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Algebraic multilevel preconditioning methods. I
SummaryA recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed. It is based onExpand
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Algebraic multilevel preconditioning methods, II
A recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed. It is based on aExpand
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On Generalizing the Algebraic Multigrid Framework
We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in theExpand
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Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations
Motivation for Preconditioning.- A Finite Element Tutorial.- A Main Goal.- Block Factorization Preconditioners.- Two-by-Two Block Matrices and Their Factorization.- Classical Examples ofExpand
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On two-grid convergence estimates
We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions forExpand
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Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations
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A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning
The generalized conjugate gradient method proposed by Axelsson is studied in the case when a variable-step preconditioning is used. This can be the case when the preconditioned system is solved app...
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Spectral AMGe (ρAMGe)
We introduce spectral element-based algebraic multigrid ($\rho$AMGe), a new algebraic multigrid method for solving systems of algebraic equations that arise in Ritz-type finite elementExpand
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Recursive Krylov-based multigrid cycles
We consider multigrid (MG) cycles based on the recursive use of a two-grid method, in which the coarse-grid system is solved by μ>1 steps of a Krylov subspace iterative method. The approach isExpand
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Multilevel iterative methods for mixed finite element discretizations of elliptic problems
SummaryFor solving second order elliptic problems discretized on a sequence of nested mixed finite element spaces nearly optimal iterative methods are proposed. The methods are within the generalExpand
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