Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs
From MaRDI portal
Publication:5161772
DOI10.1137/20M1387985WikidataQ114074115 ScholiaQ114074115MaRDI QIDQ5161772
Qiao Chen, Xue Bin Wang, Xiangmin Jiao
Publication date: 1 November 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.12779
parabolic partial differential equationspreconditioningmultilevel methodsGauss-Legendre schemesblock Schur decompositionfully implicit Runge-Kutta
Computational methods for sparse matrices (65F50) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Preconditioners for iterative methods (65F08)
Related Items (5)
Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods ⋮ Theoretical and practical aspects of space-time DG-SEM implementations ⋮ A-Stable High-Order Block Implicit Methods for Parabolic Equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A splitting preconditioner for the iterative solution of implicit Runge-Kutta and boundary value methods
- Automated solution of differential equations by the finite element method. The FEniCS book
- Preconditioning techniques for nonsymmetric and indefinite linear systems
- Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations
- Evaluation of fully implicit Runge Kutta schemes for unsteady flow calculations
- Preconditioning techniques for large linear systems: A survey
- A hybrid method and unified analysis of generalized finite differences and Lagrange finite elements
- Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes
- Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
- On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
- A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
- Strang-type preconditioners for systems of LMF-based ODE codes
- Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations
- Generalized Kronecker product splitting iteration for the solution of implicit Runge-Kutta and boundary value methods
- A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting
- A comparison of preconditioned Krylov subspace methods for large‐scale nonsymmetric linear systems
- Triangularly Implicit Iteration Methods for ODE-IVP Solvers
- A multilevel Crout ILU preconditioner with pivoting and row permutation
- Comparison of multigrid algorithms for high‐order continuous finite element discretizations
- A First Course in the Numerical Analysis of Differential Equations
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- An Optimal Circulant Preconditioner for Toeplitz Systems
- A linear time implementation of the reverse Cuthill-McKee algorithm
- Optimal and Superoptimal Circulant Preconditioners
- On the implementation of implicit Runge-Kutta methods
- An Efficient Solution Process for Implicit Runge–Kutta Methods
- A Circulant Preconditioner for the Systems of LMF-Based ODE Codes
- An Approximate Minimum Degree Ordering Algorithm
- ILUT: A dual threshold incomplete LU factorization
- HILUCSI: Simple, robust, and fast multilevel ILU for large‐scale saddle‐point problems from PDEs
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- Matlab code for sorting real Schur forms
- Analysis of Finite Difference Schemes
- Order‐Optimal Preconditioners for Implicit Runge–Kutta Schemes Applied to Parabolic PDEs
- Multilevel ILU With Reorderings for Diagonal Dominance
- Multilevel Preconditioners Constructed From Inverse-Based ILUs
- A hybrid geometric + algebraic multigrid method with semi‐iterative smoothers
- Spectral/hp Element Methods for Computational Fluid Dynamics
- A special stability problem for linear multistep methods
- Numerical Methods for Ordinary Differential Equations
This page was built for publication: Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs
