The ANCHP group is concerned with the development , analysis and implementation of numerical algorithms for solving large-scale problems, with a particular focus on linear and multilinear algebra.
Topics of current interest include linear and nonlinear eigenvalue problems, low-rank matrix and tensor techniques, numerical optimization, massively parallel algorithms, control problems , as well as data analysis. The algorithms and software produced by ANCHP have been incorporated into a number of widely used software packages, such as Matlab, LAPACK, ScaLAPACK and SLEPc.
In the ANMC group, we develop and analyse novel numerical algorithms aimed at coupling various
scales of a physical system and extracting coarse dynamics from multiscale problems. Interests
in applications include biology (macro-molecule transport in heterogeneous devices), chemistry
(numerical methods for chemical reactions), material sciences (heat distribution in micro-devices), geosciences (water infiltration in porous medium) and medicine (simulation of brain strokes).
The CMCS research group deals with the analysis, development, application of mathematical models
for the integration of complex systems. The analysis is conducted using mathematical methods in
several fields such as linear algebra, approximation theory, partial differential equations, optimization
and control. Solution methods are developed and applied to domains as diverse as flow dynamics, structural analysis, mass transport, heat transfer and in general to multiscale and multiphysics applications. Our methods have been integrated into complex multidisciplinary systems such as the Haemodel and Mathcard projects (simulation of the cardiovascular system), yacht design for America’s cup, optimization of therapeutical tools in medicine and surgery.
The CSQI chair deals with the development of reliable numerical simulation of complex models appearing
in physics, engineering and life science applications, such as fluid-structure interaction in hemodynamics,
heart electromechanics, flows in porous media, etc. In particular, the research is oriented to the
development of advanced techniques for the treatment and quantification of uncertainties which unavoidably
affect many of the parameters of a mathematical model, and consequently the quantification of the
reliability of numerical simulations outcomes.
The scientific focus of the MCSS chair is the development, analysis, and application of reliable and high-order accurate computational methods for solving time-dependent partial differential equations with a particular emphasis on wave problems and conservation laws. Closely related activities include reduced models, uncertainty quantification, efficient solvers, and multi-scale problems with a focus on techniques suitable for high-performance computing on modern computing platforms, including software development. Applications are drawn from a wide spectrum across the applied sciences and engineering, including electromagnetics, plasma physics, geoscience and general relativity.
The focus of the MNS chair is the design and analysis of numerical algorithms for partial differential equations. We are mostly interested in differential problems enjoying mathematical structures that need
to be preserved at discrete level in order to achieve accuracy and stability of the numerical schemes.
In particular, the research is oriented towards the development of novel and innovative numerical techniques aiming at improving the integration between numerical simulations and geometric modelling and processing. The targeted applications span from elasticity to electromagnetic problems.
Group Picasso GR-PI
The Group Picasso (GR-PI) is specialized in numerical analysis and scientific computing. Our goals
are to work in collaboration with various engineering laboratories and industry in order to improve existing algorithms, to create and analyze, from the mathematical point of view, new numerical schemes in order
to solve practical problems.