Aitken-Schwarz methods with non matching finite elements and spectral elements grids for the parallel simulation of an underground waste disposal site modelized by upscaling

摘要

A new methodology has been developed to take into account different geological media in underground convection-diffusion models. The mixed finite element are adapted to heterogeneity in the coefficients (diffusion, mesh) while the spectral methods are suited to smooth solutions. Both numerical (coupling of the methods) aspects and parallelization issues are considered in this paper. This methodology fits well to a smooth solution in the whole domain. A heterogeneous case where the solutibn is non smooth only in a part of the domain gives also satisfactory results. The same type of methodology (domain decomposition method on non matching grids speed up by Aitken process) has been applied to the 1 order terms of the model we presented in the first section (cf. [2]).