Analysis of a new parareal algorithm based on waveform relaxation method for time-periodic problems

DOI10.1007/s11075-013-9810-zzbMath1308.65117OpenAlexW2072683770MaRDI QIDQ483282

Bo Song, Yao-Lin Jiang

Publication date: 16 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-013-9810-z

zbMATH Keywords

convergenceparallel computationinitial value problemerror estimatewaveform relaxationparareal algorithmtime-periodic problems

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Nonlinear ordinary differential equations and systems (34A34) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (14)

Some convergence results of waveform relaxation for a class of second-order quasilinear parabolic equations ⋮ Three rapidly convergent parareal solvers with application to time‐dependent PDEs with fractional Laplacian ⋮ An effective iteration method for a class of nonlinear singular perturbed problems ⋮ Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation ⋮ Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations ⋮ Analysis of the parareal algorithm for linear parametric differential equations ⋮ Parareal algorithms with local time-integrators for time fractional differential equations ⋮ A hybrid algorithm based on parareal and Schwarz waveform relaxation ⋮ A Superlinear Convergence Estimate for the Parareal Schwarz Waveform Relaxation Algorithm ⋮ An efficient parareal algorithm for a class of time-dependent problems with fractional Laplacian ⋮ Towards essential improvement for the parareal-TR and parareal-Gauss4 algorithms ⋮ The study of parareal algorithm for the linear switched systems ⋮ A new parareal waveform relaxation algorithm for time-periodic problems ⋮ Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

Uses Software

• PARAEXP

Cites Work

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• A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations
• 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
• Schwarz waveform relaxation methods for parabolic equations in space-frequency domain
• Parallel multiple shooting for the solution of initial value problems
• A parareal algorithm based on waveform relaxation
• Periodic waveform relaxation solutions of nonlinear dynamic equations.
• Numerical Methods for Time-Periodic Solutions of Nonlinear Parabolic Boundary Value Problems
• Résolution d'EDP par un schéma en temps «pararéel »
• Analysis of Two Parareal Algorithms for Time-Periodic Problems
• Nonlinear Convergence Analysis for the Parareal Algorithm
• Toeplitz and Circulant Matrices: A Review
• Fast Numerical Solution of Time-Periodic Parabolic Problems by a Multigrid Method
• Numerical Approximation of a Periodic Linear Parabolic Problem
• Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations
• On Dynamic Iteration Methods for Solving Time-Periodic Differential Equations
• The Existence, Computation, and Number of Solutions of Periodic Parabolic Problems
• A Note on the Spectra and Pseudospectra of Waveform Relaxation Operators for Linear Differential-Algebraic Equations
• Optimized Waveform Relaxation Methods for RC Type Circuits
• On Time-Domain Simulation of Lossless Transmission Lines with Nonlinear Terminations
• Computing periodic solutions of linear differential-algebraic equations by waveform relaxation
• A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations
• The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation
• PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
• Monotonic Parareal Control for Quantum Systems
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR EQUATIONS OF EVOLUTION
• Matrix Iterative Analysis
• A note on convergence conditions of waveform relaxation algorithms for nonlinear differential-algebraic equations

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