Algebraic multigrid theory: The symmetric case
From MaRDI portal
Publication:1821503
DOI10.1016/0096-3003(86)90095-0zbMath0616.65037OpenAlexW2075536798MaRDI QIDQ1821503
Publication date: 1986
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0096-3003(86)90095-0
algebraic multigridrelaxation methodGauss-Seidel methodJacobi methodKaczmarz methodgeometric multigridnonsymmetric matricesKaczmarz relationslocal mode analyses
Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Related Items (only showing first 100 items - show all)
A detailed investigation of the model influencing parameters of the phase‐field fracture approach ⋮ A multigrid method for kernel functions acting on interacting structures with applications to biofluids ⋮ Hierarchical subspace evolution method for super large parallel computing: A linear solver and an eigensolver as examples ⋮ Learning Optimal Multigrid Smoothers via Neural Networks ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ Multigrid incomplete factorization methods in Krylov subspaces ⋮ Algebraic multigrid based on computational molecules. 1: Scalar elliptic problems ⋮ Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process ⋮ Low-Order Preconditioning for the High-Order Finite Element de Rham Complex ⋮ Analysis of preconditioned iterative solvers for incompressible flow problems ⋮ Non-modal analysis of linear multigrid schemes for the high-order flux reconstruction method ⋮ Notes on convergence of an algebraic multigrid method ⋮ A multigrid method for three-dimensional elasticity and algebraic convergence estimates ⋮ AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods ⋮ GePUP: generic projection and unconstrained PPE for fourth-order solutions of the incompressible Navier-Stokes equations with no-slip boundary conditions ⋮ Scalable preconditioning for the stabilized contact mechanics problem ⋮ A Phase-Field Approach to Pneumatic Fracture ⋮ \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner ⋮ HSL_MI20 : An efficient AMG preconditioner for finite element problems in 3D ⋮ An efficient algebraic multigrid method for quadratic discretizations of linear elasticity problems on some typical anisotropic meshes in three dimensions ⋮ An efficient parallel algebraic multigrid method for 3D injection moulding simulation based on finite volume method ⋮ Least Angle Regression Coarsening in Bootstrap Algebraic Multigrid ⋮ Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method ⋮ An algebraic multigrid method for finite element discretizations with edge elements ⋮ Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems ⋮ A cost-effective smoothed multigrid with modified neighborhood-based aggregation for Markov chains ⋮ Note on the multigrid \(W\)-cycle ⋮ Repeated Richardson extrapolation applied to the two-dimensional Laplace equation using triangular and square grids ⋮ Domain decomposition like technique with \(H/h\)-independent rate of convergence ⋮ On the Ideal Interpolation Operator in Algebraic Multigrid Methods ⋮ Improved convergence bounds for two-level methods with an aggressive coarsening and massive polynomial smoothing ⋮ A supplementary strategy for coarsening in algebraic multigrid ⋮ Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deficient least-squares problems ⋮ A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures ⋮ Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems ⋮ Goal-oriented adaptivity and multilevel preconditioning for the Poisson-Boltzmann equation ⋮ Generalization of algebraic multiscale to algebraic multigrid ⋮ Multiscale modal analysis of fully-loaded spent nuclear fuel canisters ⋮ An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients ⋮ Algebraic multigrid methods ⋮ High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions ⋮ An algebraic multigrid solver for transonic flow problems ⋮ A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows ⋮ An algebraic multigrid-based algorithm for circuit clustering ⋮ An algebraic two-level preconditioner for asymmetric, positive-definite systems ⋮ A new algebraic multigrid approach for Stokes problems ⋮ Simulation of the effect of geometric parameters on tangentially injected swirling pipe airflow ⋮ Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives ⋮ Algebraic Multigrid for Stokes Equations ⋮ Top-level acceleration of adaptive algebraic multilevel methods for steady-state solution to Markov chains ⋮ First-order system least squares and the energetic variational approach for two-phase flow ⋮ An algebraic