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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 on… Expand
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 a… Expand
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 the… Expand
Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations
- P. Vassilevski
- 12 August 2008
Motivation for Preconditioning.- A Finite Element Tutorial.- A Main Goal.- Block Factorization Preconditioners.- Two-by-Two Block Matrices and Their Factorization.- Classical Examples of… Expand
On two-grid convergence estimates
- R. Falgout, P. Vassilevski, L. Zikatanov
- Mathematics, Computer Science
- Numer. Linear Algebra Appl.
- 1 June 2005
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 for… Expand
Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations
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...
Spectral AMGe (ρAMGe)
- T. Chartier, R. Falgout, +5 authors P. Vassilevski
- Computer Science, Mathematics
- SIAM J. Sci. Comput.
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 element… Expand
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 is… Expand
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 general… Expand