ILUT

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


References in zbMATH (referenced in 171 articles , 1 standard article )

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  7. Carr, Arielle; de Sturler, Eric; Gugercin, Serkan: Preconditioning parametrized linear systems (2021)
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  11. Jiao, Xiangmin; Wang, Xuebin; Chen, Qiao: Optimal and low-memory near-optimal preconditioning of fully implicit Runge-Kutta schemes for parabolic PDEs (2021)
  12. Lin, Xue-lei; Ng, Micheal K.; Wathen, Andy: Preconditioners for multilevel Toeplitz linear systems from steady-state and evolutionary advection-diffusion equations (2021)
  13. Ye, Shuai; An, Hengbin; Xu, Xiaowen; Xu, Xinhai; Yang, Xuejun: A filter in constructing the preconditioner for solving linear equation systems of radiation diffusion problems (2021)
  14. Zheng, Qingqing; Xi, Yuanzhe; Saad, Yousef: A power Schur complement low-rank correction preconditioner for general sparse linear systems (2021)
  15. Cambier, Léopold; Chen, Chao; Boman, Erik G.; Rajamanickam, Sivasankaran; Tuminaro, Raymond S.; Darve, Eric: An algebraic sparsified nested dissection algorithm using low-rank approximations (2020)
  16. Diwan, Ganesh C.; Mohamed, M. Shadi: Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies (2020)
  17. Klockiewicz, Bazyli; Darve, Eric: Sparse hierarchical preconditioners using piecewise smooth approximations of eigenvectors (2020)
  18. Liu, Xiao; Xi, Yuanzhe; Saad, Yousef; de Hoop, Maarten V.: Solving the three-dimensional high-frequency Helmholtz equation using contour integration and polynomial preconditioning (2020)
  19. O’Hearn, Kurt A.; Alperen, Abdullah; Aktulga, Hasan Metin: Fast solvers for charge distribution models on shared memory platforms (2020)
  20. Ong, Kian Chuan; Lai, Ming-Chih: An immersed boundary projection method for simulating the inextensible vesicle dynamics (2020)

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