Nonsymmetric Algebraic Multigrid Based on Local Approximate Ideal Restriction ($\ell$AIR)
From MaRDI portal
Publication:4562339
DOI10.1137/17M1144350zbMath1412.65130arXiv1708.06065MaRDI QIDQ4562339
Ben S. Southworth, Thomas A. Manteuffel, J. W. Ruge
Publication date: 19 December 2018
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.06065
numerical resultslinear systemfilteringalgebraic multigridpreconditionersNeumann seriesparallel implementationerror reductionadvection-diffusion-reaction equationblock decompositionlumpingnonsymmetric probleminterpolation operatorideal restrictionresidual reduction\(\ell\)AIRC-pointsF-pointsideal restriction operatorlocal ideal restriction
Iterative numerical methods for linear systems (65F10) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)
Related Items (18)
Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting ⋮ An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD ⋮ Scalable preconditioning for the stabilized contact mechanics problem ⋮ Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs ⋮ A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures ⋮ Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods ⋮ Parallel Energy-Minimization Prolongation for Algebraic Multigrid ⋮ Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices ⋮ Applications of time parallelization ⋮ A comparison of element agglomeration algorithms for unstructured geometric multigrid ⋮ Diffusion Synthetic Acceleration Preconditioning for Discontinuous Galerkin Discretizations of $S_N$ Transport on High-Order Curved Meshes ⋮ AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion) ⋮ Necessary Conditions and Tight Two-level Convergence Bounds for Parareal and Multigrid Reduction in Time ⋮ Nonsymmetric Reduction-Based Algebraic Multigrid ⋮ Convergence in Norm of Nonsymmetric Algebraic Multigrid ⋮ On Fixed-Point, Krylov, and $2\times 2$ Block Preconditioners for Nonsymmetric Problems ⋮ Convergence Analysis of Inexact Two-Grid Methods: A Theoretical Framework ⋮ Space-Time Block Preconditioning for Incompressible Flow
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems
- The many proofs of an identity on the norm of oblique projections
- On algebraic multi-level methods for non-symmetric systems --- comparison results
- A note on MGR methods
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
- On block diagonal and Schur complement preconditioning
- \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
- Multigrid line smoothers for higher order upwind discretizations of convection- dominated problems
- Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation
- Multigrid methods for convection-diffusion problems discretized by a monotone scheme
- Algebraic Two-Level Preconditioners for the Schur Complement Method
- Reducing Parallel Communication in Algebraic Multigrid through Sparsification
- Non-Galerkin Coarse Grids for Algebraic Multigrid
- Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems
- DOLFIN
- Algebraic Theory of Two-Grid Methods
- Towards Adaptive Smoothed Aggregation ($\alpha$SA) for Nonsymmetric Problems
- Algebraic analysis of two-grid methods: The nonsymmetric case
- A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization
- Aggregation-Based Algebraic Multigrid for Convection-Diffusion Equations
- Compatible Relaxation and Coarsening in Algebraic Multigrid
- Coarsening by compatible relaxation
- Non-Galerkin Multigrid Based on Sparsified Smoothed Aggregation
- Multilevel Block Factorization Preconditioners
- IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
- Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
- Distance‐two interpolation for parallel algebraic multigrid
- On two‐grid convergence estimates
- Adaptive reduction-based AMG
- On MGR$[\nu $ Multigrid Methods]
- An Algebraic Interpretation of Multigrid Methods
- A Semicoarsening Multigrid Method for Elliptic Partial Differential Equations with Highly Discontinuous and Anisotropic Coefficients
- Fast Multigrid Solution of the Advection Problem with Closed Characteristics
- On the Ideal Interpolation Operator in Algebraic Multigrid Methods
- On Generalizing the Algebraic Multigrid Framework
- A robust algebraic multilevel preconditioner for non-symmetricM-matrices
- Nonsymmetric Black Box multigrid with coarsening by three
- A New Petrov–Galerkin Smoothed Aggregation Preconditioner for Nonsymmetric Linear Systems
- Nonsymmetric Reduction-Based Algebraic Multigrid
- Convergence in Norm of Nonsymmetric Algebraic Multigrid
- A multigrid method based on graph matching for convection–diffusion equations
- A Root-Node--Based Algebraic Multigrid Method
- Analysis and Comparison of Geometric and Algebraic Multigrid for Convection‐Diffusion Equations
- Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
- Theoretical bounds for algebraic multigrid performance: review and analysis
- Multigrid transfers for nonsymmetric systems based on Schur complements and Galerkin projections
- GMRES Convergence Analysis for a Convection-Diffusion Model Problem
- Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media
This page was built for publication: Nonsymmetric Algebraic Multigrid Based on Local Approximate Ideal Restriction ($\ell$AIR)
