A Cascadic Multigrid Algorithm for the Double Obstacle Problem

2010 ◽  
Author(s):  
Jiantao Gu ◽  
Caixia Liu ◽  
Liping Du
Keyword(s):  
Obstacle Problem ◽  
Multigrid Algorithm ◽  
Cascadic Multigrid

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

2015 ◽  
Vol 8 (2) ◽  
pp. 199-219 ◽  
Author(s):  
Chunxiao Wu ◽  
Justin W.L. Wan
Keyword(s):  
Obstacle Problem ◽  
Multigrid Method ◽  
Multigrid Methods ◽  
Coarse Grid ◽  
Obstacle Problems ◽  
Hjb Equations ◽  
Fine Grid ◽  
Multigrid Algorithm ◽  
Prolongation Operator ◽  
Approximate Scheme

AbstractIn 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.

A cascadic multigrid algorithm for variational inequalities

2004 ◽  
Vol 7 (3-4) ◽  
pp. 153-157 ◽  
Author(s):  
H. Blum ◽  
D. Braess ◽  
F.T. Suttmeier
Keyword(s):  
Variational Inequalities ◽  
Multigrid Algorithm ◽  
Cascadic Multigrid

A Cascadic Multigrid Algorithm for Semilinear Indefinite Elliptic Problems

Computing ◽  
2000 ◽  
Vol 64 (4) ◽  
pp. 349-366 ◽  
Author(s):  
V. V. Shaidurov ◽  
G. Timmermann
Keyword(s):  
Elliptic Problems ◽  
Multigrid Algorithm ◽  
Cascadic Multigrid

scholarly journals The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shi Sun ◽  
Ziping Huang ◽  
Cheng Wang ◽  
Liming Guo
Keyword(s):  
Finite Element Method ◽  
Multigrid Method ◽  
Order Elliptic Equation ◽  
Galerkin Finite Element Method ◽  
Weak Galerkin ◽  
Galerkin Finite Element ◽  
Multigrid Algorithm ◽  
Second Order Elliptic Equation ◽  
Cascadic Multigrid ◽  
Cascadic Multigrid Method

This paper is devoted to the analysis of the cascadic multigrid algorithm for solving the linear system arising from the weak Galerkin finite element method. The proposed cascadic multigrid method is optimal for conjugate gradient iteration and quasi-optimal for Jacobi, Gauss-Seidel, and Richardson iterations. Numerical results are also provided to validate our theoretical analysis.

scholarly journals A cascadic multigrid algorithm for the Stokes equations

1999 ◽  
Vol 82 (2) ◽  
pp. 179-191 ◽  
Author(s):  
Dietrich Braess ◽  
Wolfgang Dahmen
Keyword(s):  
Stokes Equations ◽  
Multigrid Algorithm ◽  
Cascadic Multigrid
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