M. Benzi, W. Joubert, and G. Mateescu, Numerical experiments with parallel orderings for ILU preconditioners, Electronic Transactions on Numerical Analysis, 8 (1999), pp. 88-114. Home/Search Document Details and Download
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A Scalable Parallel Algorithm for Incomplete Factor.. - Hysom, Pothen (2000) (3 citations) (Correct)
....that are related to the PILU algorithm proposed here. Earlier attempts at parallel algorithms for preconditioning (including approaches other than incomplete factorization) are surveyed in [6, 12, 33] orderings suitable for parallel incomplete factorizations have been studied inter alios in [4, 11, 13]. The surveys also describe the alternate approximate inverse approach to preconditioning. Saad [32] Sec. 12.6.1) discusses a distributed ILU(0) algorithm that has the features of graph partitioning, elimination of interior nodes in a subdomain before boundary nodes, and coloring the subdomains ....
....changing the number of subdomains, and hence, matrix ordering, a ects convergence. The basis for comparison is the iteration count when there is a single subdomain. The partitioning and ordering for these cases is identical to, and our data in close agreement with, that reported by Benzi et al. [4] for natural ordering. They report results for Problem 2 with = 1=500, but not for = 1=1000. A pleasing property of the both the constrained and unconstrained PILU algorithms is that the number of iterations increases only mildly when we increase the number of subdomains from 1 to 512 for ....
M. Benzi, W. Joubert, and G. Mateescu, Numerical experiments with parallel orderings for ILU preconditioners, Electronic Transactions on Numerical Analysis, 8 (1999), pp. 88-114.
Efficient Parallel Computation of ILU(k) Preconditioners - Hysom, Pothen (Correct)
....iterations and solution timings, but element by element comparisons between the factors themselves have apparently not been undertaken. The relationships between matrix orderings and ILU preconditioning performance is a complex issue which has, and continues to be, studied by numerous researchers [2, 5, 7, 8, 9]. At least four interrelated effects can be identified in parallel contexts. First, matrix ordering can be used to provide parallelism, i.e, as a partitioning method. Second, from a structural viewpoint, altering a matrix s ordering and ILU(k) or ILUT( p) parameters changes the amount and or ....
....statistics for Problem 2. The same trends noted for Problem 1 are evident here, although the fastest solutions required an even greater fill level. It is illuminating to note how the amounts of fill in ILU(k) preconditioners compare with the amounts commonly permitted in ILUT preconditioners. In [2], Benzi, et al. compared preconditioner performance between ILU(0) ILU(1) ILUT( 005,5) and ILUT( 001,10) 1 , for a variety of problems and matrix orderings. We noticed that, for most of the cases reported, the amount of fill permitted in the ILUT preconditioners exceeded that permitted in ....
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M. Benzi, W. Joubert, and G Mateescu. Numerical experiments with parallel orderings for ILU preconditioners. Elec. Trans. on Numer. Anal., 8:88--114, 1999.
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