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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.NA2025
A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction
Moreno Pintore, Bruno Després
We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains. One of the novelties of the method is that the flux fracti…
math.NA2024
On the quadratic stability of asymmetric Hermite basis with application to plasma physics with oscillating electric field
Ruiyang Dai, Bruno Després
We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of th…