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Speaker: Andrea Lagardere, INRIA
Title: Quasi-Trefftz method for aeroacoustic
Abstract: Variational Trefftz methods are discontinuous Galerkin methods whose basis functions are local solutions of the PDE under consideration. In the context of constant coefficient PDEs, analytical solutions, such as plane waves or Bessel functions, are available.
Aeroacoustic models involve equations whose physical characteristics depend on the spatial variables. In general, there are no available solutions in closed form. A natural idea is to resort to basis functions that are approximate solutions of the considered PDE rather than exact solutions, i.e., quasi-Trefftz functions.
In this talk we see how to build three types of quasi-Trefftz function for the heterogeneous Helmholtz equation [1] : Amplitude-based Generalized Plane Waves, Phase-based Generalized Plane Waves and polynomials. We also verify some approximation properties of these functions.
Then we present a quasi-Trefftz Discontinuous Galerkin variational formulation inspired by hyperbolic system formulation.
We show some numerical results on the solution obtained with this quasi-Trefftz method, and present some ideas to extend this work to the converted Helmholtz equation.
[1] Imbert-Gerard, L. M., & Sylvand, G. (2022). Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties. arXiv preprint arXiv:2201.12993.