Section: New Results

Various topics

Participant : Virginie Ehrlacher.

In the context of a collaboration with EDF, V. Ehrlacher, together with A. Benaceur, A. Ern (CERMICS) and S. Meunier (EDF) has developed in [35] a new reduced basis methodology for parabolic nonlinear systems of equations which enables to significantly reduce the computational time of the offline phase of the method.

V. Ehrlacher, with T. Boiveau, A. Ern (CERMICS) and A. Nouy (Centrale Nantes), has developed a new global space-time unconditionally stable approximation scheme for linear parabolic equations, which relies on the Lions-Magenes formulation of such partial differential equations, in [39]. Such a formulation is perfectly adapted for the use of tensor methods to approximate the solution of these equations at a significantly lower computational cost, based on the separation of space and time variables. Different greedy algorithms to compute this tensor approximation of the solution are compared on numerical testcases using several formulations including the new proposed one. The new approach enables to define a provably convergent algorithm with better approximation properties than the other methods.