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Adaptive FAS-multigrid method for nonlinear elliptic equations on unstructured grids
Faculty
Science
Year:
2008
Type of Publication:
Article
Pages:
1979-2002
Authors:
Mohamed, S. A
DOI:
10.1002/cnm.1089
Journal:
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING JOHN WILEY \& SONS LTD
Volume:
24
Research Area:
Engineering; Mathematics
ISSN
ISI:000261778700027
Keywords :
adaptive multigrid, unstructured grids, finite elements, nonlinear elliptic equations, 2-step assembly, nonlinear Gauss-Seidel smoother
Abstract:
A two-step, node-wise assembly procedure is developed to enhance the classical assembly process that is repeatedly required for the nonlinear finite elements method. Using the proposed assembly method, an efficient nonlinear point-wise Gauss-Seidel method is designed and used as a smoother in a full approximation storage multigrid (FAS\_MG) that results in solving nonlinear problems on unstructured grids as efficient as the linear ones. Next, the FAS\_MG solver is incorporated into an adaptive full multigrid cycle that solves the nonlinear problem on a coarse grid and uses a posteriori error estimator to adaptively and automatically construct a next finer grid. Numerical results show that the proposed method solves adaptively nonlinear finite elements elliptic problems within the textbook MG efficiency. Copyright (C) 2007 John Wiley \& Sons, Ltd.
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