SHEM: An optimal coarse space for RAS and its multiscale approximation

Abstract

In domain decomposition methods, coarse spaces are traditionally added to make the method scalable. Coarse spaces can however do much more: they can act on other error components that the subdomain iteration has difficulties with, and thus accelerate the overall solution process. We identify here the optimal coarse space for RAS, where optimal does not refer to scalable, but to best possible. This coarse space leads to convergence of the subdomain iterative method in two steps. Since this coarse space is very rich, we propose an approximation which turns out to be also very effective for multiscale problems.