Volume 8, Issue 2
Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems

Chunxiao Wu & Justin W.L. Wan

Numer. Math. Theor. Meth. Appl.,8 (2015), pp. 199-219

Published online: 2015-08

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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.

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@Article{NMTMA-8-199, author = {Chunxiao Wu and Justin W.L. Wan}, title = {Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {2}, pages = {199--219}, 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.}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w08si}, url = {http://global-sci.org/intro/article_detail/nmtma/12407.html} }

TY - JOUR T1 - Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems AU - Chunxiao Wu & Justin W.L. Wan JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 199 EP - 219 PY - 2015 DA - 2015/08 SN - 8 DO - http://dor.org/10.4208/nmtma.2015.w08si UR - https://global-sci.org/intro/article_detail/nmtma/12407.html KW - AB -

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.

Chunxiao Wu & Justin W.L. Wan. (1970). Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems. Numerical Mathematics: Theory, Methods and Applications. 8 (2). 199-219. doi:10.4208/nmtma.2015.w08si
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