Research

Introduction

The focus of our research is on the development of novel parallel numerical algorithms and tools appropriate for state-of-the-art mathematical models used in complex scientific applications, and in particular numerical simulations. The proposed research program is by nature multi-disciplinary, interweaving aspects of applied mathematics, computer science, as well as those of several specific applications, as porous media flows, elasticity, wave propagation in multi-scale media.

Our first objective is to develop numerical methods and tools for complex scientific and industrial applications, that will enhance their scalable execution on the emergent heterogeneous hierarchical models of massively parallel machines. Our second objective is to integrate the novel numerical algorithms into a middle-layer that will hide as much as possible the complexity of massively parallel machines from the users of these machines.

Last activity report : 2016

Computational kernels

Communication-avoiding algorithms   Our research focuses on a novel approach to dense and sparse linear algebra algorithms, which aims at minimizing the communication, where communication refers to both its volume and the number of messages exchanged. The main goal is to reformulate and redesign linear algebra algorithms so that they are optimal in an amount …

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Linear solvers

Our research considers domain decomposition methods and iterative methods and its goal is to develop solvers that are suitable for parallelism and that exploit the fact that the matrices are arising from the discretization of a system of PDEs on unstructured grids. We mainly consider finite element like discretization procedures, but we are also strongly …

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Modelisation and numerical simulations

Our research focuses on several important application domains, that we briefly describe in the following.  These applications also allow us to validate the algorithms and the software developed in the previous research topics. Inverse problems: we focus on methods arising from time reversal techniques and their combination with classical methods in inverse problems. Numerical methods …

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Parallel FreeFem++

This direction of research focuses on FreeFem++, a software that allows through a  domain specific language the definition of a large number of PDEs. F. Hecht is one of the co-authors of this package.  The goal of FreeFem++ is not to be a substitute for complex numerical codes, but rather to provide an efficient and …

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