce Type: replace 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.