BILUM swMATH ID: 4015 Software Authors: Saad, Yousef; Zhang, Jun Description: BILUM is a set of programs designed for solving general sparse linear systems by using Krylov subspace methods preconditioned by some multi-level block ILU (BILUM) preconditioning techniques. BILUM combines the benefits of generality and robustness of ILU preconditioning techniques with those of grid-independent convergence of multigrid methods. The multi-level algorithms implemented by BILUM are based on the block independent set ordering and multi-elimination techniques. At each level, a block independent set is found by some greedy algorithms such that each block is decoupled with other blocks in the independent set. There is an inherited parallelism associated with this technique. The coefficient matrix is then re-ordered according to the independent set ordering and an approximate block ILU factorization is performed with a reduced system of smaller size. The multi-level structure is constructed by recursively applying the above idea to the approximate Schur complement (the reduced system) until the last reduced system is small enough to be solved by a direct method or a preconditioned iterative method. Homepage: http://www.cs.uky.edu/~jzhang/bilum.html Related Software: ILUM; BILUTM; ILUT; SparseMatrix; ARMS; symrcm; LAPACK; pARMS; BPKit; Wesseling; BFSAI-IC; ITSOL; CGS; ILUS; BoomerAMG; Aztec; AztecOO; P-SPARSLIB; STRUMPACK; Albany/FELIX Cited in: 50 Publications all top 5 Cited by 65 Authors 24 Zhang, Jun 10 Saad, Yousef 3 Shen, Chi 3 Wang, Kai 2 Ge, Lixin 2 Notay, Yvan 2 Sosonkina, Masha 2 Yang, Geng 1 Benzi, Michele 1 Boman, Erik G. 1 Botta, Eugen F. F. 1 Bridson, Robert 1 Buranay, Suzan C. 1 Cambier, Léopold 1 Carpentieri, Bruno 1 Carvalho, Luiz Mariano 1 Chang, Qianshun 1 Chen, Chao 1 Chi, Xuebin 1 Chow, Edmond G. W. 1 da Cruz, Julia Sekiguchi 1 Darve, Eric 1 de Almeida, Moisés Ceni 1 Ferronato, Massimiliano 1 Glowinski, Roland 1 Goldfeld, Paulo 1 Gross, Lutz 1 Gu, Tongxiang 1 Gupta, Murli M. 1 Haws, John C. 1 Heniche, Mourad 1 Iyikal, Ovgu C. 1 Jiang, Peng 1 Li, Ruipeng 1 Li, Xiaomei 1 Li, Zhongze 1 Liao, Jia 1 Liu, Xingping 1 MacLachlan, Scott P. 1 Meerbergen, Karl 1 Rajamanickam, Sivasankaran 1 Reusken, Arnold 1 Rivera, Christian A. 1 Shi, Yuying 1 Song, Junqiang 1 Sosonkina, Maria 1 Soulaimani, Azzeddine 1 Souza, Michael 1 Suchomel, Brian 1 Tang, Wei-Pai 1 Tanguy, Philippe A. 1 Touihri, Ridha 1 Tůma, Miroslav 1 Tuminaro, Raymond S. 1 Vannieuwenhoven, Nick 1 Vassilevski, Panayot Spirov 1 Wagner, Christian 1 Wang, Ruchuan 1 Wang, Shaodi 1 Wu, Jianping 1 Wubs, Fred W. 1 Xi, Yuanzhe 1 Xiao, Tong 1 Zhao, Jennifer Jing 1 Zhao, Jun all top 5 Cited in 22 Serials 7 Applied Mathematics and Computation 7 SIAM Journal on Scientific Computing 6 SIAM Journal on Matrix Analysis and Applications 5 Numerical Linear Algebra with Applications 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 2 Journal of Computational Physics 1 Computer Methods in Applied Mechanics and Engineering 1 Computing 1 Applied Mathematics and Mechanics. (English Edition) 1 Parallel Computing 1 Numerical Methods for Partial Differential Equations 1 Journal of Parallel and Distributed Computing 1 Linear Algebra and its Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 Mathematical Problems in Engineering 1 International Journal of Numerical Modelling 1 The Korean Journal of Computational & Applied Mathematics 1 The ANZIAM Journal 1 JMMA. Journal of Mathematical Modelling and Algorithms 1 Journal of Applied Mathematics and Computing 1 ISRN Applied Mathematics all top 5 Cited in 6 Fields 50 Numerical analysis (65-XX) 15 Partial differential equations (35-XX) 6 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year