Our research is directly relevant to several steps of the numerical simulation chain. Given a numerical simulation that was expressed as a set of differential equations, our research focuses on mesh generation methods for parallel computation, novel numerical algorithms for linear and multilinear algebra, as well as algorithms and tools for their efficient and scalable implementation on high performance computers. The validation and the exploitation of the results is performed with collaborators from applications and is based on the usage of existing tools. In summary, the topics studied in our group are the following:

  • Numerical methods and algorithms
    • Middle-layer for numerical simulations with FreeFEM
    • Solvers for numerical linear algebra: domain decomposition methods, preconditioning for iterative methods, boundary integral equation methods
    • Computational kernels for numerical linear and multilinear algebra
    • Tensor computations for high dimensional problems
  • Modelisation and numerical simulations

Computational kernels

This part of our research focuses on the development of parallel algorithms for major kernels in numerical linear and multilinear algebra, that are building blocks of many applications in computational science (in particular the solvers developed in other research sections). The goal is to enable their efficient execution and scaling to emerging high-performance clusters with …

Linear solvers

This part of our research considers domain decomposition methods and Krylov subspace 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 …

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 …

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 …