This research work is proposed as part of the NumPEx (from French, Numerical Methods for Exascale) research priority program and equipment (PEPR). It belongs with the Exa-MA Project (Methods and Algorithms for Exascale) and is jointly proposed by researchers from CEA (IRESNE Institute, Cadarache center) and Inria (Bordeaux). It takes place in a work package dedicated to discretization methods and aims to build efficient numerical methods for solving Multiphysics problems, i.e., problems in which different physics interact.
Numerical simulation of phenomena involving different physics can be carried out using either a monolithic or partitioned approach.
The monolithic approach consists in representing the different physics by solving a single matrix system containing all the unknowns. This system is often ill-conditioned and requires adapted techniques to be solved. It is also important to note that the algebraic system to be solved is often very large, reaching or even exceeding the maximum capacity of current solvers.
The partitioned approach relies on efficient solvers already developed and adapted to each of the Physics considered separately. The difficulty then lies in coupling these different solvers to obtain the converged Multiphysics solution.
The aim of this thesis is to develop an efficient and generic numerical method for coupling different physics solvers used in black-box way. In addition, this approach needs to be scalable to Exascale.
The relevance and generalizability of the proposed approach will be verified on electromagnetic/acoustic/seismic and thermo-mechanical couplings. In addition, the efficiency of the numerical method will be compared with that of a monolithic resolution considered as a reference numerical approach, but including physical modeling that is often degraded. Experimental validations will also be possible.