A Superlinear Convergence Estimate for the Parareal Schwarz Waveform Relaxation Algorithm

DOI10.1137/18M1177226zbMath1414.65018OpenAlexW2938257492MaRDI QIDQ4632011

Yao-Lin Jiang, Bo Song, Martin J. Gander

Publication date: 25 April 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1177226

zbMATH Keywords

parareal algorithmSchwarz waveform relaxationparareal Schwarz waveform relaxation

Mathematics Subject Classification ID

Related Items (15)

Some convergence results of waveform relaxation for a class of second-order quasilinear parabolic equations ⋮ Time domain decomposition of parabolic control problems based on discontinuous Galerkin semi-discretization ⋮ Waveform Relaxation Methods for Lie-Group Equations ⋮ Coupling Parareal with Optimized Schwarz Waveform Relaxation for Parabolic Problems ⋮ Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation ⋮ Discrete-time analysis of optimized Schwarz waveform relaxation with Robin parameters depending on the targeted iteration count ⋮ Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations ⋮ Analysis of a new accelerated waveform relaxation method based on the time-parallel algorithm ⋮ Applications of time parallelization ⋮ Riemannian Modified Polak--Ribière--Polyak Conjugate Gradient Order Reduced Model by Tensor Techniques ⋮ Improved uniform error bounds on parareal exponential algorithm for highly oscillatory systems ⋮ A hybrid algorithm based on parareal and Schwarz waveform relaxation ⋮ The study of parareal algorithm for the linear switched systems ⋮ Asymptotic analysis for overlap in waveform relaxation methods for RC type circuits ⋮ Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime

Uses Software

• PARAEXP

Cites Work

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• A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations
• Toward an efficient parallel in time method for partial differential equations
• Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems
• Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for parabolic problems
• A hybrid parareal spectral deferred corrections method
• Waveform relaxation for reaction-diffusion equations
• A parareal in time procedure for the control of partial differential equations
• Multi-grid dynamic iteration for parabolic equations
• Fast parareal iterations for fractional diffusion equations
• Waveform relaxation methods for fractional differential equations with the Caputo derivatives
• A parareal algorithm based on waveform relaxation
• Overlapping Schwarz waveform relaxation for the heat equation in \(n\) dimensions
• Space-time domain decomposition for parabolic problems
• Parallelization in time through tensor-product space-time solvers
• Résolution d'EDP par un schéma en temps «pararéel »
• 50 Years of Time Parallel Time Integration
• A Direct Solver for Time Parallelization
• Analysis of Two Parareal Algorithms for Time-Periodic Problems
• The Optimized Schwarz Method with a Coarse Grid Correction
• A homographic best approximation problem with application to optimized Schwarz waveform relaxation
• Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation
• Toward Parallel Coarse Grid Correction for the Parareal Algorithm
• Nonlinear Convergence Analysis for the Parareal Algorithm
• Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics
• Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations
• Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation
• Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
• A Note on the Spectra and Pseudospectra of Waveform Relaxation Operators for Linear Differential-Algebraic Equations
• Solving time‐periodic fractional diffusion equations via diagonalization technique and multigrid
• Optimized Waveform Relaxation Methods for RC Type Circuits
• A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods
• A Direct Time Parallel Solver by Diagonalization for the Wave Equation
• On Time-Domain Simulation of Lossless Transmission Lines with Nonlinear Terminations
• Computing periodic solutions of linear differential-algebraic equations by waveform relaxation
• Parallel-in-time simulation of the unsteady Navier–Stokes equations for incompressible flow
• A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations
• The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation
• Stability of the Parareal Algorithm
• Absorbing boundary conditions for the wave equation and parallel computing
• A new parareal waveform relaxation algorithm for time-periodic problems
• Parallel Time Integration with Multigrid
• PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
• Monotonic Parareal Control for Quantum Systems
• Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Overlapping Schwarz Waveform Relaxation for Convection-Dominated Nonlinear Conservation Laws
• Optimized Schwarz Methods
• Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems
• A note on convergence conditions of waveform relaxation algorithms for nonlinear differential-algebraic equations
• Multigrid interpretations of the parareal algorithm leading to an overlapping variant and MGRIT

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