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 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 eigenvalues in the subdomains and applying a well-chosen operator to the selected eigenvectors.

翻译：区域分解方法是大规模线性系统并行计算中的自然策略，其可扩展性取决于两层方法中粗空间的设计。本文提出的自适应粗空间分析具有普适性，适用于对称/非对称问题、对称预条件子（如加性Schwarz方法）与非对称预条件子（如限制性加性Schwarz方法），以及精确/非精确子域求解。该粗空间通过求解子域广义特征值问题，并对选定的特征向量施加特定算子而构建。