Approximate Cyclic Reduction Preconditioning

Reusken, Arnold

doi:10.1007/978-3-642-58734-4_14

Cited by 9 publications

(7 citation statements)

References 17 publications

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“…The major differences between ILUM and the method of [8] include the different choice of the reduced system and the sparsification strategy. Other multilevel methods have been designed or analyzed in [4,5,6,31] and elsewhere. These are not necessarily block methods, but they exploit Schur complements, similarly to ILUM and BILUM.…”

Section: Introductionmentioning

confidence: 99%

BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems

Saad¹,

Zhang²

1999

SIAM J. Sci. Comput.

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We introduce block versions of the multielimination incomplete LU (ILUM) factorization preconditioning technique for solving general sparse unstructured linear systems. These preconditioners have a multilevel structure and, for certain types of problems, may exhibit properties that are typically enjoyed by multigrid methods. Several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed. The advantages of block ILUM over point ILUM include increased robustness and efficiency. We compare several versions of the block ILUM, point ILUM, and the dual-threshold-based ILUT preconditioners. In particular, tests with some convection-diffusion problems show that it may be possible to obtain convergence that is nearly independent of the Reynolds number as well as of the grid size.

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Section: Introductionmentioning

confidence: 99%

BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems

Saad¹,

Zhang²

1999

SIAM J. Sci. Comput.

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“…For the Schur-ILU preconditioning, the parameter lfil speci es the amount of ll-ins in the whole local matrix A i in the processor i (see equation (3)). Thus, with an increase in lfil, as it can be inferred from equation (13), the accuracy of the approximations to the parts of L i and U i increases. However, an increase in the accuracy of the preconditioning operation does not necessarily lead to a smaller CPU time cost (cf., for example, the numerical results for VENKAT50 in Figure 4).…”

Section: Tests With Approximate Schur-ilu Preconditioningmentioning

confidence: 92%

Domain decomposition and multi-level type techniques for general sparse linear systems

Saad¹,

Sosonkina²,

Zhang³

1998

Domain Decomposition Methods 10

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Domain-decomposition and multi-level techniques are often formulated for linear systems that arise from the solution of elliptic-type Partial Di erential Equations. In this paper, generalizations of these techniques for irregularly structured sparse linear systems are considered. An interesting common approach used to derive successful preconditioners is to resort to Schur complements. In particular, we discuss a multi-level domain decompositiontype algorithm for iterative solution of large sparse linear systems based on independent subsets of nodes. We also discuss a Schur complement technique that utilizes incomplete LU factorizations of local matrices.

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“…Algebraic multilevel preconditioners have become popular in recent years. Several algebraic multigrid approaches focus on incomplete LU or Schur-complement approaches [4,5,14,6,30,31] while others are based on the analogy to geometric multigrid methods [10,32,24,21,29,23]. Here we will concentrate on the second class of approaches.…”

Section: Multilevel Preconditionersmentioning

confidence: 99%

Algebraic Multilevel Methods and Sparse Approximate Inverses

Bollhöfer¹,

Mehrmann

2002

SIAM J. Matrix Anal. & Appl.

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In this paper we introduce a new approach to algebraic multilevel methods and their use as preconditioners in iterative methods for the solution of symmetric positive definite linear systems. The multilevel process and in particular the coarsening process is based on the construction of sparse approximate inverses and their augmentation with corrections of smaller size. We present comparisons of the effectiveness of the resulting multilevel technique and numerical results.Keywords: sparse approximate inverse, large sparse matrices, algebraic multilevel method.

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Approximate Cyclic Reduction Preconditioning

Cited by 9 publications

References 17 publications

BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems

BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems

Domain decomposition and multi-level type techniques for general sparse linear systems

Algebraic Multilevel Methods and Sparse Approximate Inverses

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