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Two‐level additive Schwarz algorithms for nonlinear complementarity problem with an M ‐function
Author(s) -
Xu Hongru,
Zeng Jinping,
Sun Zhe
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.650
Subject(s) - schwarz alternating method , additive schwarz method , nonlinear complementarity problem , monotonic function , mathematics , nonlinear system , mixed complementarity problem , complementarity (molecular biology) , algorithm , function (biology) , mathematical optimization , complementarity theory , class (philosophy) , computer science , mathematical analysis , domain decomposition methods , finite element method , artificial intelligence , physics , genetics , quantum mechanics , evolutionary biology , biology , thermodynamics
Nonlinear complementarity problem (NCP) is a wide class of problems. In this paper, some two‐level additive Schwarz algorithms for NCPs with an M ‐function are developed and analyzed. The algorithms are proved to be convergent monotonically and can reach the solution of the problem within finite steps. They may also offer a possibility of making use of fast nonlinear solvers for solving the subproblems involved in the algorithms. Some preliminary numerical results are reported. Copyright © 2009 John Wiley & Sons, Ltd.