A Two-level Substructuring method tailored to Schur based Domain Decomposition Methods

The method presented here is a parallel mesh generation method leading to subdomains well-suited to Schur based domain decomposition solvers such as the FETI and BDD methods. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinements and mesh deformations techniques. The proposed methodology aims at limiting the occurrence of known pathological situations (jagged interfaces, misplaced heterogeneity with respect to the interfaces, ...) that penalize the convergence of the solver because of a strong degradation of the condition number of the problem. Some cures (based for instance on multipreconditioning, GenEO spectral coarse spaces, ...) were developed earlier for these situations but they require important additional computational resources. The goal, here, is to reach the solution without the help of these expensive methodologies, while making parallel the usually expensive steps dealing with mesh generation and splitting. The method has a good parallel efficiency in terms of strong and weak scaling and improves the convergence rates of the FETI method when dealing with very strong hetrogeneity ratios. We are currently investigating other solver improvements that could be obtained from this substructuring framework.