Smoothing factor, order of prolongation and actual multigrid convergence

DOI10.1007/s00211-011-0362-7zbMath1227.65122OpenAlexW2106457025MaRDI QIDQ634611

Artem Napov, Yvan Notay

Publication date: 16 August 2011

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

Full work available at URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/90854/7/VcycFourierREP.pdf

zbMATH Keywords

convergencemultigridFourier methodV-cyclesmoothing factor

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10)

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Uses Software

• Wesseling
• LFA

Cites Work

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• More on the order of prolongations and restrictions
• Comparison of bounds for V-cycle multigrid
• Convergence analysis of two-grid methods for elliptic Toeplitz and PDEs matrix-sequences
• On the order of prolongations and restrictions in multigrid procedures
• Algebraic Multigrid Based on Element Interpolation (AMGe)
• On Three-Grid Fourier Analysis for Multigrid
• An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matrices
• When does two-grid optimality carry over to the V-cycle?
• Multilevel Block Factorization Preconditioners
• Analysis of Aggregation-Based Multigrid
• Multigrid Methods for Variational Problems: General Theory for the V-Cycle
• An Algebraic Theory for Multigrid Methods for Variational Problems
• Rigorous Quantitative Analysis of Multigrid, I. Constant Coefficients Two-Level Cycle with $L_2 $-Norm
• Coarse-Grid Correction for Nonelliptic and Singular Perturbation Problems
• Spectral AMGe ($\rho$AMGe)

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