A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems

Benzi, 2002, Preconditioning techniques for large linear systems: a survey, J. Comput. Phys., 182, 418, 10.1006/jcph.2002.7176 Benzi, 1999, A two-level parallel preconditioner based on sparse approximate inverses Benzi, 1996, A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput., 17, 1135, 10.1137/S1064827594271421 Benzi, 1998, A sparse approximate inverse preconditioner for nonsymmetric linear systems, SIAM J. Sci. Comput., 19, 968, 10.1137/S1064827595294691 Bollhoefer Bollhöfer, 2003, A robust and efficient ILU that incorporates the growth of the inverse triangular factors, SIAM J. Sci. Comput., 25, 86, 10.1137/S1064827502403411 Bollhöfer, 2006, Multilevel preconditioners constructed from inverse–based ILUs, SIAM J. Sci. Comput., 27, 1627, 10.1137/040608374 Carpentieri, 2007, Fast iterative solution methods in electromagnetic scattering, Prog. Electromagn. Res., 79, 151, 10.2528/PIER07100802 Carpentieri, 2012, Symmetric inverse-based multilevel ILU preconditioning for solving dense complex non-Hermitian systems in electromagnetics, Prog. Electromagn. Res., 128, 55, 10.2528/PIER12041006 Carpentieri, 2005, Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations, SIAM J. Sci. Comput., 27, 774, 10.1137/040603917 Carpentieri, 2014, VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems, J. Comput. Appl. Math., 259, 164, 10.1016/j.cam.2013.04.036 Chow, 2000, A priori sparsity patterns for parallel sparse approximate inverse preconditioners, SIAM J. Sci. Comput., 21, 1804, 10.1137/S106482759833913X Chow, 2001, Parallel implementation and practical use of sparse approximate inverses with a priori sparsity patterns, Int. J. High Perform. Comput. Appl., 15, 56, 10.1177/109434200101500106 Chow, 1998, Approximate inverse preconditioners via sparse-sparse iterations, SIAM J. Sci. Comput., 19, 995, 10.1137/S1064827594270415 Davis Duff, 1999, The design and use of algorithms for permuting large entries to the diagonal of sparse matrices, SIAM J. Matrix Anal. Appl., 20, 889, 10.1137/S0895479897317661 Duff, 1989, The effect of ordering on preconditioned conjugate gradient, BIT Numer. Math., 29, 635, 10.1007/BF01932738 Ferronato, 2014, A generalized block FSAI preconditioner for nonsymmetric linear systems, J. Comput. Appl. Math., 256, 230, 10.1016/j.cam.2013.07.049 George, 1981 Grigori, 2015, Overlapping for preconditioners based on incomplete factorizations and nested arrow form, Numer. Linear Algebra Appl., 22, 48, 10.1002/nla.1937 Grote, 1997, Parallel preconditionings with sparse approximate inverses, SIAM J. Sci. Comput., 18, 838, 10.1137/S1064827594276552 HSL Huckle, 2010, An efficient parallel implementation of the MSPAI preconditioner, Parallel Comput., 36, 273, 10.1016/j.parco.2009.12.007 Huckle, 2010, Smoothing and regularization with modified sparse approximate inverses, Int. J. Comput. Electr. Eng., 2010, 1 Janna, 2011, Adaptive pattern research for block FSAI preconditioning, SIAM J. Sci. Comput., 33, 3357, 10.1137/100810368 Janna, 2010, A block FSAI-ILU parallel preconditioner for symmetric positive definite linear systems, SIAM J. Sci. Comput., 32, 2468, 10.1137/090779760 Janna, 2013, Enhanced block FSAI preconditioning using domain decomposition techniques, SIAM J. Sci. Comput., 35, S229, 10.1137/120880860 Karypis, 1999, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput., 20, 359, 10.1137/S1064827595287997 Kolotilina, 1993, Factorized sparse approximate inverse preconditionings. I: Theory, SIAM J. Matrix Anal. Appl., 14, 45, 10.1137/0614004 Kolotilina, 1995, Factorized sparse approximate inverse preconditionings. II: Solution of 3D FE systems on massively parallel computers, Int. J. High Speed Comput., 7, 191, 10.1142/S0129053395000117 Kolotilina, 1999, Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising efficiency, Numer. Linear Algebra Appl., 6, 515, 10.1002/(SICI)1099-1506(199910/11)6:7<515::AID-NLA176>3.0.CO;2-0 Kolotilina, 2000, Factorized sparse approximate inverse preconditionings. III: Iterative construction of preconditioners, J. Math. Sci., 101, 3237, 10.1007/BF02672769 Li, 2013, GPU-accelerated preconditioned iterative linear solvers, J. Supercomput., 63, 443, 10.1007/s11227-012-0825-3 Manguoglu, 2011, A domain-decomposing parallel sparse linear system solver, J. Comput. Appl. Math., 236, 319, 10.1016/j.cam.2011.07.017 Meijerink, 1977, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput., 31, 148 Monga Made, 2000, Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix, Commun. Numer. Methods Eng., 11, 801, 10.1002/1099-0887(200011)16:11<801::AID-CNM377>3.0.CO;2-M Pan, 2014, Improved algebraic preconditioning for MoM solutions of large-scale electromagnetic problems, IEEE Antennas Wirel. Propag. Lett., 13, 106, 10.1109/LAWP.2013.2295239 Pan, 2014, Sparse approximate inverse preconditioner for multiscale dynamic electromagnetic problems, Radio Sci., 49, 1041, 10.1002/2014RS005387 Quarteroni, 1999 Saad, 2003 Saad, 2005, Multilevel ILU with reorderings for diagonal dominance, SIAM J. Sci. Comput., 27, 1032, 10.1137/030602733 Saad, 1986, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 856, 10.1137/0907058 Saad, 2004, Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems, Appl. Numer. Math., 51, 305, 10.1016/j.apnum.2004.06.017 Saad, 2002, ARMS: an algebraic recursive multilevel solver for general sparse linear systems, Numer. Linear Algebra Appl., 9, 359, 10.1002/nla.279 Yeremin, 2004, Factorized-sparse-approximate-inverse preconditionings of linear systems with unsymmetric matrices, J. Math. Sci., 121, 2448, 10.1023/B:JOTH.0000026282.08256.45