ILUT: A dual threshold incomplete LU factorization. In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill-in element using only the graph of the matrix. Then each fill-in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill-ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes

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  1. Zhang, Jun; Xiao, Tong: A multilevel block incomplete Cholesky preconditioner for solving normal equations in linear least squares problems (2003)
  2. Benzi, Michele: Preconditioning techniques for large linear systems: A survey (2002)
  3. Bergamaschi, Luca; Putti, Mario: Numerical comparison of iterative eigensolvers for large sparse symmetric positive definite matrices (2002)
  4. Bollhöfer, Matthias; Saad, Yousef: On the relations between ILUs and factored approximate inverses (2002)
  5. Bollhöfer, Matthias; Saad, Yousef: A factored approximate inverse preconditioner with pivoting (2002)
  6. Marburg, Steffen: Developments in structural-acoustic optimization for passive noise control (2002)
  7. Rognlien, T. D.; Xu, X. Q.; Hindmarsh, A. C.: Application of parallel implicit methods to edge-plasma numerical simulations. (2002)
  8. Wang, Kai; Zhang, Jun: Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning (2002)
  9. Zhang, Jun: A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices (2002)
  10. Arany, I.: Numerical experiences of solving elasticity systems by PCG methods. (2001)
  11. Ben Salah, Nizar; Soulaimani, Azzeddine; Habashi, Wagdi G.: A finite element method for magnetohydrodynamics (2001)
  12. Szabó, Barna (ed.); Balla, Katalin (ed.); Galántai, Aurél (ed.); Szeidl, György (ed.): Special issue: Numerical methods and computational mechanics. Selected papers from the Eighth international conference (NMCM98), Miskolc, Hungary, August 24--27, 1998 (2001)
  13. Zhang, Jun: A grid-based multilevel incomplete LU factorization preconditioning technique for general sparse matrices (2001)
  14. Elkadri Elyamani, Nacer-Eddine; Soulaïmani, Azzeddine; Deschênes, Claire: A finite element formulation of compressible flows using various sets of independent variables (2000)
  15. Saad, Yousef; Sosonkina, Maria: Distributed Schur complement techniques for general sparse linear systems (2000)
  16. Zhang, Jun: Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications (2000)
  17. Zhang, Jun: Preconditioned iterative methods and finite difference schemes for convection-diffusion (2000)
  18. Arany, I.: Solving systems of elastic bar structures by preconditioned conjugate gradient method (1999)
  19. Soulaimani, Azzeddine; Saad, Yousef: An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows (1998)
  20. Chow, Edmond; Saad, Yousef: Experimental study of ILU preconditioners for indefinite matrices (1997)

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