ILUM swMATH ID: 7244 Software Authors: Saad, Y. Description: ILUM: A multi-elimination ILU preconditioner for general sparse matrices Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism, in general. A few of the alternatives advocated so far consist of either using some form of polynomial precoditioning or applying the usual ILU factorization to a matrix obtained from a multicolor ordering.par We present an incomplete factorization technique based on independent set orderings and multicoloring. We note that in order to improve robustness, it is necessary to allow the preconditioner to have an arbitrary high accuracy, as is done with ILUs based on threshold techniques. The ILUM factorization described in this paper is in this category. It can be viewed as a multifrontal version of a Gaussian elimination procedure with threshold dropping which has a high degree of potential parallelism.par The emphasis is on methods that deal specifically with general unstructured sparse matrices such as those arising from finite element methods on unstructured meshes. Homepage: http://dl.acm.org/citation.cfm?id=239734 Keywords: sparse linear systems; incomplete LU factorizations; preconditioning; multicolor ordering; Gaussian elimination; finite element methods Related Software: BILUM; BILUTM; SparseMatrix; ARMS; ILUT; pARMS; symrcm; LAPACK; SPARSKIT; BPKit; DRIC; ITSOL; PETSc; AMD; ILUS; BoomerAMG; Wesseling; MC21A; CIRR; ARPACK Cited in: 64 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year ILUM: A multi-elimination ILU preconditioner for general sparse matrices. Zbl 0858.65029Saad, Y. 1996 all top 5 Cited by 82 Authors 18 Saad, Yousef 12 Zhang, Jun 4 Notay, Yvan 4 Xi, Yuanzhe 3 Ferronato, Massimiliano 3 Gebremedhin, Assefaw Hadish 3 Kalantzis, Vassilis 3 Manne, Fredrik 3 Wubs, Fred W. 2 Benzi, Michele 2 Boman, Erik G. 2 Botta, Eugen F. F. 2 Bozdağ, Doruk 2 Çatalyürek, Ümit V. 2 Janna, Carlo 2 Khojasteh Salkuyeh, Davod 2 Li, Ruipeng 2 MacLachlan, Scott P. 2 Osei-Kuffuor, Daniel 2 Reusken, Arnold 2 Shen, Chi 2 Sosonkina, Masha 2 Souhar, O. 2 van der Ploeg, Auke 2 Vuik, Cornelis 2 Wang, Kai 1 Bertolazzi, Enrico 1 Bollhöfer, Matthias 1 Buranay, Suzan C. 1 Carpentieri, Bruno 1 Castillo, Paul E. 1 Chan, Tony Fan-Cheong 1 Chang, Qianshun 1 Chen, Ke 1 Chi, Xuebin 1 Chow, Edmond G. W. 1 de Zeeuw, Paul M. 1 Dekker, Kees 1 Dillon, Geoffrey 1 Frego, Marco 1 Gambolati, Giuseppe 1 Grigori, Laura 1 Gross, Lutz 1 Gu, Tongxiang 1 Haws, John C. 1 Heath, Lenwood S. 1 Hénon, Pascal 1 Horesh, Lior 1 Iyikal, Ovgu C. 1 Jimack, Peter K. 1 Kelmanson, Mark A. 1 Kraus, Johannes K. 1 Li, Xiaomei 1 Li, Zhongze 1 Liao, Jia 1 Liu, Xingping 1 Meerbergen, Karl 1 Meijerink, J. A. 1 Ozguner, Fusun 1 Pemmaraju, Sriram V. 1 Peterson, Richard C. 1 Pini, Giorgio 1 Pothen, Alex 1 Rafiei, Amin 1 Ribbens, Calvin J. 1 Roohani, Hadi 1 Sequeira, Filánder A. 1 Shi, Yuying 1 Sleijpen, Gerard L. G. 1 Song, Junqiang 1 Sosonkina, Maria 1 Soulaimani, Azzeddine 1 Stüben, Klaus 1 Suchomel, Brian 1 Touihri, Ridha 1 Toutounian, Faezeh 1 Tůma, Miroslav 1 Vannieuwenhoven, Nick 1 Vassilevski, Panayot Spirov 1 Wu, Jianping 1 Xiang, Hua 1 Zhao, Jun all top 5 Cited in 21 Serials 18 SIAM Journal on Scientific Computing 7 Numerical Linear Algebra with Applications 5 Applied Numerical Mathematics 4 Applied Mathematics and Computation 4 Journal of Computational and Applied Mathematics 3 SIAM Journal on Matrix Analysis and Applications 2 Journal of Computational Physics 2 International Journal for Numerical Methods in Engineering 2 Journal of Parallel and Distributed Computing 2 Mathematical Problems in Engineering 2 Journal of Applied Mathematics and Computing 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Applied Mathematics and Mechanics. (English Edition) 1 Mathematical and Computer Modelling 1 SIAM Review 1 Opuscula Mathematica 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 The ANZIAM Journal 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 ISRN Applied Mathematics all top 5 Cited in 10 Fields 59 Numerical analysis (65-XX) 16 Partial differential equations (35-XX) 7 Fluid mechanics (76-XX) 3 Combinatorics (05-XX) 3 Computer science (68-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year