pARMS: A package for solving general sparse linear systems on parallel computers This paper presents an overview of pARMS, a package for solving sparse linear systems on parallel platforms. Preconditioners constitute the most important ingredient in the solution of linear systems arising from realistic scientific and engineering applications. The most common parallel preconditioners used for sparse linear systems adapt domain decomposition concepts to the more general framework of “distributed sparse linear systems”. The parallel Algebraic Recursive Multilevel Solver (pARMS) is a recently developed package which integrates together variants from both Schwarz procedures and Schur complement-type techniques. This paper discusses a few of the main ideas and design issues of the package. A few details on the implementation of pARMS are provided.

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  1. Ferronato, M.; Janna, C.; Pini, G.: Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models (2012)
  2. Kalinkin, A.A.; Laevskij, Yu.M.: Iterative solver for systems of linear equations with a sparse stiffness matrix for clusters (2012)
  3. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  4. Aliaga, José I.; Bollhöfer, Matthias; Martín, Alberto F.; Quintana-Ortí, Enrique S.: Exploiting thread-level parallelism in the iterative solution of sparse linear systems (2011)
  5. Tang, Jok M.; Saad, Yousef: Domain-decomposition-type methods for computing the diagonal of a matrix inverse (2011)
  6. Giraud, L.; Haidar, A.; Saad, Y.: Sparse approximations of the Schur complement for parallel algebraic hybrid solvers in 3D (2010)
  7. Osei-Kuffuor, Daniel; Saad, Yousef: Preconditioning Helmholtz linear systems (2010)
  8. Bonfiglioli, A.; Carpentieri, B.; Sosonkina, M.: Performance analysis of parallel algebraic preconditioners for solving the RANS equations using fluctuation splitting schemes (2008)
  9. Bergamaschi, L.; Gambolati, G.; Pini, G.: A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations (2007)
  10. Hénon, Pascal; Saad, Yousef: A parallel multistage ILU factorization based on a hierarchical graph decomposition (2006)
  11. Kendall, Ricky A.; Sosonkina, Masha; Gropp, William D.; Numrich, Robert W.; Sterling, Thomas: Parallel programming models applicable to cluster computing and beyond (2006)
  12. Li, Na; Saad, Yousef: MIQR: a multilevel incomplete QR preconditioner for large sparse least-squares problems (2006)
  13. Li, Zhongze; Saad, Yousef: SchurRAS: A restricted version of the overlapping Schur complement preconditioner (2006)
  14. Yang, Ulrike Meier: Parallel algebraic multigrid methods -- high performance preconditioners (2006)
  15. Bergamaschi, Luca; Martínez, Ángeles: Parallel acceleration of Krylov solvers by factorized approximate inverse preconditioners (2005)
  16. Frayssé, Valéire; Giraud, Luc; Gratton, Serge; Langou, Julien: Algorithm 842: A set of GMRES routines for real and complex arithmetics on high performance computers (2005)
  17. Notay, Y.: Algebraic multigrid and algebraic multilevel methods: a theoretical comparison. (2005)
  18. Shen, Chi; Zhang, Jun; Wang, Kai: Distributed block independent set algorithms and parallel multilevel ILU preconditioners (2005)
  19. Saad, Yousef; Soulaimani, Azzeddine; Touihri, Ridha: Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems (2004)
  20. Vainikko, Eero; Graham, Ivan G.: A parallel solver for PDE systems and application to the incompressible Navier-Stokes equations (2004)

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