SPIKE swMATH ID: 2780 Software Authors: Polizzi, Eric; Sameh, Ahmed Description: SPIKE: A parallel environment for solving banded linear systems. The hybrid banded linear solver SPIKE is proposed as a parallel environment for solving banded systems that are either dense or sparse within the band. The SPIKE algorithm is a domain decomposition technique that allows performing independent calculations on each subdomain or partition of the original linear system. The interface problem leads to a reduced linear system of much smaller size than that of the original system. Three different members of the SPIKE family are described. Each handles the reduced system in a different way depending on the characteristics of the system and the architecture of the high-end parallel computing platform. Numerical experiments are presented that demonstrate the effectiveness of our parallel scheme. Comparison with the corresponding algorithms of ScaLAPACK are also provided for those banded systems that are dense within the band. A SPIKE scheme with multi-level parallelism is also introduced for solving large banded systems that are sparse within the band. Homepage: http://www.spike-solver.org Related Software: PARDISO; SparseMatrix; MUMPS; LAPACK; PSPIKE; ScaLAPACK; SuperLU; SuperLU-DIST; HSL; MKL; METIS; BoomerAMG; PETSc; UMFPACK; CSparse; BLAS; GitHub; SaPGPU; Chrono; MC21A Cited in: 39 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year SPIKE: A parallel environment for solving banded linear systems. Zbl 1181.76110Polizzi, Eric; Sameh, Ahmed 2007 all top 5 Cited by 76 Authors 11 Manguoglu, Murat 10 Sameh, Ahmed H. 3 Negrut, Dan 3 Polizzi, Eric 3 Tezduyar, Tayfun E. 2 Bazilevs, Yuri 2 Esmaily Moghadam, Mahdi 2 Jayakumar, Paramsothy 2 Li, Ang 2 Marsden, Alison L. 2 Melanz, Daniel 2 Naumov, Maxim 2 Serban, Radu 2 Takizawa, Kenji 1 Abide, Stéphane 1 Aykanat, Cevdet 1 Barnaś, Dawid 1 Bertozzi, Andrea Louise 1 Bieniasz, Lesław K. 1 Binous, M. S. 1 Bolukbasi, Ercan Selcuk 1 Brown, Jed 1 Buttari, Alfredo 1 Capuano, Francesco 1 Carpentieri, Bruno 1 Constantinescu, Emil M. 1 Çuğu, İlke 1 De Angelis, E. M. 1 Dessole, Monica 1 Dimakopoulos, Yannis 1 Dudson, B. D. 1 Esmaily, Mahdi 1 Fang, Luning 1 Filelis-Papadopoulos, Christos K. 1 Ghosh, Debojyoti 1 Grama, Ananth Y. 1 Gravvanis, George A. 1 Gu, Tongxiang 1 Gu, Xian-Ming 1 Hauberg, Søren 1 Hill, P. A. 1 Iaccarino, Gianluca 1 Jofre, Lluís 1 Jönsthövel, Tom B. 1 Kim, Jaewook 1 Kodsi, Costy 1 Koyuturk, Mehmet 1 Li, Zhilin 1 Luo, Weihua 1 MacLachlan, Scott P. 1 Marcuzzi, Fabio 1 Mastellone, A. 1 Mata, Matthew R. 1 Maurer, Daniel 1 Mikkelsen, Carl Christian Kjelgaard 1 Mo, Zeyao 1 Parker, Jason T. 1 Sathe, Sunil 1 Scarpas, A. 1 Spring, Braegan S. 1 Stanciulescu, Ilinca 1 Stratulat, Sorin 1 Torun, F. Sukru 1 Torun, Tugba 1 Tselepidis, N. A. 1 Van Gijzen, Martin Bastiaan 1 Vuik, Cornelis 1 Wieners, Christian 1 Xia, Jianlin 1 Xu, Xiaowen 1 Ye, Xin 1 Zeghmati, Belkacem 1 Zhang, Aiqing 1 Zhang, Zhengyi 1 Zlatev, Zahari 1 Zuo, Xianyu all top 5 Cited in 18 Serials 6 Journal of Computational and Applied Mathematics 5 SIAM Journal on Scientific Computing 4 Journal of Computational Physics 4 Computational Mechanics 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 ACM Transactions on Mathematical Software 1 International Journal for Numerical Methods in Engineering 1 Mathematics and Computers in Simulation 1 Journal of Symbolic Computation 1 SIAM Journal on Matrix Analysis and Applications 1 Numerical Algorithms 1 Journal of Non-Newtonian Fluid Mechanics 1 Numerical Linear Algebra with Applications 1 International Journal of Computational Fluid Dynamics 1 International Journal of Computational Methods all top 5 Cited in 11 Fields 35 Numerical analysis (65-XX) 14 Fluid mechanics (76-XX) 5 Mechanics of deformable solids (74-XX) 3 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Partial differential equations (35-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year