Multigrid Methods with Newton-Gauss-Seidel Smoothing and Constraint Preserving Interpolation for Obstacle Problems. Issue 2 (28th May 2015)

• Record Type: Journal Article
• Authors: Wu, Chunxiao; Wan, Justin W.L.
• Is Part Of: Numerical mathematics. Volume 8:Issue 2(2015)
• Page Start: 199
• Page End: 219
• Publication Date: 2015-05-28
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.w08si
• Languages: English
• ISSNs: 1004-8979

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>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.</p> </abstract>