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).

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  1. Gupta, Anshul: Enhancing performance and robustness of ILU preconditioners by blocking and selective transposition (2017)
  2. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  3. Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices (2016)
  4. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  5. 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)
  6. Carpentieri, Bruno; Liao, Jia; Sosonkina, Masha: VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems (2014)
  7. Nagler, Loris; Rong, Ping; Schanz, Martin; von Estorff, Otto: Sound transmission through a poroelastic layered panel (2014)
  8. Castillo, P.E.; Sequeira, F.A.: Computational aspects of the local discontinuous Galerkin method on unstructured grids in three dimensions (2013)
  9. Li, Ruipeng; Saad, Yousef: Divide and conquer low-rank preconditioners for symmetric matrices (2013)
  10. Vannieuwenhoven, Nick; Meerbergen, Karl: IMF: an incomplete multifrontal $LU$-factorization for element-structured sparse linear systems (2013)
  11. Ferronato, Massimiliano: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives (2012)
  12. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  13. Philip, Bobby; Chartier, Timothy P.: Adaptive algebraic smoothers (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. Neytcheva, Maya; Bängtsson, Erik; Linnér, Elisabeth: Finite-element based sparse approximate inverses for block-factorized preconditioners (2011)
  16. Tang, Jok M.; Saad, Yousef: Domain-decomposition-type methods for computing the diagonal of a matrix inverse (2011)
  17. Osei-Kuffuor, Daniel; Saad, Yousef: Preconditioning Helmholtz linear systems (2010)
  18. Mense, C.; Nabben, R.: On algebraic multi-level methods for non-symmetric systems --- comparison results (2008)
  19. Meyer, Renate; Cai, Bo; Perron, François: Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2 (2008)
  20. Maclachlan, Scott; Saad, Yousef: Greedy coarsening strategies for nonsymmetric problems (2007)

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