3 papers
math.NA2026
A multigrid and neural network approach to reduce the computational cost of phi-FEM
Raphaël Bulle, Michel Duprez, Vanessa Lleras +1
In this work, we present a combination of a multigrid approach and the phi-FEM immersed boundary finite element method to reduce its computational cost while preserving its accurac…
math.NA2026
A penalized Ï-FEM scheme for the Poisson Dirichlet problem
Raphaël Bulle, Michel Duprez, Vanessa Lleras +1
In this work, we analyze a penalized variant of the Ï-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The Ï-FEM is a recently introduced unfitted finite e…
math.NA2025
Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries
Michel Duprez, Vanessa Lleras, Alexei Lozinski +2
In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we u…