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. Fournié, Michel; Karaa, Samir: Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative (2006)
  2. Lee, Eun-Joo; Zhang, Jun: Hybrid reordering strategies for ILU preconditioning of indefinite sparse matrices (2006)
  3. Mayer, Jan: Alternative weighted dropping strategies for ILUTP (2006)
  4. Wang, Jie; Zhong, Weijun; Zhang, Jun: High order compact computation and nonuniform grids for streamfunction vorticity equations (2006)
  5. Bängtsson, Erik; Neytcheva, Maya: Algebraic preconditioning versus direct solvers for dense linear systems as arising in crack propagation problems (2005)
  6. Guessous, N.; Souhar, O.: The effect of block red-black ordering on block ILU preconditioner for sparse matrices (2005)
  7. Guessous, N.; Souhar, O.: Recursive two-level ILU preconditioner for nonsymmetric M-matrices (2004)
  8. Gu, Tongxiang; Chi, Xuebin; Liu, Xingping: AINV and BILUM preconditioning techniques (2004)
  9. Kechroud, Riyad; Soulaimani, Azzeddine; Saad, Yousef; Gowda, Shivaraju: Preconditioning techniques for the solution of the Helmholtz equation by the finite element method (2004)
  10. Mayer, Jan: The ILUCP preconditioner (2004)
  11. Bollhöfer, Matthias: A robust and efficient ILU that incorporates the growth of the inverse triangular factors (2003)
  12. Larrazábal, G.; Torres, C. R.; Castillo, J.: An efficient and robust algorithm for 2D stratified fluid flow calculations. (2003)
  13. Lee, Jeonghwa; Zhang, Jun; Lu, Cai-Cheng: Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems (2003)
  14. Li, Na; Saad, Yousef; Chow, Edmond: Crout versions of ILU for general sparse matrices (2003)
  15. Mazzia, Annamaria; Pini, Giorgio: Numerical performance of preconditioning techniques for the solution of complex sparse linear systems (2003)
  16. Moore, Peter K.: Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions. (2003)
  17. Moore, Peter K.: An incomplete assembly with thresholding algorithm for systems of reaction--diffusion equations in three space dimensions IAT for reaction--diffusion systems (2003)
  18. Qaddouri, Abdessamad; Côté, Jean: Preconditioning for an iterative elliptic solver on a vector processor (2003)
  19. Schneider, Stefan; Marburg, Steffen: Performance of iterative solvers for acoustic problems. II: Acceleration by ILU-type preconditioner. (2003)
  20. Wang, Li; Zhang, Jun: A new stabilization strategy for incomplete LU preconditioning of indefinite matrices (2003)

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