Section: New Results

Schur domain decomposition methods

We have introduced spectral coarse spaces for the BDD and FETI methods in [5] . These coarse spaces are specifically designed for the two-level methods to be scalable and robust with respect to the coefficients in the equation and the choice of the decomposition. We achieve this by solving generalized eigenvalue problems on the interfaces between subdomains to identify the modes which slow down convergence. Theoretical bounds for the condition numbers of the preconditioned operators which depend only on a chosen threshold and the maximal number of neighbours of a subdomain were proved. For FETI there are two versions of the two-level method: one based on the full Dirichlet preconditioner and the other on the, cheaper, lumped preconditioner. Some numerical tests confirm these results.