References for Multi-Level Block ILU Preconditioning Techniques

Here are some references related to multi-level preconditioning techniques. Most of them are related to the hierarchical basis multi-level in finite element analysis, recursive red-black factorization in finite difference analysis, multigrid methods with matrix-dependent transfer operators, algebraic multigrid methods, and blackbox multigrid methods. In other words, only a few of them can be used to solve general sparse linear systems. If you have other relevant references that are not listed here, please send me an e-mail message (jzhang@cs.uky.edu).
References that are most relevant to BILUM:

  1. Yousef Saad, ILUM: a multi-elimination ILU preconditioner for general sparse matrices, SIAM Journal on Scientific Computing, Vol. 17, 830--847 (1996).
  2. Yousef Saad and Jun Zhang, BILUM: block versions of multi-elimination and multi-level ILU preconditioner for general sparse linear systems, accepted for publication in SIAM Journal on Scientific Computing. Technical Report UMSI 97/126, Minnesota Supercomputer Institute, University of Minnesota, MN, 1997.
    Abstract. Download the paper in a postscript file bilum.ps.gz
  3. Yousef Saad, Maria Sosonkina, and Jun Zhang, Domain decomposition and multi-level type techniques for general sparse linear systems, Technical Report UMSI 97/244, Minnesota Supercomputer Institute, University of Minnesota, MN, 1997.
    Also in Domain Decomposition Methods 10, J. Mandel, C. Farhat and X.-C. Cai. editors, AMS, Providence, RI, 1998, pp. 200-216.
    Abstract. Download the paper in a postscript file domain.ps.gz
  4. Yousef Saad and Jun Zhang, Diagonal threshold techniques in robust multi-level preconditioners for general sparse linear system, Technical Report UMSI 98/7, Minnesota Supercomputer Institute, University of Minnesota, MN, 1998.
    Abstract. Download the paper in a postscript file diag.ps.gz
  5. Yousef Saad and Jun Zhang, Enhanced multi-level ILU preconditioning strategies for general sparse linear systems, Technical Report UMSI 98/98, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, 1998.
    Abstract. Download the compressed postscript file enhanced.ps.
  6. Yousef Saad and Jun Zhang, BILUTM: a domain-based multi-level block ILUT preconditioner for general sparse matrices, accepted for publication in SIAM Journal on Matrix Analysis and Applications. Technical Report UMSI 98/118, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, 1998.
    Abstract. Download the compressed postscript file bilutm.ps.
Other references that are, to some extend, related to multi-level preconditioning techniques:

  1. Owe Axelsson and Panayot S. Vassilevski, Algebraic multilevel preconditioning methods. Part I, Numerische Mathematic, Vol. 56, 157--177 (1989). Part II, SIAM Journal on Numerical Analysis, Vol. 27, 1569--1590 (1990).
  2. Randolph E. Bank and Jinchao Xu, The hierarchical basis multigrid method and incomplete LU decomposition, in Domain Decomposition Methods in Science and Engineering, (D. Keyes and J. Xu, eds.), American Mathematical Society, Providence, RI, 1994, pp. 163--173.
  3. Eugen F.F. Botta and F. W. Wubs, MRILU: it's the preconditioning that counts, Technical Report W-9703, department of Mathematics, University of Groningen, The Netherlands, 1997.
  4. James H. Bramble, Joe E. Pasciak, and Jinchao Xu, Parallel multilevel preconditioner, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1990, pp. 341--357.
  5. Tony F. Chan, Susie Go, and Jun Zou, Multilevel domain decomposition and multigrid methods for unstructured meshes: algorithms and theory, Technical Report 95-24, Department of Mathematics, University of California at Lo Angeles, 1996.
  6. Paul M. de Zeeuw, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, Journal of Computational and Applied Mathematics, Vol. 3, 1--27 (1990).
  7. Joe E. Dendy, Black box multigrid, Journal of Computational Physics, Vol. 48, 366--396 (1982).
  8. Arnold Reusken, Fourier analysis of a robust multigrid method for convection-diffusion equation, Numerische Mathematik, Vol. 71, 365--398 (1995).
  9. John W. Ruge and Klaus Stuben, Efficient solution of finite difference and finite element equations, in Multigrid Methods for Integral and Differential Equations, (D. J. Paddon and H. Holstein, eds.), Clarendon Press, Oxford, 169--212 (1985).
  10. John W. Ruge and Klaus Stuben, Algebraic multigrid, in Multigrid Methods (S.F. McCormick, ed.), SIAM, Philadelphia, PA, 1987.

For problems and suggestions, send an e-mail to: jzhang@cs.uky.edu.

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