A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems
DOI10.2140/camcos.2023.18.55arXiv2103.12571OpenAlexW4390108763MaRDI QIDQ6183191
Gayatri Čaklović, Martin Frank, Robert Speck
Publication date: 26 January 2024
Published in: Communications in Applied Mathematics and Computational Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.12571
iterative methodscollocationdiagonalizationhigh-performance computingparallel-in-time integrationpetsc4py
Iterative numerical methods for linear systems (65F10) Roundoff error (65G50) Parallel numerical computation (65Y05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Complexity and performance of numerical algorithms (65Y20) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)
Cites Work
- Toward an efficient parallel in time method for partial differential equations
- Wave propagation characteristics of Parareal
- Generalized inverses of certain Toeplitz matrices
- Convergence analysis of a \textit{periodic-like} waveform relaxation method for initial-value problems via the diagonalization technique
- Explicit parallel-in-time integration of a linear acoustic-advection system
- Résolution d'EDP par un schéma en temps «pararéel »
- 50 Years of Time Parallel Time Integration
- Volterra Integral Equations
- Interweaving PFASST and Parallel Multigrid
- Analysis of a Krylov subspace enhanced parareal algorithm for linear problems
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Preconditioning and Iterative Solution of All-at-Once Systems for Evolutionary Partial Differential Equations
- A Direct Time Parallel Solver by Diagonalization for the Wave Equation
- Stability of the Parareal Algorithm
- A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator
- Stable Parareal in Time Method for First- and Second-Order Hyperbolic Systems
- Algorithm 997
- An All-at-Once Preconditioner for Evolutionary Partial Differential Equations
- Algorithm 1016
- Twelve Ways to Fool the Masses When Giving Parallel-in-Time Results
- A Uniform Spectral Analysis for a Preconditioned All-at-Once System from First-Order and Second-Order Evolutionary Problems
- A Diagonalization-Based Parareal Algorithm for Dissipative and Wave Propagation Problems
- Parallel Time Integration with Multigrid
- Convergence of Parareal for the Navier-Stokes Equations Depending on the Reynolds Number
- Algorithm 965
- PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
- Parallel methods for integrating ordinary differential equations
- A Fast Block $\alpha$-Circulant Preconditoner for All-at-Once Systems From Wave Equations
- Parallel methods for ODEs
- Applications of time parallelization
- PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method
This page was built for publication: A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems