Aggregation based on graph matching and inexact coarse grid solve for algebraic two grid

References

• Y. Achdou and F. Nataf, Low frequency tangential filtering decomposition, Numer. Linear Algebra Appl. 14 (2006), pp. 129–147. doi: 10.1002/nla.512
   Web of Science ®Google Scholar
• J.I. Aliaga, M. Bollhofer, A. Martin, and E. Quintana-Orti, ILUPACK, in Invited Book Chapter in Springer Encyclopedia of Parallel Computing, D. Padua, ed., Springer, New York, 2012, pp. 917–926.
   Google Scholar
• R. Barret, M. 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, 2nd ed., SIAM, Philadelphia, PA, 1994.
   Google Scholar
• M. Benzi and A. sM. Tuma, A comparative study of sparse approximate inverse preconditioners, Appl. Numer. Math. 30 (1999), pp. 305–340. doi: 10.1016/S0168-9274(98)00118-4
   Web of Science ®Google Scholar
• D. Braess, Towards algebraic multigrid for elliptic problems of second order, Computing 55(4) (1995), pp. 379–393. doi: 10.1007/BF02238488
   Web of Science ®Google Scholar
• J.H. Bramble, J.E. Pasciak, and A.T. Vassilev, Analysis of non-overlapping domain decomposition algorithms with inexact solves, Math. Comp. 67 (1998), pp. 1–19. doi: 10.1090/S0025-5718-98-00879-5
   Web of Science ®Google Scholar
• M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, Adaptive smoothed aggregation (αSA) multigrid, SIAM Rev. 47(2), pp. 317–346. doi: 10.1137/050626272
   Web of Science ®Google Scholar
• T.A. Davis and Y. Hu, The university of Florida sparse matrix collection, ACM Trans. Math. Softw. 38(1) (2011), pp. 1–25.
   Web of Science ®Google Scholar
• V.E. Henson and U.M. Yang, Boomer AMG: A parallel algebraic multigrid solver and preconditioner, Appl. Num. Math. 41(1) (2002), pp. 155–177. doi: 10.1016/S0168-9274(01)00115-5
   Web of Science ®Google Scholar
• N.J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, Philadelphia, 2002.
   Google Scholar
• G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM, Philadelphia, J. Sci. Comp. 20(1) (1999), pp. 359–392. doi: 10.1137/S1064827595287997
   Web of Science ®Google Scholar
• H. Kim, J. Xu, and L. Zikatanov, A multigrid method based on graph matching for convection–diffusion equations, Numer. Linear Algebra Appl. 10 (2003), pp. 181–195. doi: 10.1002/nla.317
   Web of Science ®Google Scholar
• P. Kumar, L. Grigori, F. Nataf, and Q. Niu, Combinative preconditioning based on relaxed nested factorization and tangential filtering preconditioner, INRIA HAL Report RR-6955, 2009.
   Google Scholar
• Z. Li, Y. Saad, and M. Sosonkina, pARMS: A parallel version of the algebraic recursive multilevel solver, Num. Linear Algebra Appl. 10 (2003), pp. 485–509. doi: 10.1002/nla.325
   Web of Science ®Google Scholar
• J.A. Meijerink and H.A. van der Vorst, An iterative solution method for linear system of which the coefficient matrix is a symmetric M-matrix, Math. Comp. 31 (1977), pp. 148–162.
   Web of Science ®Google Scholar
• Y. Notay, Convergence analysis of perturbed two-grid and multigrid methods, SIAM J. Matrix Anal. Appl. 45 (2007), pp. 1035–1044.
   Web of Science ®Google Scholar
• Y. Notay, An aggregation based algebraic multigrid method, Electron. Trans. Numer. Anal. 37 (2010), pp. 123–146.
   Web of Science ®Google Scholar
• Y. Notay, AGMG: Agregation based AMG. Available at http://homepages.ulb.ac.be/ynotay.
   Google Scholar
• C.R. Rao and M.B. Rao, Matrix Algebra and its Applications to Statistics and Econometrics, World Scientific Publishing, Singapore, 2004.
   Google Scholar
• M. Rasquin, H. Deconinck, and G. Degrez, FLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solver, Int. J. Numer. Meth. Eng. 82 (2010), pp. 1510–1536.
   Web of Science ®Google Scholar
• J.W. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, Frontiers of Applied Mathematics, Vol. 3, S.F. McCormick, ed., SIAM, Philadelphia, PA, 1987, pp. 73–130.
   Google Scholar
• Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, MA, 1996.
   Google Scholar
• Y. Saad, Matlab Suite. Available at http://www-users.cs.umn.edu/saad/software.
   Google Scholar
• Y. Saad and B. Suchomel, ARMS: An algebraic recursive multilevel solver for general sparse linear systems, NLAA 9 (2002), pp. 359–378.
   Web of Science ®Google Scholar
• K. Stüben, A review of algebraic multigrid, J. Comput. Appl. Math. 128(1–2) (2001), pp. 281–309; Numer. Anal. VII (2000), Partial differential equations. doi: 10.1016/S0377-0427(00)00516-1
   Web of Science ®Google Scholar
• U. Trottenberg, C.W. Oosterlee, and A. Schüller, Multigrid, Academic Press Inc., San Diego, CA, 2001, with contributions by Brandt A, Oswald P, and Stüben K.
   Google Scholar
• C. Wagner, Tangential frequency filtering decompositions for symmetric matrices, Numer. Math. 78 (1997), pp. 119–142. doi: 10.1007/s002110050307
   Web of Science ®Google Scholar
• C. Wagner, Tangential frequency filtering decompositions for unsymmetric matrices, Numer. Math. 78 (1997), pp. 143–163. doi: 10.1007/s002110050308
   Web of Science ®Google Scholar
• C. Wagner and G. Wattum, Adaptive filtering, Numer. Math. 78 (1997), pp. 305–382. doi: 10.1007/s002110050314
   Web of Science ®Google Scholar
• R. Wienands and W. Joppich, Practical Fourier Analysis for Multigrid Methods, Taylor and Francis Inc., Boca Raton, FL, 2004.
   Google Scholar