Research Statement

My past and present research activities consist in proposing and studying efficient numerical methods applicable to resolution of a wide range of partial differential equations (PDEs) and optimization problems. In particular, in the past four years, I have been developing • algebraic multigrid methods by smoothed aggregation: an efficient multigrid solver of sparse systems of linear equations. The main application fields have been compressible and incom-pressible fluid simulations, linear elasticity, and electromagnetism. • shape optimization algorithms: conception of multi-level parametrization techniques to ac-celerate convergence of standard optimization methods. The main application area was the aerodynamic design of a small business jet for supersonic and transonic régimes. • mesh generation algorithms: a non-Delaunay approach for automatic anisotropic mesh gen-eration, applied then to produce a set of coarser meshes for setup of geometric multigrid. Algebraic multigrid by aggregation Speeding up resolution of sparse linear systems of equations presents a rewarding challenge, as most of the CPU time in engineering simulation and optimization processes is spent for inverting sparse matrices. One of the few known optimal iterative solvers is the multigrid method, exploitin