Estimates for multigrid methods based on red-black Gauss-Seidel smoothings

DOI10.1007/BF01395819zbMath0633.65096MaRDI QIDQ1096358

Seymour V. Parter

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133261

zbMATH Keywords

rate of convergencePoisson equationmultigrid algorithmsnon-convex polygonal domainsred-black Gauss-Seidel smoothingW-cycle estimates

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (3)

Smoothing Analysis of Two Robust Multigrid Methods for Elliptic Optimal Control Problems ⋮ CACHING IN WITH MULTIGRID ALGORITHMS: PROBLEMS IN TWO DIMENSIONS ⋮ An efficient red-black skewed extrapolation cascadic multigrid method for two-dimensional Poisson equation

Cites Work

• The contraction number of a multigrid method with mesh ratio 2 for solving Poisson's equation
• A note on MGR methods
• A study of some multigrid ideas
• Remarks on multigrid convergence theorems
• Multigrid methods for symmetric variational problems: A general theory and convergence estimates for usual smoothers
• The contraction number of a multigrid method for solving the Poisson equation
• Multigrid Methods for Variational Problems: Further Results
• The Covergence Rate of a Multigrid Method with Gauss-Seidel Relaxation for the Poisson Equation
• A New Convergence Proof for the Multigrid Method Including the V-Cycle
• Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration
• Multigrid Methods for Variational Problems: General Theory for the V-Cycle
• On an Estimate for the Three-Grid MGR Multigrid Method
• Multigrid Methods for Variational Problems

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