54 citations · 214 across the 28 of their papers we have counts for
31 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 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…
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…
Phi-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations
Michel Duprez, Vanessa Lleras, Alexei Lozinski
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strat…
Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix
Michel Duprez, Manuel González-Burgos, Diego A. Souza
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of cons…
-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…
Optimization of spatial control strategies for population replacement, application to Wolbachia
Michel Duprez, Romane Hélie, Yannick Privat +1
In this article, we are interested in the analysis and simulation of solutions to an optimal control problem motivated by population dynamics issues. In order to control the spread…
Optimal control strategies for the sterile mosquitoes technique
Luís Almeida, Michel Duprez, Yannick Privat +1
Mosquitoes are responsible for the transmission of many diseases such as dengue fever, zika or chigungunya. One way to control the spread of these diseases is to use the sterile in…
How Best Can Finite-Time Social Distancing Reduce Epidemic Final Size?
Pierre-Alexandre Bliman, Michel Duprez
Given maximal social distancing duration and intensity, how can one minimize the epidemic final size, or equivalently the total number of individuals infected during the outbreak?…
Optimal immunity control by social distancing for the SIR epidemic model
Pierre-Alexandre Bliman, Michel Duprez, Yannick Privat +1
Until a vaccine or therapy is found against the SARS-CoV-2 coronavirus, reaching herd immunity appears to be the only mid-term option. However, if the number of infected individual…
Minimal cost-time strategies for population replacement using the IIT
Luis Almeida, Jesús Bellver, Michel Duprez +1
Vector control plays a central role in the fight against vector-borne diseases and, in particular, arboviruses. The use of the endosymbiotic bacterium Wolbachia has proven effectiv…
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…
Bilinear local controllability to the trajectories of the Fokker-Planck equation with a localized control
Michel Duprez, Pierre Lissy
This work is devoted to the control of the Fokker-Planck equation, posed on a smooth bounded domain of R^d, with a localized drift force. We prove that this equation is locally con…
-FEM: a finite element method on domains defined by level-sets
Michel Duprez, Alexei Lozinski
We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the bou…
Control strategies on mosquitos population for the fight against arboviruses
Luís Almeida, Michel Duprez, Yannick Privat +1
In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of vector, \textit{Aedes} mosquitoes in this case…
Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field
Michel Duprez, Morgan Morancey, Francesco Rossi
In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localiz…
Finite element method with local damage on the mesh
Michel Duprez, Vanessa Lleras, Alexei Lozinski
We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piece…
Control of the Grushin equation: non-rectangular control region and minimal time
Michel Duprez, Armand Koenig
This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangul…
Quantifying discretization errors for soft-tissue simulation in computer assisted surgery: a preliminary study
Michel Duprez, Stéphane P. A. Bordas, Marek Bucki +7
Errors in biomechanics simulations arise from modeling and discretization. Modeling errors are due to the choice of the mathematical model whilst discretization errors measure the…
Approximate and exact controllability of the continuity equation with a localized vector field
Michel Duprez, Morgan Morancey, Francesco Rossi
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector fi…
Minimal time problem for discrete crowd models with a localized vector field
Michel Duprez, Morgan Morancey, Francesco Rossi
In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localiz…