Titlebook: Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications; Proceedings of the E Wolfgang Hackbusch,Gabriel Wittum Conference pr

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A new approximate factorization method,A new incomplete factorization method is presented, differing from the previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with other basic incomplete factorization methods, displaying the superiority of the new one, particularly for systems arising from anisotropic elliptic PDEs.

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Relaxed ILU Preconditioning for the CG Solution of a Singular Boundary Value Problem for Pressure,cond-order singular boundary value problem for the determination of pressure. A finite volume discretization based on a nonuniform grid is applied to this problem, producing a linear system of equations whose coefficient matrix is symmetric positive semidefinite. We give an account of our experience

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Locally Refined Solution of Unsymmetric and Nonlinear Problems,ariant of the BPX preconditioner but it is motivated from the viewpoint of the classical multigrid method. This has several advantages: In the case of quasi-uniform refinement the method is equivalent to the classical multigrid method. All well known smoothing algorithms can be used, including incom

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Incomplete Factorizations with S/P and Modified S/P Consistently Ordered M-Factors,tly ordered” M-matrices. An ordered undirected graph is called S/P consistently ordered if whenever a pair of nodes . < . has a common neighbour . with . < ., then either it has also a common neighbour ℓ with . < ℓ or neither . has any neighbour ℓ with ℓ > . nor . any neighbour ℓ with ℓ > .. Incompl

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Modification of the ILU-Method for Enhanced Parallel Efficiency,parallelization of this method is possible when the dimension of the processor array is less than that of the problem. However, in terms of parallelism, ILU methods suffer from two disadvantages: the procedure is not well vectorizable and it has a very fine granularity, making it unsuitable for some