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. Cerdán, J.; Marín, J.; Mas, J.: Low-rank updates of balanced incomplete factorization preconditioners (2017)
  2. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  3. Marín, J.; Mas, J.; Guerrero, D.; Hayami, K.: Updating preconditioners for modified least squares problems (2017)
  4. Pouransari, Hadi; Coulier, Pieter; Darve, Eric: Fast hierarchical solvers for sparse matrices using extended sparsification and low-rank approximation (2017)
  5. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  6. Lin, Lin; Lu, Jianfeng: Decay estimates of discretized Green’s functions for Schrödinger type operators (2016)
  7. Zhang, Jianhua; Dai, Hua: Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides (2016)
  8. Janna, Carlo; Castelletto, Nicola; Ferronato, Massimiliano: The effect of graph partitioning techniques on parallel block FSAI preconditioning: a computational study (2015)
  9. Janna, Carlo; Ferronato, Massimiliano; Sartoretto, Flavio; Gambolati, Giuseppe: FSAIPACK: a software package for high-performance factored sparse approximate inverse preconditioning (2015)
  10. Li, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Ren, Zhi-Gang: Effective preconditioning through minimum degree ordering interleaved with incomplete factorization (2015)
  11. Mirkov, Nikola; Rašuo, Boško; Kenjereš, Saša: On the improved finite volume procedure for simulation of turbulent flows over real complex terrains (2015)
  12. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  13. Zhang, Jianhua; Dai, Hua: A new quasi-minimal residual method based on a biconjugate $A$-orthonormalization procedure and coupled two-term recurrences (2015)
  14. Zhang, Jianhua; Dai, Hua: A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems (2015)
  15. Zhu, Wei: Simulation of liquid crystal elastomers using Chebyshev spectral method with a new preconditioner (2015)
  16. Carpentieri, Bruno; Liao, Jia; Sosonkina, Masha: VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems (2014)
  17. Scott, Jennifer; Tůma, Miroslav: HSL_MI28: an efficient and robust limited-memory incomplete Cholesky factorization code (2014)
  18. Andrzejewski, Janusz: On optimizing Jacobi-Davidson method for calculating eigenvalues in low dimensional structures using eight band $\boldk\cdot\boldp$ model (2013)
  19. Duff, Iain S.; Kaya, Kamer: Preconditioners based on strong subgraphs (2013)
  20. Jia, Zhongxiao; Zhang, Qian: Robust dropping criteria for F-norm minimization based sparse approximate inverse preconditioning (2013)

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