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Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems

Published online by Cambridge University Press:  28 May 2015

Chunxiao Wu  and
Justin W.L. Wan
Chunxiao Wu
Affiliation:
Centre for Computational Mathematics in Industry and Commerce, University of Waterloo, Waterloo, Ontario, Canada
Justin W.L. Wan
Affiliation:
David R. Cheriton School of Computer Science and Centre for Computational Mathematics in Industry and Commerce, University of Waterloo, Waterloo, Ontario, Canada
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Abstract

In this paper, we propose a multigrid algorithm based on the full approximate scheme for solving the membrane constrained obstacle problems and the minimal surface obstacle problems in the formulations of HJB equations. A Newton-Gauss-Seidel (NGS) method is used as smoother. A Galerkin coarse grid operator is proposed for the membrane constrained obstacle problem. Comparing with standard FAS with the direct discretization coarse grid operator, the FAS with the proposed operator converges faster. A special prolongation operator is used to interpolate functions accurately from the coarse grid to the fine grid at the boundary between the active and inactive sets. We will demonstrate the fast convergence of the proposed multigrid method for solving two model obstacle problems and compare the results with other multigrid methods.

Keywords

65M5565M2265F1065F50Multigrid methodobstacle problemelliptic variational inequalitycomplementarity problemHamilton-Jacobi-Bellman equationfull approximation scheme
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 2 , May 2015 , pp. 199 - 219
Copyright
Copyright © Global-Science Press 2015 

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