On the performance of parallel waveform relaxations for differential systems

DOI10.1016/0168-9274(95)00116-6zbMath0855.65074OpenAlexW2082383413MaRDI QIDQ1917442

Carolyn Dyke, Bert Pohl, Kevin Burrage

Publication date: 7 July 1996

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00116-6

zbMATH Keywords

performancedifferential systemsnumerical comparisonsdistributed memory waveform relaxation package

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Complexity and performance of numerical algorithms (65Y20)

Related Items

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations ⋮ Non-stationary wave relaxation methods for general linear systems of Volterra equations: convergence and parallel GPU implementation ⋮ Optimal Schwarz waveform relaxation for fractional diffusion-wave equations ⋮ A parallel four step domain decomposition scheme for coupled forward-backward stochastic differential equations ⋮ Schwarz Waveform Relaxation with Adaptive Pipelining ⋮ Parallel methods for weakly singular Volterra integral equations on GPUs ⋮ A note on convergence conditions of waveform relaxation algorithms for nonlinear differential-algebraic equations ⋮ Parallel Schwarz waveform relaxation method for a semilinear heat equation in a cylindrical domain ⋮ GPU-acceleration of waveform relaxation methods for large differential systems ⋮ Convergence of the parallel chaotic waveform relaxation method for stiff systems

Uses Software

• VODE
• LSODE

Cites Work

• Remarks on Picard-Lindelöf iteration
• Numerical experiments with nonlinear multigrid waveform relaxation on a parallel processor
• Implementing an ODE code on distributed memory computers
• Preconditioning waveform relaxation iterations for differential systems
• Convergence of Dynamic Iteration Methods for Initial Value Problems
• Multi-Splittings of Matrices and Parallel Solution of Linear Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• VODE: A Variable-Coefficient ODE Solver
• Waveform Iteration and the Shifted Picard Splitting
• Waveform Relaxation with Overlapping Splittings
• The performance of preconditioned waveform relaxation techniques for pseudospectral methods
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