Fourier mode analysis of the multigrid waveform relaxation and time- parallel multigrid methods

DOI10.1007/BF02238230zbMath0826.65087OpenAlexW1501940787MaRDI QIDQ1893149

Stefan Vandewalle, Graham Horton

Publication date: 26 November 1995

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238230

zbMATH Keywords

convergenceparallel computingmultigridFourier mode analysisnumerical experimentmultigrid waveform relaxationtime-parallel multigrid methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Parallel numerical computation (65Y05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items

Interweaving PFASST and Parallel Multigrid ⋮ Multigrid methods with space-time concurrency ⋮ Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations ⋮ A generalized predictive analysis tool for multigrid methods ⋮ A waveform relaxation Newmark method for structural dynamics problems ⋮ Fourier analysis of a time-simultaneous two-grid algorithm using a damped Jacobi waveform relaxation smoother for the one-dimensional heat equation ⋮ Multigrid Waveform Relaxation for the Time-Fractional Heat Equation ⋮ Multigrid method based on a space-time approach with standard coarsening for parabolic problems ⋮ Applications of time parallelization ⋮ Multigrid methods for parabolic distributed optimal control problems ⋮ Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study ⋮ Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT) ⋮ A smoothing process of multicolor relaxation for solving partial differential equation by multigrid method ⋮ A Time-Simultaneous Multigrid Method for Parabolic Evolution Equations ⋮ An angular multigrid method for computing mono-energetic particle beams in flatland ⋮ A parallel nearly implicit time-stepping scheme ⋮ Analysis of two-grid methods: The nonnormal case ⋮ Space-time isogeometric analysis of parabolic evolution problems ⋮ Rigorous convergence proof of space-time multigrid with coarsening in space

Uses Software

• Wesseling

Cites Work

• Multi-grid dynamic iteration for parabolic equations
• Numerical experiments with nonlinear multigrid waveform relaxation on a parallel processor
• A time-parallel multigrid-extrapolation method for parabolic partial differential equations
• Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations
• The time‐parallel multigrid method
• On Dynamic Iteration Methods for Solving Time-Periodic Differential Equations
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Multigrid Schemes for Time-Dependent Incompressible Navier-Stokes Equations
• An Algorithm with Polylog Parallel Complexity for Solving Parabolic Partial Differential Equations
• A Space-Time Multigrid Method for Parabolic Partial Differential Equations
• Multigrid Waveform Relaxation of Spatial Finite Element Meshes: The Continuous-Time Case
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Fourier mode analysis of the multigrid waveform relaxation and time- parallel multigrid methods