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Zh. Vychisl. Mat. Mat. Fiz., 1997, Volume 37, Number 11, Pages 1294–1300 (Mi zvmmf1989)  

This article is cited in 2 scientific papers (total in 2 papers)

Renumbering strategies based on multi-level techniques combined with ILU-decompositions

E. F. F. Botta, A. van der Ploeg

Groningen, Netherlands

Abstract: 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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English version:
Computational Mathematics and Mathematical Physics, 1997, 37:11, 1252–1258

Bibliographic databases:
UDC: 519.612
MSC: Primary 65F10; Secondary 65F35
Received: 15.05.1996
Language:

Citation: E. F. F. Botta, A. van der Ploeg, “Renumbering strategies based on multi-level techniques combined with ILU-decompositions”, Zh. Vychisl. Mat. Mat. Fiz., 37:11 (1997), 1294–1300; Comput. Math. Math. Phys., 37:11 (1997), 1252–1258

Citation in format AMSBIB
\Bibitem{BotVan97}
\by E.~F.~F.~Botta, A.~van der Ploeg
\paper Renumbering strategies based on multi-level techniques combined with ILU-decompositions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1997
\vol 37
\issue 11
\pages 1294--1300
\mathnet{http://mi.mathnet.ru/zvmmf1989}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1489503}
\zmath{https://zbmath.org/?q=an:0946.65019}
\transl
\jour Comput. Math. Math. Phys.
\yr 1997
\vol 37
\issue 11
\pages 1252--1258


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    This publication is cited in the following articles:
    1. Naumov M., Arsaev M., Castonguay P., Cohen J., Demouth J., Eaton J., Layton S., Markovskiy N., Reguly I., Sakharnykh N., Sellappan V., Strzodka R., “Amgx: a Library For Gpu Accelerated Algebraic Multigrid and Preconditioned Iterative Methods”, SIAM J. Sci. Comput., 37:5 (2015), S602–S626  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kopal J., Rozloznik M., Tuma M., “An Adaptive Multilevel Factorized Sparse Approximate Inverse Preconditioning”, Adv. Eng. Softw., 113:SI (2017), 19–24  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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