Parallel-In-Time Multigrid with Adaptive Spatial Coarsening for The Linear Advection and Inviscid Burgers Equations

DOI10.1137/17M1144982zbMath1407.65040MaRDI QIDQ4623142

Jacob B. Schroder, Alexander J. M. Howse, Scott MacLachlan, Robert Falgout, Hans De Sterck

Publication date: 19 February 2019

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

zbMATH Keywords

hyperbolic problemsparallel-in-timeadaptive spatial coarseningmultigrid reduction in time (MGRIT)xbraid

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Iterative numerical methods for linear systems (65F10) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (16)

Convergence Analysis of a Mixed Precision Parareal Algorithm ⋮ On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations ⋮ Convergence analysis of space-time domain decomposition method for parabolic equations ⋮ Multigrid reduction in time for non-linear hyperbolic equations ⋮ Asynchronous Truncated Multigrid-Reduction-in-Time ⋮ A posteriori error analysis for a space‐time parallel discretization of parabolic partial differential equations ⋮ Efficient multigrid reduction-in-time for method-of-lines discretizations of linear advection ⋮ Applications of time parallelization ⋮ A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics ⋮ Parallel-in-time simulation of an electrical machine using MGRIT ⋮ Toward error estimates for general space-time discretizations of the advection equation ⋮ Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators ⋮ Multigrid reduction in time with Richardson extrapolation ⋮ Multilevel Convergence Analysis of Multigrid-Reduction-in-Time ⋮ Necessary Conditions and Tight Two-level Convergence Bounds for Parareal and Multigrid Reduction in Time ⋮ A note on parallel preconditioning for all-at-once evolutionary PDEs

Uses Software

• UMFPACK
• CHOLMOD
• pyParareal

Cites Work

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