Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems

DOI10.1137/15M1046605zbMath1342.65225arXiv1411.0519OpenAlexW2594128612MaRDI QIDQ5739801

Publication date: 20 July 2016

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

Full work available at URL: https://arxiv.org/abs/1411.0519

zbMATH Keywords

parabolic problems strong and weak scalability DG-discretizations multigrid in space-time space-time parallel methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items

A parallel-in-time approach for accelerating direct-adjoint studies, A multigrid ghost-point level-set method for incompressible Navier-Stokes equations on moving domains with curved boundaries, Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting, A New Approach to Space-Time Boundary Integral Equations for the Wave Equation, On the Time-Domain Decomposition of Parabolic Optimal Control Problems, Time Parallelization for Nonlinear Problems Based on Diagonalization, A parallel-in-time multiple shooting algorithm for large-scale PDE-constrained optimal control problems, Space-time discontinuous Galerkin discretizations for linear first-order hyperbolic evolution systems, On the scalability of classical one-level domain-decomposition methods, A Parallel Algorithm for Solving Linear Parabolic Evolution Equations, Toward Parallel Coarse Grid Correction for the Parareal Algorithm, Multigrid methods with space-time concurrency, Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time, Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations, A Fully Parallelizable Space-Time Multilevel Monte Carlo Method for Stochastic Differential Equations with Additive Noise, Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems, A low-rank solver for the stochastic unsteady Navier-Stokes problem, A Parallel Fast Multipole Method for a Space-Time Boundary Element Method for the Heat Equation, Fourier analysis of a time-simultaneous two-grid algorithm using a damped Jacobi waveform relaxation smoother for the one-dimensional heat equation, Multilevel space-time block diagonal preconditioners for parabolic problems, A Unified Analysis Framework for Iterative Parallel-in-Time Algorithms, Multigrid method based on a space-time approach with standard coarsening for parabolic problems, Convergence analysis of space-time domain decomposition method for parabolic equations, Theoretical and practical aspects of space-time DG-SEM implementations, Numerical modeling and open-source implementation of variational partition-of-unity localizations of space-time dual-weighted residual estimators for parabolic problems, Low-rank parareal: a low-rank parallel-in-time integrator, A block Toeplitz preconditioner for all-at-once systems from linear wave equations, 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, Combining Space-Time Multigrid Techniques with Multilevel Monte Carlo Methods for SDEs, A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs, Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems, A parallel space-time boundary element method for the heat equation, Preconditioning and Iterative Solution of All-at-Once Systems for Evolutionary Partial Differential Equations, Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study, Time-Parallel Iterative Solvers for Parabolic Evolution Equations, An efficient solver for space-time isogeometric Galerkin methods for parabolic problems, PARAOPT: A Parareal Algorithm for Optimality Systems, A Superlinear Convergence Estimate for the Parareal Schwarz Waveform Relaxation Algorithm, Multipatch Space-Time Isogeometric Analysis of Parabolic Diffusion Problems, An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization, An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem, On the space-time discretization of variational retarded potential boundary integral equations, Fast parallel solver for the space-time IgA-DG discretization of the diffusion equation, A Time-Simultaneous Multigrid Method for Parabolic Evolution Equations, Some high order formulae for approximating Caputo fractional derivatives, A Direct Time Parallel Solver by Diagonalization for the Wave Equation, AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion), An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems, Space-Time Balancing Domain Decomposition, Multilevel Space-Time Additive Schwarz Methods for Parabolic Equations, Space-Time FE-DG Discretization of the Anisotropic Diffusion Equation in Any Dimension: The Spectral Symbol, Lossy data compression reduces communication time in hybrid time-parallel integrators, Space-Time Discretized Retarded Potential Boundary Integral Operators: Quadrature for Collocation Methods, Artificial viscosity joint spacetime multigrid method for Hamilton-Jacobi-Bellman and Kolmogorov-Fokker-Planck system arising from mean field games, 50 Years of Time Parallel Time Integration, Localized MQ-RBF meshless techniques for modeling unsaturated flow, A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs, Variational space-time elements for large-scale systems, Parallel and Robust Preconditioning for Space-Time Isogeometric Analysis of Parabolic Evolution Problems, Rigorous convergence proof of space-time multigrid with coarsening in space, Galerkin–collocation approximation in time for the wave equation and its post-processing, Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions., Convergence analysis of a \textit{periodic-like} waveform relaxation method for initial-value problems via the diagonalization technique, An All-at-Once Preconditioner for Evolutionary Partial Differential Equations, Further results on a space-time FOSLS formulation of parabolic PDEs, A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations

Uses Software

Cites Work