A parallel nearly implicit time-stepping scheme

DOI10.1016/S0377-0427(01)00358-2zbMath0991.65067OpenAlexW1965344495WikidataQ126654183 ScholiaQ126654183MaRDI QIDQ5953929

Henk A. van der Vorst, Mikhail A. Botchev

Publication date: 1 September 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(01)00358-2

zbMATH Keywords

stabilitydomain decompositionparallel computationGMRESparallel time integrationparallelism across the problemspeed upstiff ODEs

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Parallel numerical computation (65Y05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations ⋮ Time-Parallel Iterative Solvers for Parabolic Evolution Equations ⋮ Unconditionally stable integration of Maxwell's equations

Uses Software

• LAPACK
• RKC
• VAC

Cites Work

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• Multi-grid dynamic iteration for parabolic equations
• RKC: An explicit solver for parabolic PDEs
• Stability control for approximate implicit time stepping schemes with minimum residual iterations
• Fourier mode analysis of the multigrid waveform relaxation and time- parallel multigrid methods
• Matrix-free \(W\)-methods using a multiple Arnoldi iteration
• Reducing the effect of global communication in \(\text{GMRES} (m)\) and CG on parallel distributed memory computers
• Iterative Solution of Linear Equations in ODE Codes
• A Time-Stepping Algorithm for Parallel Computers
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVP<scp>s</scp> for ODE<scp>s</scp>
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• Numerical Linear Algebra for High-Performance Computers
• A Newton basis GMRES implementation
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Exponential Integrators for Large Systems of Differential Equations
• An Algorithm with Polylog Parallel Complexity for Solving Parabolic Partial Differential Equations
• A Space-Time Multigrid Method for Parabolic Partial Differential Equations
• The Science of Computer Benchmarking
• Parallel methods for ODEs