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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  10. Klockiewicz, Bazyli; Darve, Eric: Sparse hierarchical preconditioners using piecewise smooth approximations of eigenvectors (2020)
  11. 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)
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  13. Tielen, R.; Möller, M.; Göddeke, D.; Vuik, C.: (p)-multigrid methods and their comparison to (h)-multigrid methods within isogeometric analysis (2020)
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  18. Paludetto Magri, Victor A.; Franceschini, Andrea; Janna, Carlo: A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems (2019)
  19. Slak, J.; Kosec, Gregor: Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain (2019)
  20. Anzt, Hartwig; Chow, Edmond; Dongarra, Jack: ParILUT -- a new parallel threshold ILU factorization (2018)

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