J. Zhang. A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices. Technical Report 283-99, Department of Computer Science, University of Kentucky, 1999. Home/Search Document Details and Download
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ARMS: An Algebraic Recursive Multilevel Solver for general.. - Saad, Suchomel (2001) (3 citations) (Correct)
....is their excellent scalability with respect to mesh size. Their scope however is limited. A number of methods developed in the last decade have aspired to combine the good intrinsic properties of multigrid techniques and the generality of preconditioned Krylov subspace methods. Among these we cite [3, 5, 9, 7, 19, 22, 23, 26, 27, 28]. Multigrid methods are difficult to surpass when they work. However, their implementation requires multilevel grids and specialized tuning is often needed. The Algebraic Multigrid (AMG) methods were introduced in the seventies initially by Ruge and Stuben [18] to remedy these limitations. ....
J. Zhang. A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices. Technical Report 283-99, Department of Computer Science, University of Kentucky, 1999.
A Multilevel Dual Reordering Strategy for Robust Incomplete LU.. - Zhang (1999) (2 citations) Self-citation (Zhang) (Correct)
....is combined with a partial ILU factorization procedure to construct recursive Schur complement matrices. The preconditioner is a multilevel ILU preconditioner. However, the constructed preconditioner (MDRILU) is different from all existing multilevel preconditioners in a fundamental concept [40, 49]. MDRILU never intends to utilize any traditional multilevel property, it uses the Schur complement approach solely for the purpose of removing small pivots. The idea used in this paper departs from traditional concept of multilevel treatment of different error components. Thus preconditioners ....
J. Zhang. A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices. Technical Report No. 283-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999.
A Multilevel Dual Reordering Strategy for Robust Incomplete LU.. - Zhang (1999) (2 citations) Self-citation (Zhang) (Correct)
....is combined with a partial ILU factorization procedure to construct recursive Schur complement matrices. The preconditioner is a multilevel ILU preconditioner. However, the constructed preconditioner (MDRILU) is different from all existing multilevel preconditioners in a fundamental concept [37, 47]. MDRILU never intends to utilize any traditional multilevel property, it uses the Schur complement approach solely for the purpose of removing small pivots. We conducted analyses on simplified model problems to find out how the size of the small diagonal elements and other elements is modified ....
J. Zhang. A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices. Technical Report No. 283-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999.
RILUM: A General Framework for Robust Multilevel Recursive.. - Zhang (1999) (1 citation) Self-citation (Zhang) (Correct)
....of smaller memory usage. In addition, these preconditioners are highly parallel and their inherent parallelism can be exploited on parallel computers [37] There are other multilevel preconditioning methods that are also derived from multilevel incomplete factorization of the coefficient matrices [2, 5, 12, 16, 18, 30, 39, 50] and that are based on different construction techniques [3, 4, 6, 7, 23, 24] Multilevel and multigrid techniques employ the idea that different error components can be treated efficiently on different level scales. This is the fundamental philosophy behind many multiscale computation techniques. ....
....of coarse level iterations so that a new preconditioner does not have to be recomputed. 2. 2 Relation to algebraic multigrid method Although the coarse level system in multilevel preconditioning techniques is used as fine level system in algebraic multigrid method [40] It has been shown in [50] that such a difference is not of vital importance as long as the approximate solution with respect to the fine and coarse level systems can be obtained in an efficient way. In multilevel preconditioning techniques, the solution with D ff is usually obtained without iterations [38, 39] In ....
J. Zhang. A grid based multilevel incomplete LU factorization preconditioning technique for general sparse matrices. Technical Report No. 283-99, Department of Computer Science, University of Kentucky, Lexington, KY, 1999.
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