54 citations · 54 across the 11 of their papers we have counts for
11 papers
phi-FD, a second order finite difference scheme for geometries defined by a level-set function: the Neumann case
Michel Duprez, Vanessa Lleras, Alexei Lozinski +2
We extend the phi-FD finite-difference scheme, which handles domains described by a level-set function on a Cartesian grid, to Neumann boundary conditions. The condition is relaxed…
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…
A penalized ϕ-FEM scheme for the Poisson Dirichlet problem
Raphaël Bulle, Michel Duprez, Vanessa Lleras +1
In this work, we analyze a penalized variant of the ϕ-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The ϕ-FEM is a recently introduced unfitted finite ele…
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…
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…
phi-FEM for the heat equation: optimal convergence on unfitted meshes in space
Michel Duprez, Vanessa Lleras, Alexei Lozinski +1
Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh…