NOSAS: NOnoverlapping Spectral Additive Schwarz

Marcus Sarkis

Department of Mathematical Sciences, Worcester Polytechnic Institute, USA

Monday 22nd May 2023

16:00:00

Aula seminari III piano

NOSAS is a family of adaptive Schwarz preconditioners designed originally for solving elliptic problems with highly heterogeneous coefficients. It has flavors from both overlapping and nonoverlapping methods. Different from the overlapping methods, like GDSW and GeoEo, NOSAS has no local problems on extended subdomains, and different from the nonoverlapping methods, like BDD, BDDC, FETI and FETI-DP, NOSAS has no weighting operator to average local solutions on the interface. In RASHO, all the local factorizations and eigensolvers are done inside the nonoverlapping subdomains, and like BDD the coarse degrees of freedom are related to the bad nodes inside each of these subdomains, however, with a better corresponding coarse stiffness in terms of sparsity. RASHO is very flexible, can be designed to have condition number from (1+log H/h)^2 to (1+H/h)^2 without solving any eigenvalue problem. Finally, RASHO is easy to implement. In this talk we introduce the predecessor of NOSAS, the Average Additive Schwarz Method introduced by Bjorstad and Dryja 99', and then move to the vanilla version of NOSAS and then to the adaptive versions, economical versions and three-level versions. We show numerical experiments and some comparisons with GeoEo and Adaptive BDDC. Contatto: paola.antonietti@polimi.it