PSBLAS swMATH ID: 4026 Software Authors: D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore Description: On the development of PSBLAS-based parallel two-level Schwarz preconditioners. Design and implementation issues that concern the development of a package of parallel algebraic two-level Schwarz preconditioners are discussed. The computations are based on the parallel sparse BLAS (PSBLAS) library. The package implements various versions of additive Schwarz preconditioners and applies a smoothed aggregation technique to generate a coarse-level correction. The coarse matrix can be either replicated on the processors or distributed among them; the corresponding system is solved by factorization or block Jacobi sweeps, respectively. The design of the package starts from a description of the preconditioners in terms of parallel basic linear algebra operators, in order to develop software based on standard kernels. Suitable preconditioner data structures are defined to fully exploit the existing PSBLAS functionalities; however, the implementation of the preconditioner requires also an extension of the set of basic library kernels. The results of experiments carried out on different test matrices show that the package is competitive in terms of runtime efficiency. Homepage: http://www.ce.uniroma2.it/psblas/ Related Software: MLD2P4; 2LEV-D2P4; Trilinos; PETSc; UMFPACK; SParC-LES; MPI; BLAS; LAPACK; hypre; BoomerAMG; Aztec; SparseMatrix; BLACS; Matlab; MUMPS; ML; ScaLAPACK; SMMP; GitHub Cited in: 23 Publications all top 5 Cited by 32 Authors 14 Filippone, Salvatore 11 D’Ambra, Pasqua 10 di Serafino, Daniela 3 Aprovitola, Andrea 3 Bertaccini, Daniele 3 Durastante, Fabio 2 Buttari, Alfredo 2 Denaro, Filippo Maria 1 Abdullahi Hassan, Ambra 1 Abdullahi, Ambra 1 Badia, Santiago 1 Bender, Michael A. 1 Borzì, Alfio 1 Cardellini, Valeria 1 Colajanni, Michele 1 Çuğu, İlke 1 De Simone, Valentina 1 Fagerberg, Rolf 1 Gentle, James E. 1 Guarracino, Mario Rosario 1 Jacob, Riko 1 Ling, Siqi 1 Manguoglu, Murat 1 Martín, Alberto F. 1 Perla, Francesca 1 Praetorius, Simon 1 Principe, Javier R. 1 Stølting Brodal, Gerth 1 Vicari, Elias 1 Voigt, Axel 1 Witkowski, Thomas 1 Zanetti, Paolo all top 5 Cited in 15 Serials 4 Computers & Mathematics with Applications 3 ACM Transactions on Mathematical Software 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 Numerical Algorithms 1 Applicable Algebra in Engineering, Communication and Computing 1 SIAM Journal on Scientific Computing 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 Theory of Computing Systems 1 International Journal of Applied Mathematics and Computer Science 1 Archives of Computational Methods in Engineering 1 Parallel Processing Letters 1 Springer Texts in Statistics 1 Monographs and Research Notes in Mathematics all top 5 Cited in 7 Fields 22 Numerical analysis (65-XX) 4 Fluid mechanics (76-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 2 Computer science (68-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) Citations by Year