Decomposition into subspaces preconditioning: abstract framework

DOI10.1007/s11075-019-00671-4zbMath1434.65259OpenAlexW2911514766WikidataQ128449417 ScholiaQ128449417MaRDI QIDQ2287855

Zdeněk Strakoš, Ivana Pultarová, Jakub Hrnčíř

Publication date: 22 January 2020

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00671-4

zbMATH Keywords

multilevel methodsstable splittingadditive Schwarz methodsoperator preconditioningdecomposition into infinite-dimensional subspacesnorm and spectral equivalence of operatorsseparate displacement preconditioning

Mathematics Subject Classification ID

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) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (2)

Numerical approximation of the spectrum of self-adjoint operators in operator preconditioning ⋮ Preconditioners for Krylov subspace methods: An overview

Cites Work

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• Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations
• Inexact linear solvers for control volume discretizations in porous media
• On function spaces related to finite element approximation theory
• Equivalent operator preconditioning for elliptic problems
• Robust algebraic multilevel methods and algorithms.
• On the multi-level splitting of finite element spaces
• Algebraic multilevel preconditioning methods. I
• Multilevel preconditioning
• Iterative methods for the solution of the Navier equations of elasticity
• CBS constants \& their role in error estimation for stochastic Galerkin finite element methods
• On the abstract theory of additive and multiplicative Schwarz algorithms
• The numerical solution of \(\nabla\cdot a\nabla u = f\) by a semi-explicit alternating-direction iterative technique
• Operator preconditioning
• On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations
• Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
• Preconditioning discretizations of systems of partial differential equations
• Nonstandard Norms and Robust Estimates for Saddle Point Problems
• Convergence Estimates for Multigrid Algorithms without Regularity Assumptions
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Parallel Multilevel Preconditioners
• Multilevel Block Factorization Preconditioners
• Finite element exterior calculus: from Hodge theory to numerical stability
• From Functional Analysis to Iterative Methods
• Preconditioning by inverting the Laplacian: an analysis of the eigenvalues
• Theoretical Numerical Analysis
• The Role of the Strengthened Cauchy–Buniakowskii–Schwarz Inequality in Multilevel Methods
• Iterative Methods by Space Decomposition and Subspace Correction
• The construction of iterative methods based on the use of spectrally equivalent operators
• On the Additive Version of the Algebraic Multilevel Iteration Method for Anisotropic Elliptic Problems
• The method of alternating projections and the method of subspace corrections in Hilbert space
• Preconditioning in H(𝑑𝑖𝑣) and applications
• Preconditioning discrete approximations of the Reissner-Mindlin plate model
• Displacement decomposition—incomplete factorization preconditioning techniques for linear elasticity problems
• Iterative Solution Methods
• BLOCK AND MULTILEVEL PRECONDITIONING FOR STOCHASTIC GALERKIN PROBLEMS WITH LOGNORMALLY DISTRIBUTED PARAMETERS AND TENSOR PRODUCT POLYNOMIALS
• Laplacian Preconditioning of Elliptic PDEs: Localization of the Eigenvalues of the Discretized Operator
• Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs
• Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition
• The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques
• Schur complement preconditioners for multiple saddle point problems of block tridiagonal form with application to optimization problems

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