HECHT , Frédéric

Scalability of parallel solvers for problems with high heterogeneities relies on adaptive coarse spaces built from generalized eigenvalue problems in the subdomains. The corresponding theory is powerful and flexible but the development of an efficient parallel implementation is challenging. We report here on recent advances in adaptive coarse...

In this document, we present a parallel implementation in Freefem++ of scalable two-level domain decomposition methods. Numerical studies with highly heterogeneous problems are then performed on large clusters in order to assert the performance of our code.

In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order curl-conforming finite elements is quite delicate, especially in the three-dimensional case. Here, we...

As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the...

Nous considérons une discrétisation par éléments finis des équations de Navier-Stokes couplées localement avec l'équation de l'énergie cinétique turbulente par une viscosité turbulente. Nous prouvons des estimations d'erreur a posteriori qui permettent de déterminer automatiquement la zône où l'énergie cinétique turbulente doit être insérée...

In this paper, we propose a local projection stabilization (LPS) finite element method applied to numerically solve natural convection problems. This method replaces the projection-stabilized structure of standard LPS methods by an interpolation-stabilized structure, which only acts on the high frequencies components of the flow. This approach...

This paper deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Iterative microwave tomographic imaging requires the solution of an inverse problem based on a minimization algorithm (e.g. gradient or Newton-like methods) with successive solutions of a direct...

This article deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Iterative microwave tomographic imaging requires the solution of an inverse problem based on a minimization algorithm (e.g., gradient based) with successive solutions of a direct problem such as the...

This paper deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Microwave tomographic imaging requires the solution of an inverse problem based on a minimization algorithm (e.g. gradient based) with successive solutions of a direct problem such as the accurate...

The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem relying on a minimization algorithm (for example, gradient-based), where successive iterations consist in repeated solutions of a direct problem. The reconstruction algorithm is extremely...