Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems

Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of adaptive coarse spaces we present here is quite general since it applies to symmetric and non-symmetric problems, to symmetric preconditioners such as the additive Schwarz method (ASM) and to the non-symmetric preconditioner restricted additive Schwarz (RAS), as well as to exact or inexact subdomain solves. The coarse space is built by solving generalized eigenproblems in the subdomains and applying a well-chosen operator to the selected eigenvectors.