Time-Parallel Iterative Solvers for Parabolic Evolution Equations

DOI10.1137/18M1172466zbMath1450.65106arXiv1802.08126OpenAlexW2788680046MaRDI QIDQ4613503

Martin Neumüller, Iain Smears

Publication date: 1 February 2019

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

Full work available at URL: https://arxiv.org/abs/1802.08126

zbMATH Keywords

parabolic partial differential equationsparallel complexityinf-sup stabilityanalysis of iterative methods and preconditionerstime-parallel methodsweak and strong scaling

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20) Preconditioners for iterative methods (65F08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

A well-conditioned direct pint algorithm for first- and second-order evolutionary equations ⋮ A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations ⋮ A Parallel Algorithm for Solving Linear Parabolic Evolution Equations ⋮ A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations ⋮ Interpolation operators for parabolic problems ⋮ A Diagonalization-Based Parareal Algorithm for Dissipative and Wave Propagation Problems ⋮ Minimal residual space-time discretizations of parabolic equations: asymmetric spatial operators ⋮ Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods ⋮ Parallel and Robust Preconditioning for Space-Time Isogeometric Analysis of Parabolic Evolution Problems ⋮ Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs

Uses Software

• hypre
• FFTW
• PARAEXP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Toward an efficient parallel in time method for partial differential equations
• Space-time domain decomposition for parabolic problems
• Theory and practice of finite elements.
• Error-bounds for finite element method
• Résolution d'EDP par un schéma en temps «pararéel »
• Analysis of iterative methods for saddle point problems: a unified approach
• The $L^2$-Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations
• 50 Years of Time Parallel Time Integration
• Natural Preconditioning and Iterative Methods for Saddle Point Systems
• A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
• Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations
• A Time-Stepping Algorithm for Parallel Computers
• The time‐parallel multigrid method
• Solution of Sparse Indefinite Systems of Linear Equations
• Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
• Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems
• Preconditioning and Iterative Solution of All-at-Once Systems for Evolutionary Partial Differential Equations
• On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations
• The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation
• Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method
• An Algorithm with Polylog Parallel Complexity for Solving Parabolic Partial Differential Equations
• A Space-Time Multigrid Method for Parabolic Partial Differential Equations
• A Parallel Space-Time Algorithm
• Parallel Time Integration with Multigrid
• Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs
• Preconditioning
• PARAEXP: A Parallel Integrator for Linear Initial-Value Problems
• Parallel methods for integrating ordinary differential equations
• Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations
• An improved error bound for reduced basis approximation of linear parabolic problems
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems
• Limits on Parallelism in the Numerical Solution of Linear Partial Differential Equations
• A parallel nearly implicit time-stepping scheme