Convergence rate analysis of a multiplicative Schwarz method for variational inequalities

• Main Authors: Badea, Lori, Tai, Xue Cheng, Wang, Junping
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
• Online Access: https://hdl.handle.net/10356/91828; http://hdl.handle.net/10220/6043; http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:EBSCO_APH&id=doi:&genre=&isbn=&issn=00361429&date=2003&volume=41&issue=3&spage=1052&epage=&aulast=Badea&aufirst=%20Lori&auinit=&title=SIAM%20Journal%20on%20Numerical%20Analysis&atitle=CONVERGENCE%20RATE%20ANALYSIS%20OF%20A%20MULTIPLICATIVE%20SCHWARZ%20METHOD%20FOR%20VARIATIONAL%20INEQUALITIES%2E&sici.
• Institution: Nanyang Technological University

This paper derives a linear convergence for the Schwarz overlapping domain decomposition method when applied to constrained minimization problems. The convergence analysis is based on a minimization approach to the corresponding functional over a convex set. A general framework of convergence is established for some multiplicative Schwarz algorithm. The abstract theory is particularly applied to some obstacle problems, which yields a linear convergence for the corresponding Schwarz overlapping domain decomposition method of one and two levels. Numerical experiments are presented to confirm the convergence estimate derived in this paper.