Wavelet-In-Time Multigrid-In-Space Preconditioning of Parabolic Evolution Equations
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Publication:3464424
DOI10.1137/140998639zbMath1329.65200OpenAlexW2287476413MaRDI QIDQ3464424
Publication date: 27 January 2016
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140998639
Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) 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)
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Cites Work
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- Space-time discretization of the heat equation
- Boundary integral operators for the heat equation
- Parallel multiple shooting for the solution of initial value problems
- On the convergence of a multigrid method for linear reaction-diffusion problems
- Fourier mode analysis of the multigrid waveform relaxation and time- parallel multigrid methods
- On the \(H^1\)-stability of the \(L_2\)-projection onto finite element spaces
- Stability of Petrov-Galerkin discretizations: application to the space-time weak formulation for parabolic evolution problems
- A sparse grid space-time discretization scheme for parabolic problems
- Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
- Conditional space-time stability of collocation Runge-Kutta for parabolic evolution equations
- Résolution d'EDP par un schéma en temps «pararéel »
- An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations
- 50 Years of Time Parallel Time Integration
- Sparse space-time Galerkin BEM for the nonstationary heat equation
- Parallel multistep methods for linear evolution problems
- Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs
- Space-time adaptive wavelet methods for parabolic evolution problems
- Sparse Tensor Discretization of Elliptic sPDEs
- Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results
- Nonstandard Norms and Robust Estimates for Saddle Point Problems
- The adaptive tensor product wavelet scheme: sparse matrices and the application to singularly perturbed problems
- Numerical solution of saddle point problems
- The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
- Schwarz Waveform Relaxation Algorithms
- LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
- Fast Numerical Solution of Time-Periodic Parabolic Problems by a Multigrid Method
- Biorthogonal bases of compactly supported wavelets
- Stabilizing the Hierarchical Basis by Approximate Wavelets II: Implementation and Numerical Results
- Solving Generalized Least-Squares Problems with LSQR
- A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature
- A Space-Time Multigrid Method for Parabolic Partial Differential Equations
- Multigrid Waveform Relaxation of Spatial Finite Element Meshes: The Continuous-Time Case
- Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
- Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
- Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems
- Computational scales of Sobolev norms with application to preconditioning
- The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
- Preconditioning
- Analysis of the Parareal Time‐Parallel Time‐Integration Method
- Space-Time Approximation with Sparse Grids
- Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems
- Multiharmonic finite element analysis of a time-periodic parabolic optimal control problem
