Geodesic
Renumbering strategies based on multi-level techniques combined with ILU-decompositions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 37 (1997) no. 11, pp. 1294-1300 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we present an incomplete factorization technique which uses a renumbering of the unknowns, based on a sequence of grids as in multi-grid. For many problems discretised on structured grids, we obtain almost grid-independent convergence when this factorization is combined with some conjugate gradient-like method. Also, a similar preconditioning technique is described which can be used for matrices with arbitrary sparsity patterns as those arising from finite element methods on unstructured grids. During the factorization we use a reordering to guarantee that the diagonal blocks to be inverted remain strongly diagonally dominant. This makes it possible to approximate the needed inverses by only a diagonal matrix, leading to more potential parallelism. The method is demonstrated for a number of test problems and compared to some standard methods. 
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E. F. F. Botta; A. van der Ploeg. Renumbering strategies based on multi-level techniques combined with ILU-decompositions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 37 (1997) no. 11, pp. 1294-1300. http://geodesic.mathdoc.fr/item/ZVMMF_1997_37_11_a1/

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