4 papers
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…
Enriching continuous Lagrange finite element approximation spaces using neural networks
Hélène Barucq, Michel Duprez, Florian Faucher +5
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural netw…
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…
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…