multigrid solver for finite element computations in solid mechanics ⋮ Convergence of algebraic multigrid methods for symmetric positive definite matrices with weak diagonal dominance ⋮ The deflated conjugate gradient method: convergence, perturbation and accuracy ⋮ Toward Cost-Effective Reservoir Simulation Solvers on GPUs ⋮ Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs ⋮ A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticity ⋮ Two-Level Hierarchical PCG Methods for the Quadratic FEM Discretizations of 2D Concrete Aggregate Models ⋮ A robust adaptive algebraic multigrid linear solver for structural mechanics ⋮ A filter in constructing the preconditioner for solving linear equation systems of radiation diffusion problems ⋮ A Novel Algebraic Multigrid Approach Based on Adaptive Smoothing and Prolongation for Ill-Conditioned Systems ⋮ An algebraic study of a local multigrid method for variational problems ⋮ Analysis of algebraic multigrid parameters for two-dimensional steady-state heat diffusion equations ⋮ A review of algebraic multigrid ⋮ Multigrid methods for two‐player zero‐sum stochastic games ⋮ An adaptive algebraic multigrid for multigroup neutron diffusion reactor core calculations ⋮ Two-level Preconditioner with Small Coarse Grid Appropriate for Unstructured Meshes ⋮ Fast Hierarchical Solvers For Sparse Matrices Using Extended Sparsification and Low-Rank Approximation ⋮ Exact interpolation scheme with approximation vector used as a column of the prolongator ⋮ Convergence theory of exact interpolation scheme for computing several eigenvectors ⋮ Data-sparse algebraic multigrid methods for large scale boundary element equations ⋮ Computing interpolation weights in AMG based on multilevel Schur complements ⋮ Algebraic multigrid methods based on element preconditioning ⋮ An efficient algebraic multigrid method for solving optimality systems ⋮ Constraint Preconditioning for the Coupled Stokes--Darcy System ⋮ A fast algebraic multigrid preconditioned conjugate gradient solver ⋮ Performance of a Petrov-Galerkin algebraic multilevel preconditioner for finite element modeling of the semiconductor device drift-diffusion equations ⋮ A meshless geometric multigrid method based on a node-coarsening algorithm for the linear finite element discretization ⋮ A stable and scalable hybrid solver for rate-type non-Newtonian fluid models ⋮ A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics ⋮ Analysis of two-grid methods: The nonnormal case ⋮ 3D numerical simulation of compressible swirling flow induced by means of tangential inlets ⋮ Algebraic analysis of two-level multigrid methods for edge elements ⋮ Fully coupled thermo‐hydro‐mechanical analysis by an algebraic multigrid method ⋮ Coarsening in algebraic multigrid using Gaussian processes ⋮ Algebraic analysis of two-grid methods: The nonsymmetric case ⋮ Iterative preconditioned methods in Krylov spaces: trends of the 21st century ⋮ When does two-grid optimality carry over to the V-cycle? ⋮ Algebraic multigrid within defect correction for the linearized Euler equations ⋮ Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methods ⋮ Improving algebraic multigrid interpolation operators for linear elasticity problems ⋮ Operator-based interpolation for bootstrap algebraic multigrid ⋮ Algebraic Two-Level Convergence Theory for Singular Systems ⋮ Adaptive algebraic smoothers ⋮ Parallel adaptive subspace correction schemes with applications to elasticity ⋮ A fast constrained image segmentation algorithm ⋮ Symmetry breaking and the generation of spin ordered magnetic states in density functional theory due to Dirac exchange for a hydrogen molecule ⋮ Theoretical bounds for algebraic multigrid performance: review and analysis ⋮ A scalable, robust parallel algorithm on handling of sliding non-conformal interfaces with an efficient supermesh method ⋮ Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure
Cites Work
- Algebraic multigrid (AMG): Experiences and comparisons
- Multivariate interpolation at arbitrary points made simple
- Black box multigrid
- Projection method for solving a singular system of linear equations and its applications
- Local Mesh Refinement Multilevel Techniques
- The Multi-Grid Method for the Diffusion Equation with Strongly Discontinuous Coefficients
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- An Accelerated Relaxation Algorithm for Iterative Solution of Elliptic Equations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Algebraic multigrid theory: The symmetric case