Bi-CG swMATH ID: 76 Software Authors: Mokhtarzadeh, M.R.; Mokhtary, R.; Chegini, N.G. Description: Bi-CG: An effective solver for three fields domain decomposition method in parallel environments After applying the substructuring preconditioner for a linear system stemming from the three fields domain decomposition method for elliptic boundary value problems, the preconditioned system will be nonsymmetric and the bi-conjugate gradient (Bi-CG) method can be applied. We show that in parallel environments the Bi-CG method works as preconditioned conjugate gradient (PCG) method which was applied by S. Bertoluzza [Math. Comp. 73, No. 246, 659–689 (2003)], and in this case extensive numerical tests, performed on both conforming and nonconforming formulation, show that Bi-CG can work faster than PCG Homepage: http://netlib.org/linalg/html_templates/node32.html Keywords: Three fields domain decomposition method; Bi-Conjugate Gradient method; Galerkin method; numerical examples; preconditioning; comparison of methods; elliptic boundary value problems Related Software: CGS; GpBiCg; BiCGstab; na1; ILUT; Harwell-Boeing sparse matrix collection; SPARSKIT; ITSOL; BLAS; PARDISO; tn; LSQR; PILS Cited in: 34 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Bi-CG: An effective solver for three fields domain decomposition method in parallel environments. Zbl 1091.65033Mokhtarzadeh, M. R.; Mokhtary, R.; Chegini, N. G. 2006 all top 5 Cited by 43 Authors 9 Van der Vorst, Henk Albertus 5 Sleijpen, Gerard L. G. 3 Fokkema, Diederik R. 3 Zhang, Shao-Liang 2 Fujino, Seiji 2 Pina, Heitor L. G. 2 Valente, F. P. 1 Bergeles, George C. 1 Cao, Zhihao 1 Chegini, Nabi G. 1 Chen, Rushan 1 Chernov, K. G. 1 Chieng, Ching-Chang 1 de Zeeuw, Paul M. 1 Doi, Shun 1 Fasano, Giovanni 1 Ganina, S. M. 1 Ginkin, V. P. 1 Guo, Xinglin 1 Khoo, Boo Cheong 1 Kluzner, Vladimir 1 Mansur, Webe Joao 1 Mokhtari, Reza 1 Nodera, Takashi 1 Papadakis, George 1 Romate, Johan Egbert 1 Santiago, J. A. F. 1 Schenk, Olaf 1 Sha, Desong 1 Sheng, Zhaohan 1 Sidi, Avram 1 Sogabe, Tomohiro 1 Sonneveld, Peter 1 Sugihara, Masaaki 1 Telles, José Claudio de Faria 1 Van Gijzen, Martin Bastiaan 1 Wang, Chunwu 1 Wang, Daoxiang 1 Wu, Chengwei 1 Yang, Zhongchao 1 Yung, Edward Kai-Ning 1 Zhang, Zhongding 1 Zhao, Jiabao all top 5 Cited in 21 Serials 2 International Journal for Numerical Methods in Fluids 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Engineering Analysis with Boundary Elements 1 Journal of Computational Physics 1 Transport Theory and Statistical Physics 1 Applied Mathematics and Computation 1 Computing 1 SIAM Journal on Scientific and Statistical Computing 1 Computational Mechanics 1 Journal of Southwest Jiaotong University 1 Journal of Dalian University of Technology 1 Journal of Southeast University 1 Numerical Algorithms 1 Linear Algebra and its Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 ELA. The Electronic Journal of Linear Algebra 1 Optimization Methods & Software 1 International Journal of Numerical Modelling 1 Advances in Numerical Methods for Large Sparse Sets of Linear Equations 1 Cambridge Monographs on Applied and Computational Mathematics all top 5 Cited in 7 Fields 32 Numerical analysis (65-XX) 9 Partial differential equations (35-XX) 5 Fluid mechanics (76-XX) 3 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year