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. Bertaccini, Daniele; Durastante, Fabio: Solving mixed classical and fractional partial differential equations using short-memory principle and approximate inverses (2017)
  2. Bertaccini, Daniele; Filippone, Salvatore: Sparse approximate inverse preconditioners on high performance GPU platforms (2016)
  3. D’Ambra, Pasqua; Filippone, Salvatore: A parallel generalized relaxation method for high-performance image segmentation on GPUs (2016)
  4. Witkowski, T.; Ling, S.; Praetorius, S.; Voigt, A.: Software concepts and numerical algorithms for a scalable adaptive parallel finite element method (2015)
  5. Badia, Santiago; Martín, Alberto F.; Principe, Javier: Implementation and scalability analysis of balancing domain decomposition methods (2013)
  6. D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: Performance analysis of parallel Schwarz preconditioners in the LES of turbulent channel flows (2013)
  7. Filippone, Salvatore; Buttari, Alfredo: Object-oriented techniques for sparse matrix computations in Fortran 2003 (2012)
  8. 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)
  9. Bender, Michael A.; Brodal, Gerth Stølting; Fagerberg, Rolf; Jacob, Riko; Vicari, Elias: Optimal sparse matrix dense vector multiplication in the I/O-model (2010)
  10. D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: MLD2P4: a package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 (2010)
  11. 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
  12. Buttari, Alfredo; D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: 2LEV-D2P4: a package of high-performance preconditioners for scientific and engineering applications (2007)
  13. D’Ambra, Pasqua; di Serafino, Daniela; Filippone, Salvatore: On the development of PSBLAS-based parallel two-level Schwarz preconditioners (2007)
  14. Guarracino, Mario Rosario; Perla, Francesca; Zanetti, Paolo: A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers (2006)
  15. Filippone, Salvatore; Colajanni, Michele: PSBLAS. a library for parallel linear algebra computation on sparse matrices. (2000) ioport