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.

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  1. D’Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore: AMG preconditioners for linear solvers towards extreme scale (2021)
  2. Çuğu, İlke; Manguoğlu, Murat: A parallel multithreaded sparse triangular linear system solver (2020)
  3. Abdullahi, Ambra; D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: Parallel aggregation based on compatible weighted matching for AMG (2018)
  4. Bertaccini, Daniele; Durastante, Fabio: Iterative methods and preconditioning for large and sparse linear systems with applications (2018)
  5. Bertaccini, Daniele; Durastante, Fabio: Solving mixed classical and fractional partial differential equations using short-memory principle and approximate inverses (2017)
  6. Gentle, James E.: Matrix algebra. Theory, computations and applications in statistics (2017)
  7. Bertaccini, Daniele; Filippone, Salvatore: Sparse approximate inverse preconditioners on high performance GPU platforms (2016)
  8. D’Ambra, Pasqua; Filippone, Salvatore: A parallel generalized relaxation method for high-performance image segmentation on GPUs (2016)
  9. Aprovitola, Andrea; D’Ambra, Pasqua; Denaro, Filippo M.; di Serafino, Daniela; Filippone, Salvatore: SParc-LES: enabling large eddy simulations with parallel sparse matrix computation tools (2015)
  10. Witkowski, T.; Ling, S.; Praetorius, S.; Voigt, A.: Software concepts and numerical algorithms for a scalable adaptive parallel finite element method (2015)
  11. Badia, Santiago; Martín, Alberto F.; Principe, Javier: Implementation and scalability analysis of balancing domain decomposition methods (2013)
  12. Borzì, Alfio; De Simone, Valentina; di Serafino, Daniela: Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems (2013)
  13. D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: Performance analysis of parallel Schwarz preconditioners in the LES of turbulent channel flows (2013)
  14. Filippone, Salvatore; Buttari, Alfredo: Object-oriented techniques for sparse matrix computations in Fortran 2003 (2012)
  15. Aprovitola, Andrea; D’Ambra, Pasqua; Denaro, Filippo; Di Serafino, Daniela; Filippone, Salvatore: Scalable algebraic multilevel preconditioners with application to CFD (2010)
  16. Aprovitola, Andrea; D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: On the use of aggregation-based parallel multilevel preconditioners in the LES of wall-bounded turbulent flows (2010)
  17. Bender, Michael A.; Brodal, Gerth Stølting; Fagerberg, Rolf; Jacob, Riko; Vicari, Elias: Optimal sparse matrix dense vector multiplication in the I/O-model (2010)
  18. D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: MLD2P4: a package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 (2010)
  19. O’Reilly, Una-May; Robinson, Eric; Mohindra, Sanjeev; Mullen, Julie; Bliss, Nadya: Hogs and slackers: Using operations balance in a genetic algorithm to optimize sparse algebra computation on distributed architectures (2010) ioport
  20. Buttari, Alfredo; D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: 2LEV-D2P4: a package of high-performance preconditioners for scientific and engineering applications (2007)

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