Algebraic multilevel preconditioning methods. I
From MaRDI portal
Publication:1113631
DOI10.1007/BF01409783zbMath0661.65110MaRDI QIDQ1113631
Owe Axelsson, Panayot S. Vassilevski
Publication date: 1989
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/133390
finite elementconjugate gradient methodstiffness matrixcondition numbersmultilevel splittingaccelerated iterative methodalgebraic multilevel preconditioning methodsapproximate W-cycle
Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10)
Related Items
Splitting-based block preconditioning methods for block two-by-two matrices of real square blocks, Graph coarsening: from scientific computing to machine learning, Recursive two-level ILU preconditioner for nonsymmetric M-matrices, Low-rank improvements of two-level grid preconditioned matrices, A class of new hybrid algebraic multilevel preconditioning methods, Sobolev space preconditioning for Newton's method using domain decomposition, Numerical study of three multilevel preconditioners for solving \(2D\) unsteady Navier-Stokes equations, Semi-coarsening AMLI preconditioning of anisotropic trilinear FEM systems, Parallel hybrid algebraic multilevel iterative methods, Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids, Experience in implementing the algebraic multilevel iteration method on a SIMD-type computer, A class of hybrid algebraic multilevel preconditioning methods, Efficient approximate solution of sparse linear systems, Computational methods for boundary optimal control and identification problems, Vectorizable preconditioners for mixed finite element solution of second-order elliptic problems, Unnamed Item, Multilevel preconditioned QMR methods for unstructured mesh computation, On the robustness and optimality of algebraic multilevel methods for reaction-diffusion type problems, An algebraic multilevel iteration method for finite element matrices, New variants of the algebraic multilevel preconditioning methods, An algebraic two-level preconditioner for asymmetric, positive-definite systems, Robust Balanced Semi-coarsening Multilevel Preconditioning of Bicubic FEM Systems, Robust semi-coarsening multilevel preconditioning of biquadratic FEM systems, A Survey of Optimal Control Problems for PDEs, A survey of multilevel preconditioned iterative methods, Preconditioned conjugate gradient methods for large-scale fluid flow applications, Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives, Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations, On hybrid v-cycle version (i) algebraic multilevel preconditionings, Hierarchical basis in \(H^{\operatorname{div}}\) space for a mixed finite element formulation of the Darcy problem, Multilevel block ILU preconditioner for sparse nonsymmetric \(M\)-matrices., Robust AMLI methods for parabolic Crouzeix-Raviart FEM systems, An approach to construct algebraic two-grid preconditioners on hierarchical triangular grids, BPX-preconditioning for isogeometric analysis, Algebraic multilevel preconditioning in isogeometric analysis: construction and numerical studies, Unnamed Item, An efficient preconditioning method for state box-constrained optimal control problems, Multilevel preconditioners for elliptic problems by substructuring, The method of diagonal compensation of reduced matrix entries and multilevel iteration, An algebraic hierarchical basis preconditioner, Multilevel preconditioning of rotated bilinear non-conforming FEM problems, Applications of the PRESB Preconditioning Method for OPT-PDE Problems, Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs, Low-Rank Factorizations in Data Sparse Hierarchical Algorithms for Preconditioning Symmetric Positive Definite Matrices, On a relaxation procedure for domain decomposition methods with many subdomains and inexact solver, On algebraic multi-level methods for non-symmetric systems --- comparison results, A Brief History of the Parallel Dawn in Karl-Marx-Stadt/Chemnitz, Incomplete factorization by local exact factorization (ILUE), Numerical simulation of fluid-structure interaction problems with hyperelastic models: a monolithic approach, VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems, A review of algebraic multigrid, Auxiliary space multigrid method based on additive Schur complement approximation, Milestones in the development of iterative solution methods, Iterative solution methods, Spectrally equivalent preconditioners for mixed hybrid discretizations of diffusion equations on distorted meshes, Motivations and realizations of Krylov subspace methods for large sparse linear systems, Optimal preconditioners of a given sparsity pattern, Block SSOR preconditionings for high order 3D FE systems, Multilevel Preconditioning for Variational Problems, Algebraic multilevel iterative preconditioning methods for h-matrices, Parallel multilevel iterative methods, Decomposition into subspaces preconditioning: abstract framework, Application of Hierarchical Decomposition: Preconditioners and Error Estimates for Conforming and Nonconforming FEM, Multilevel Preconditioning of Rotated Trilinear Non-conforming Finite Element Problems, The Effect of a Minimum Angle Condition on the Preconditioning of the Pivot Block Arising from 2-Level-Splittings of Crouzeix-Raviart FE-Spaces, PARALLEL SOLUTION METHODS AND PRECONDITIONERS FOR EVOLUTION EQUATIONS, A robust algebraic multilevel preconditioner for non-symmetricM-matrices, Strengthened Cauchy-Bunyakowski-Schwarz inequality for a three-dimensional elasticity system, A unified framework for the construction of various algebraic multilevel preconditioning methods, Auxiliary Space Multigrid Method for Elliptic Problems with Highly Varying Coefficients, A new multilevel algebraic preconditioner for the diffusion equation in heterogeneous media, Multigrid methods for convection-diffusion problems discretized by a monotone scheme, Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methods, Reducing complexity of algebraic multigrid by aggregation, Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods, Multi-level incomplete factorizations for the iterative solution of non-linear finite element problems, Parallel adaptive subspace correction schemes with applications to elasticity, The stabilized \(V\)-cycle method, Robust multilevel methods for quadratic finite element anisotropic elliptic problems, Multigrid transfers for nonsymmetric systems based on Schur complements and Galerkin projections, Matrix Reordering Using Multilevel Graph Coarsening for ILU Preconditioning, Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems, Implementation strategies for block recursive factorizations, Iterative solution of linear systems in the 20th century, Robust multigrid methods for nonsmooth coefficient elliptic linear systems, Numerical linear algebra algorithms and software, Krylov-based Uzawa algorithms for the solution of the Stokes equations using discontinuous-pressure tetrahedral finite elements, Asymptotic work estimates for AMLI methods, Preconditioning techniques for large linear systems: A survey, Algebraic multilevel iteration method for lowest order Raviart-Thomas space and applications
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- On the multi-level splitting of finite element spaces
- The hierarchical basis multigrid method
- The contraction number of a multigrid method for solving the Poisson equation
- A New Convergence Proof for the Multigrid Method Including the V-Cycle
- An Optimal Order Process for Solving Finite Element Equations
- Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation