A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2

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• 作者：Ryadh Haferssas^a ; ^b ; ^{ryadh.haferssas@ljll.math.upmc.fr" class="auth_mail" title="E-mail the corresponding author} ; Pierre Jolivet^a ; ^b ; ^{jolivet@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author} ; Fré ; dé ; ric Nataf^a ; ^b ; ^{nataf@ann.jussieu.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：353
• 期：10
• 页码：959-963
• 全文大小：304 K

文摘

Optimized Schwarz methods (OSM) are very popular methods that were introduced in [11] for elliptic problems and in [3] for propagative wave phenomena. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm [17] and by identifying the problematic modes using two different generalized eigenvalue problems instead of only one as in [16] and [15] for the ASM (Additive Schwarz method), BDD (Balancing Domain Decomposition [12]) or FETI (Finite-Element Tearing and Interconnection [6]) methods.