ARMS

The paper describes new recursive multilevel method for preconditioning of general sparse linear systems. This strategy is used in the new solver (ARMS) that generalize previous authors’ codes BILUM and BILUTM. All these methods are based on a block incomplete LU factorization. The ARMS is fully recursive and employs the nested dissection reordering and inner-level iterations. Assumptions, under which the new preconditioning is exact, are given together with the proof that eigenvalues of the preconditioned matrix are close to 1. \parExtensive numerical tests are presented and cover various features of the method. They show that the solver ARMS is more robust, saves memory, but performs slower than ILUT and ILUTP (incomplete LU factorization with threshold and with threshold and pivoting).


References in zbMATH (referenced in 53 articles , 1 standard article )

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  1. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  2. Li, Ruipeng; Saad, Yousef: Low-rank correction methods for algebraic domain decomposition preconditioners (2017)
  3. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  4. Zhu, Yao; Sameh, Ahmed H.: $\textPSPIKE+$: A family of parallel hybrid sparse linear system solvers (2017)
  5. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  6. Estrin, R.; Greif, C.: Towards an optimal condition number of certain augmented Lagrangian-type saddle-point matrices. (2016)
  7. Li, Ruipeng; Xi, Yuanzhe; Saad, Yousef: Schur complement-based domain decomposition preconditioners with low-rank corrections. (2016)
  8. Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices (2016)
  9. Janna, Carlo; Ferronato, Massimiliano; Sartoretto, Flavio; Gambolati, Giuseppe: FSAIPACK: a software package for high-performance factored sparse approximate inverse preconditioning (2015)
  10. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  11. van Slingerland, P.; Vuik, C.: Scalable two-level preconditioning and deflation based on a piecewise constant subspace for (SIP)DG systems for diffusion problems (2015)
  12. Carpentieri, Bruno; Liao, Jia; Sosonkina, Masha: VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems (2014)
  13. Nagler, Loris; Rong, Ping; Schanz, Martin; von Estorff, Otto: Sound transmission through a poroelastic layered panel (2014)
  14. Sousedík, Bedřich; Ghanem, Roger G.; Phipps, Eric T.: Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods. (2014)
  15. Castillo, P.E.; Sequeira, F.A.: Computational aspects of the local discontinuous Galerkin method on unstructured grids in three dimensions (2013)
  16. Li, Ruipeng; Saad, Yousef: Divide and conquer low-rank preconditioners for symmetric matrices (2013)
  17. Vannieuwenhoven, Nick; Meerbergen, Karl: IMF: an incomplete multifrontal $LU$-factorization for element-structured sparse linear systems (2013)
  18. Ferronato, Massimiliano: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives (2012)
  19. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  20. Philip, Bobby; Chartier, Timothy P.: Adaptive algebraic smoothers (2012)

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