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. Pouransari, Hadi; Coulier, Pieter; Darve, Eric: Fast hierarchical solvers for sparse matrices using extended sparsification and low-rank approximation (2017)
  2. Suñé, Víctor; Carrasco, Juan Antonio: Implicit ODE solvers with good local error control for the transient analysis of Markov models (2017)
  3. Villanueva, Carlos H.; Maute, Kurt: CutFEM topology optimization of 3D laminar incompressible flow problems (2017)
  4. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  5. Yue, Xiaoqiang; Xu, Xiaowen; Shu, Shi: JASMIN-based two-dimensional adaptive combined preconditioner for radiation diffusion equations in inertial fusion research (2017)
  6. Aminfar, Amirhossein; Darve, Eric: A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite-element matrices (2016)
  7. Ferronato, Massimiliano; Janna, Carlo; Pini, Giorgio: Parallel Jacobi-Davidson with block FSAI preconditioning and controlled inner iterations. (2016)
  8. Lin, Lin; Lu, Jianfeng: Decay estimates of discretized Green’s functions for Schrödinger type operators (2016)
  9. Li, Ruipeng; Xi, Yuanzhe; Saad, Yousef: Schur complement-based domain decomposition preconditioners with low-rank corrections. (2016)
  10. Martínez, Ángeles: Tuned preconditioners for the eigensolution of large SPD matrices arising in engineering problems. (2016)
  11. Oberai, Assad A.; Jagalur-Mohan, Jayanth: Approximate optimal projection for reduced-order models (2016)
  12. Zhang, Jianhua; Dai, Hua: Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides (2016)
  13. Zhang, Zhengyi; Sameh, Ahmed H.: A parallel sparse linear system solver based on Hermitian/skew-Hermitian splitting (2016)
  14. Janna, Carlo; Castelletto, Nicola; Ferronato, Massimiliano: The effect of graph partitioning techniques on parallel block FSAI preconditioning: a computational study (2015)
  15. Janna, Carlo; Ferronato, Massimiliano; Sartoretto, Flavio; Gambolati, Giuseppe: FSAIPACK: a software package for high-performance factored sparse approximate inverse preconditioning (2015)
  16. Li, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Ren, Zhi-Gang: Effective preconditioning through minimum degree ordering interleaved with incomplete factorization (2015)
  17. Mirkov, Nikola; Rašuo, Boško; Kenjereš, Saša: On the improved finite volume procedure for simulation of turbulent flows over real complex terrains (2015)
  18. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  19. Zhang, Jianhua; Dai, Hua: A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems (2015)
  20. Zhang, Jianhua; Dai, Hua: A new quasi-minimal residual method based on a biconjugate (A)-orthonormalization procedure and coupled two-term recurrences (2015)

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