Coarse Spaces for Nonsymmetric Two-Level Preconditioners Based on Local Extended Generalized Eigenproblems

Abstract. Domain decomposition 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 nonsymmetric problems, to symmetric preconditioners such as the additive Schwarz method, and to the nonsymmetric preconditioner restricted additive Schwarz, 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.