4 citations · 9 across the 6 of their papers we have counts for
7 papers · 1 filter
A ϕ-FEM approach for time-dependent domains with unfitted meshes
Michel Duprez, Johan Marguet, Alexei Lozinski +1
In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the ϕ-FEM paradigm in which the computational…
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…
-FEM: an efficient simulation tool using simple meshes for problems in structure mechanics and heat transfer
Stephane Cotin, Michel Duprez, Vanessa Lleras +2
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, g…
A new -FEM approach for problems with natural boundary conditions
Michel Duprez, Vanessa Lleras, Alexei Lozinski
We present a new finite element method, called -FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simpl…