ARMS swMATH ID: 48 Software Authors: Saad, Y.; Suchomel, B. Description: ARMS: an algebraic recursive multilevel solver for general sparse linear systems. The paper describes new recursive multilevel method for preconditioning of general sparse linear systems. This strategy is used in the new solver (ARMS) that generalize previous authors’ codes BILUM and BILUTM. All these methods are based on a block incomplete LU factorization. The ARMS is fully recursive and employs the nested dissection reordering and inner-level iterations. Assumptions, under which the new preconditioning is exact, are given together with the proof that eigenvalues of the preconditioned matrix are close to 1. par Extensive numerical tests are presented and cover various features of the method. They show that the solver ARMS is more robust, saves memory, but performs slower than ILUT and ILUTP (incomplete LU factorization with threshold and with threshold and pivoting). Homepage: http://www-users.cs.umn.edu/~saad/software/ Keywords: incomplete LU factorization; ILUT; multilevel ILU preconditioner; Krylov subspace methods; multi-elimination; recursive solution; Nested dissection; mutigrid Related Software: ILUT; SparseMatrix; pARMS; ILUM; BILUTM; BILUM; ILUPACK; symrcm; MUMPS; PARDISO; LAPACK; VBARMS; AMD; BFSAI-IC; BoomerAMG; hypre; PETSc; SuperLU; FSAIPACK; BPKit Cited in: 71 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year ARMS: an algebraic recursive multilevel solver for general sparse linear systems. Zbl 1071.65001Saad, Y.; Suchomel, B. 2002 all top 5 Cited by 115 Authors 26 Saad, Yousef 5 Ferronato, Massimiliano 5 Li, Ruipeng 5 Xi, Yuanzhe 4 Janna, Carlo 3 Bollhöfer, Matthias 3 MacLachlan, Scott P. 3 Osei-Kuffuor, Daniel 3 Sameh, Ahmed H. 3 Sosonkina, Masha 2 Benzi, Michele 2 Carpentieri, Bruno 2 Franceschini, Andrea 2 Gambolati, Giuseppe 2 Kalantzis, Vassilis 2 Li, Zhongze 2 Schmidt, Douglas C. 2 Van Slingerland, Paulien 2 Vuik, Cornelis 2 Zheng, Qingqing 1 Aliaga, José Ignacio 1 Baggag, Abdelkader 1 Bängtsson, Erik 1 Beik, Fatemeh Panjeh Ali 1 Boavida, Fernando 1 Bu, Yiming 1 Cai, Bo 1 Castillo, Paul E. 1 Chan, Jennifer So Kuen 1 Chartier, Timothy P. 1 Chen, Jie 1 Chen, Qiao 1 Chiou, Yih-Peng 1 Derbal, Youcef 1 Dillon, Geoffrey 1 Du, Cheng-Han 1 El Maliki, Abderrahman 1 Elashoff, Robert M. 1 Estrin, Ron 1 Filelis-Papadopoulos, Christos K. 1 Fortin, Michel 1 Fujiwara, Yoshi 1 Ghai, Aditi 1 Ghanem, Roger G. 1 Gravvanis, George A. 1 Greif, Chen 1 Gross, Lutz 1 Guénette, Robert 1 Guillaume, Philippe 1 Gupta, Anshul 1 Hénon, Pascal 1 Huang, Ting-Zhu 1 Jiang, Yuanlin 1 Jiang, Yunfei 1 Jiao, Xiangmin 1 Kestyn, James 1 Könik, Tolga 1 Kyziropoulos, Panagiotis E. 1 Laird, John E. 1 Lam, Yeh 1 Lavagna, Michèle 1 Leung, Moon K. 1 Liao, Jia 1 Linnér, Elisabeth 1 Little, Leigh 1 Liu, Qun 1 Magri, Victor A. P. 1 Martín, Alberto F. 1 Meerbergen, Karl 1 Melson, John T. 1 Mense, Christian 1 Meyer, Renate 1 Nabben, Reinhard 1 Neytcheva, Maya G. 1 Orvalho, João 1 Paludetto Magri, Victor Antonio 1 Perron, François 1 Philip, Bobby 1 Phipps, Eric T. 1 Polizzi, Eric 1 Quintana-Ortí, Enrique S. 1 Sangiovanni, Guido 1 Sartoretto, Flavio 1 Schenk, Olaf 1 Sequeira, Filánder A. 1 Shen, Zhaoli 1 Shu, Shi 1 Smoch, Laurent 1 Sosonkina, Maria 1 Soulaimani, Azzeddine 1 Sousedík, Bedřich 1 Suchomel, Brian 1 Suzuki, Yasuhiro 1 Takabayashi, Junji 1 Tanaka, Hiroshi 1 Tang, Jok M. 1 Tchelepi, Hamdi A. 1 Tezduyar, Tayfun E. 1 Toselli, Andrea 1 Touihri, Ridha ...and 15 more Authors all top 5 Cited in 29 Serials 16 SIAM Journal on Scientific Computing 10 Numerical Linear Algebra with Applications 5 Journal of Computational and Applied Mathematics 4 Applied Numerical Mathematics 4 SIAM Journal on Matrix Analysis and Applications 2 Computer Methods in Applied Mechanics and Engineering 2 Computational Geosciences 1 Artificial Intelligence 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 ACM Transactions on Mathematical Software 1 Biometrical Journal 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Numerische Mathematik 1 Parallel Computing 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Machine Learning 1 Linear Algebra and its Applications 1 Computational Statistics and Data Analysis 1 Advances in Computational Mathematics 1 Taiwanese Journal of Mathematics 1 International Journal of Computational Methods 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 S\(\vec{\text{e}}\)MA Journal 1 ISRN Applied Mathematics 1 Dolomites Research Notes on Approximation 1 East Asian Journal on Applied Mathematics all top 5 Cited in 14 Fields 58 Numerical analysis (65-XX) 11 Partial differential equations (35-XX) 9 Computer science (68-XX) 6 Fluid mechanics (76-XX) 4 Statistics (62-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Mechanics of deformable solids (74-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year