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. Anciaux-Sedrakian, A.; Grigori, L.; Jorti, Z.; Papež, J.; Yousef, S.: Adaptive solution of linear systems of equations based on a posteriori error estimators (2020)
  2. Du, Cheng-Han; Chiou, Yih-Peng; Wang, Weichung: Compressed hierarchical Schur algorithm for frequency-domain analysis of photonic structures (2019)
  3. Franceschini, Andrea; Paludetto Magri, Victor Antonio; Ferronato, Massimiliano; Janna, Carlo: A robust multilevel approximate inverse preconditioner for symmetric positive definite matrices (2018)
  4. Kyziropoulos, Panagiotis E.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: A class of symmetric factored approximate inverses and hybrid two-level solver (2018)
  5. Moutafis, Byron E.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: Parallel Schur complement techniques based on multiprojection methods (2018)
  6. Li, Ruipeng; Saad, Yousef: Low-rank correction methods for algebraic domain decomposition preconditioners (2017)
  7. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  8. Chen, Jie; McInnes, Lois C.; Zhang, Hong: Analysis and practical use of flexible biCGStab (2016)
  9. Romero, Eloy; Roman, Jose E.: A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc (2014)
  10. Sousedík, Bedřich; Ghanem, Roger G.; Phipps, Eric T.: Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods. (2014)
  11. Ferronato, M.; Janna, C.; Pini, G.: Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models (2012)
  12. Kalinkin, A. A.; Laevskij, Yu. M.: Iterative solver for systems of linear equations with a sparse stiffness matrix for clusters (2012)
  13. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  14. 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)
  15. Tang, Jok M.; Saad, Yousef: Domain-decomposition-type methods for computing the diagonal of a matrix inverse (2011)
  16. Aprovitola, Andrea; D’Ambra, Pasqua; Denaro, Filippo; Di Serafino, Daniela; Filippone, Salvatore: Scalable algebraic multilevel preconditioners with application to CFD (2010)
  17. D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: MLD2P4: a package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 (2010)
  18. Giraud, L.; Haidar, A.; Saad, Y.: Sparse approximations of the Schur complement for parallel algebraic hybrid solvers in 3D (2010)
  19. Osei-Kuffuor, Daniel; Saad, Yousef: Preconditioning Helmholtz linear systems (2010)
  20. Bonfiglioli, A.; Carpentieri, B.; Sosonkina, M.: Performance analysis of parallel algebraic preconditioners for solving the RANS equations using fluctuation splitting schemes (2008)

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