Parallel multistep methods for linear evolution problems

DOI10.1093/imanum/drq040zbMath1248.65100OpenAlexW2145180832MaRDI QIDQ2902209

Lehel Banjai, Daniel Peterseim

Publication date: 17 August 2012

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/drq040

zbMATH Keywords

heat equationwave equationnumerical examplesparallel computationmethod of linesHelmholtz equationmultigridRunge-Kutta time discretizationtriangular Toeplitz systemsfinite element method in spaceshifted Laplacian preconditioner

Mathematics Subject Classification ID

Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Preconditioners for iterative methods (65F08)

Related Items (9)

Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations ⋮ Parallel-in-time preconditioner for the Sinc-Nyström systems ⋮ A Parallel-In-Time Block-Circulant Preconditioner for Optimal Control of Wave Equations ⋮ PinT Preconditioner for Forward-Backward Evolutionary Equations ⋮ Space-time discretization of the heat equation ⋮ Preconditioners for all-at-once system from the fractional mobile/immobile advection-diffusion model ⋮ A preconditioning technique for all-at-once system from the nonlinear tempered fractional diffusion equation ⋮ Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems ⋮ A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations

Uses Software

• BiCGstab

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