Daniele Boffi1, Zhongjie Lu2, Luca F. Pavarino3
Daniele Boffi, Zhongjie Lu, Luca F. Pavarino. ITERATIVE ILU PRECONDITIONERS FOR LINEAR SYSTEMS AND EIGENPROBLEMS[J]. Journal of Computational Mathematics, 2021, 39(4): 633-654.
[1] A. Abdelfattah, H. Anzt, J. Dongarra, M. Gates, A. Haidar, J. Kurzak, P. Luszczek, S. Tomov, I. Yamazaki, and A. YarKhan. Linear algebra software for large-scale accelerated multicore computing. Acta Numerica, 25(2016), 1-160. [2] E. Anderson and Y. Saad. Solving sparse triangular linear systems on parallel computers. Internat. J. High Speed Comput., 1:01(1989), 73-95,. [3] H. Anzt, E. Chow, and J. Dongarra. ParILUT—a new parallel threshold ILU factorization. SIAM J. Sci. Comput., 40:4(2018), C503-C519,. [4] C.C. Ashcraft and R. G. Grimes. On vectorizing incomplete factorization and ssor preconditioners. SIAM J. Sci. Statist. Comput., 9:1(1988), 122-151. [5] S. Balay, S. Abhyankar, M. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. Gropp, D. Kaushik, et al. Petsc users manual revision 3.8. Technical report, Argonne National Lab.(ANL), Argonne, IL (United States), 2017. [6] R. Barrett, M.W. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst. Templates for the solution of linear systems: building blocks for iterative methods, volume 43. SIAM, 1994. [7] M. Benzi. Preconditioning techniques for large linear systems: a survey. J. Comput. Phys., 182:2(2002), 418-477. [8] M. Bern, J.R. Gilbert, B. Hendrickson, N. Nguyen, and S. Toledo. Support-graph preconditioners. SIAM J. Matrix Anal. Appl., 27:4(2006), 930-951. [9] D. Boffi. Finite element approximation of eigenvalue problems. Acta Numer., 19(2010), 1-120. [10] D. Boffi, F. Brezzi, and M. Fortin. Mixed finite element methods and applications, volume 44. Springer, 2013. [11] D. Boffi, D. Gallistl, F. Gardini, and L. Gastaldi. Optimal convergence of adaptive fem for eigenvalue clusters in mixed form. Math. Comp., 86:307(2017), 2213-2237. [12] A. Buluç and J.R. Gilbert. Parallel sparse matrix-matrix multiplication and indexing: Implementation and experiments. SIAM J. Sci. Comput., 34:4(2012), C170-C191. [13] C. Calgaro, J.P. Chehab, and Y. Saad. Incremental incomplete LU factorizations with applications. Numer. Linear Algebra Appl., 17:5(2010), 811-837. [14] E. Chow and A. Patel. Fine-grained parallel incomplete LU factorization. SIAM J. Sci. Comput., 37:2(2015), C169-C193. [15] T.A. Davis and Y. Hu. The University of Florida sparse matrix collection. ACM T. Math. Software (TOMS), 38:1(2011), 1. [16] H.C. Elman. A stability analysis of incomplete LU factorizations. Math. Comp., 1986, 191-217. [17] L. Ghezzi, L.F. Pavarino, and E. Zampieri. Overlapping schwarz preconditioned eigensolvers for spectral element discretizations. Appl. Math. Comput., 218:15(2012), 7700-7710. [18] J.R. Gilbert, C. Moler, and R. Schreiber. Sparse matrices in matlab: Design and implementation. SIAM J. Matrix Anal. Appl., 13:1(1992), 333-356. [19] A. Greenbaum. Iterative methods for solving linear systems, volume 17. SIAM, 1997. [20] I. Gustafsson. A class of first order factorization methods. BIT, 18:2(1978), 142-156. [21] P. Hénon and Y. Saad. A parallel multistage ILU factorization based on a hierarchical graph decomposition. SIAM J. Sci. Comput., 28:6(2006), 2266-2293. [22] D. Hysom and A. Pothen. A scalable parallel algorithm for incomplete factor preconditioning. SIAM J. Sci. Comput., 22:6(2001), 2194-2215. [23] D. Hysom and A. Pothen. Level-based incomplete LU factorization: Graph model and algorithms. Preprint UCRL-JC-150789, US Department of Energy, Nov, 2002. [24] D. S. Kershaw. The incomplete Cholesky conjugate gradient method for the iterative solution of systems of linear equations. J. Comput. Phys., 26:1(1978), 43-65. [25] A.V. Knyazev. Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput., 23:2(2001), 517-541. [26] X.S. Li. An overview of SuperLU: algorithms, implementation, and user interface. ACM T. Math. Software (TOMS), 31:3(2005), 302-325. [27] S. MacLachlan, D. Osei-Kuffuor, and Y. Saad. Modification and compensation strategies for threshold-based incomplete factorizations. SIAM J. Sci. Comput., 34:1(2012), A48-A75. [28] M. Magolu monga Made and H.A. van der Vorst. A generalized domain decomposition paradigm for parallel incomplete LU factorization preconditionings. Future Gener. Comp. Sy., 17:8(2001), 925-932. [29] M. McCourt, B. Smith, and H. Zhang. Sparse matrix-matrix products executed through coloring. SIAM J. Matrix Anal. Appl., 36:1(2015), 90-109. [30] Y. Notay. Conditioning analysis of modified block incomplete factorizations. Linear Algebra Appl., 154(1991), 711-722. [31] Y. Saad. ILUT: A dual threshold incomplete LU factorization. Numer. Linear Algebra Appl., 1:4(1994), 387-402. [32] Y. Saad. Iterative Methods for Sparse Linear Systems, volume 82. SIAM, 2003. [33] J. Scott and M. Tuma. Improving the stability and robustness of incomplete symmetric indefinite factorization preconditioners. Numer. Linear Algebra Appl., 24:5(2017), e2099. [34] E. Vecharynski and A.V. Knyazev. Preconditioned locally harmonic residual method for computing interior eigenpairs of certain classes of hermitian matrices. SIAM J. Sci. Comput., 37:5(2015), S3-S29. [35] A.J. Wathen. Preconditioning. Acta Numer., 24(2015), 329-376. |
[1] | Qilong Zhai, Xiaozhe Hu, Ran Zhang. THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS [J]. Journal of Computational Mathematics, 2020, 38(4): 606-623. |
[2] | Hai Bi, Yidu Yang, Yuanyuan Yu, Jiayu Han. NEW ERROR ESTIMATES FOR LINEAR TRIANGLE FINITE ELEMENTS IN THE STEKLOV EIGENVALUE PROBLEM [J]. Journal of Computational Mathematics, 2018, 36(5): 682-692. |
[3] | Yunfeng Cai, Zhaojun Bai, John E. Pask, N. Sukumar. CONVERGENCE ANALYSIS OF A LOCALLY ACCELERATED PRECONDITIONED STEEPEST DESCENT METHOD FOR HERMITIAN-DEFINITE GENERALIZED EIGENVALUE PROBLEMS [J]. Journal of Computational Mathematics, 2018, 36(5): 739-760. |
[4] | Yingxia Xi, Xia Ji. RECURSIVE INTEGRAL METHOD FOR THE NONLINEAR NON-SELFADJOINT TRANSMISSION EIGENVALUE PROBLEM [J]. Journal of Computational Mathematics, 2017, 35(6): 828-838. |
[5] | Davide Forti, Alfio Quarteroni, Simone Deparis. A PARALLEL ALGORITHM FOR THE SOLUTION OF LARGE-SCALE NONCONFORMING FLUID-STRUCTURE INTERACTION PROBLEMS IN HEMODYNAMICS [J]. Journal of Computational Mathematics, 2017, 35(3): 363-380. |
[6] | Xiaole Han, Hehu Xie, Fei Xu. A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM [J]. Journal of Computational Mathematics, 2017, 35(1): 74-90. |
[7] | K.C. Chang, Sihong Shao, Dong Zhang. THE 1-LAPLACIAN CHEEGER CUT: THEORY AND ALGORITHMS [J]. Journal of Computational Mathematics, 2015, 33(5): 443-467. |
[8] | Youai Li. CONVERGENCE ANALYSIS FOR THE ITERATED DEFECT CORRECTION SCHEME OF FINITE ELEMENT METHODS ON RECTANGLE GRIDS [J]. Journal of Computational Mathematics, 2015, 33(3): 297-306. |
[9] | John C. Urschel, Jinchao Xu, Xiaozhe Hu, Ludmil T. Zikatanov. A CASCADIC MULTIGRID ALGORITHM FOR COMPUTING THE FIEDLER VECTOR OF GRAPH LAPLACIANS [J]. Journal of Computational Mathematics, 2015, 33(2): 209-226. |
[10] | Darko Volkov. A NUMERICAL BOUNDARY EIGENVALUE PROBLEM FOR ELASTIC CRACKS IN FREE AND HALF SPACE [J]. Journal of Computational Mathematics, 2011, 29(5): 543-573. |
[11] | Hua Dai, Zhong-Zhi Bai. ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS [J]. Journal of Computational Mathematics, 2010, 28(6): 745-766. |
[12] | Xin Huang, Zhaojun Bai, Yangfeng Su . NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM [J]. Journal of Computational Mathematics, 2010, 28(2): 218-234. |
[13] | Zhongzhi Bai, Yonghua Gao . MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIXEQUATION [J]. Journal of Computational Mathematics, 2007, 25(5): 498-511. |
[14] | Haixia Liang, Erxiong Jiang . AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES [J]. Journal of Computational Mathematics, 2007, 25(5): 620-630. |
[15] | Jianhua Yuan. AN ADAPTIVE INVERSE ITERATION FEM FOR THE INHOMOGENEOUS DIELECTRIC WAVEGUIDES [J]. Journal of Computational Mathematics, 2007, 25(2): 169-184. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||