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. Tielen, R.; Möller, M.; Göddeke, D.; Vuik, C.: (p)-multigrid methods and their comparison to (h)-multigrid methods within isogeometric analysis (2020)
  2. Yushu, Dewen; Matouš, Karel: The image-based multiscale multigrid solver, preconditioner, and reduced order model (2020)
  3. Behrou, Reza; Ranjan, Ram; Guest, James K.: Adaptive topology optimization for incompressible laminar flow problems with mass flow constraints (2019)
  4. Cockayne, Jon; Oates, Chris J.; Ipsen, Ilse C. F.; Girolami, Mark: A Bayesian conjugate gradient method (with discussion) (2019)
  5. Franceschini, Andrea; Paludetto Magri, Victor A.; Mazzucco, Gianluca; Spiezia, Nicolò; Janna, Carlo: A robust adaptive algebraic multigrid linear solver for structural mechanics (2019)
  6. Paludetto Magri, Victor A.; Franceschini, Andrea; Janna, Carlo: A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems (2019)
  7. Slak, J.; Kosec, Gregor: Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain (2019)
  8. Anzt, Hartwig; Chow, Edmond; Dongarra, Jack: ParILUT -- a new parallel threshold ILU factorization (2018)
  9. Ben-Ahmed, E.; Sadik, M.; Wakrim, M.: Radial basis function partition of unity method for modelling water flow in porous media (2018)
  10. Cerdán, J.; Guerrero, D.; Marín, J.; Mas, J.: Preconditioners for nonsymmetric linear systems with low-rank skew-symmetric part (2018)
  11. Chiu, Pao-Hsiung: An improved divergence-free-condition compensated method for solving incompressible flows on collocated grids (2018)
  12. Fernández-Pato, J.; Morales-Hernández, M.; García-Navarro, P.: Implicit finite volume simulation of 2D shallow water flows in flexible meshes (2018)
  13. Huang, Zhuo-Hong; Huang, Ting-Zhu: Semi-convergence analysis of the GSS iteration methods for singular saddle point problems (2018)
  14. Kraus, Johannes; Lymbery, Maria: Incomplete factorization by local exact factorization (ILUE) (2018)
  15. Lungten, Sangye; Schilders, Wil H. A.; Maubach, Joseph M. L.: Threshold incomplete factorization constraint preconditioners for saddle-point matrices (2018)
  16. Moutafis, Byron E.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: Parallel Schur complement techniques based on multiprojection methods (2018)
  17. Sushnikova, Daria A.; Oseledets, Ivan V.: “Compress and eliminate” solver for symmetric positive definite sparse matrices (2018)
  18. Cerdán, J.; Marín, J.; Mas, J.: Low-rank updates of balanced incomplete factorization preconditioners (2017)
  19. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  20. Marín, J.; Mas, J.; Guerrero, D.; Hayami, K.: Updating preconditioners for modified least squares problems (2017)

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