과제정보
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01072168).
참고문헌
- D. N. Arnold, R. S. Falk, and R. Winther, Preconditioning discrete approximations of the Reissner-Mindlin plate model, RAIRO Model. Math. Anal. Numer., 31 (1997), no. 4, 517-557. https://doi.org/10.1051/m2an/1997310405171
- D. N. Arnold, R. S. Falk, and R. Winther, Preconditioning in H(div) and applications, Math. Comp., 66 (1997), no. 219, 957-984. https://doi.org/10.1090/S0025-5718-97-00826-0
- D. N. Arnold, R. S. Falk, and R. Winther, Multigrid preconditioning in H(div) on non-convex polygons, Comput. Appl. Math., 17 (1998), no. 3, 303-315.
- D. N. Arnold, R. S. Falk, and R. Winther, Multigrid in H(div) and H(curl), Numer. Math., 85 (2000), no. 2, 197-217. https://doi.org/10.1007/PL00005386
- S. C. Brenner and D.-S. Oh, Multigrid methods for H(div) in three dimensions with nonoverlapping domain decomposition smoothers, Numer. Linear Algebra Appl., 25 (2018), no. 5, e2191, 14.
- S. C. Brenner and D.-S. Oh, A smoother based on nonoverlapping domain decomposition methods for H(div) problems: a numerical study, in Domain decomposition methods in science and engineering XXIV, Springer, Cham, 2018, 523-531.
- F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991.
- Z. Cai, R. D. Lazarov, T. A. Manteuffel, and S. F. McCormick, First-order system least squares for second-order partial differential equations: Part I, SIAM J. Numer. Anal., 31 (1994), no. 6, 1785-1799. https://doi.org/10.1137/0731091
- Z. Cai, C. Tong, P. S. Vassilevski, and C. Wang, Mixed finite element methods for incompressible flow: stationary Stokes equations, Numer. Methods Partial Differential Equations, 26 (2010), no. 4, 957-978. https://doi.org/10.1002/num.20467
- C. R. Dohrmann, K. H. Pierson, and O. B. Widlund, Vertex-based preconditioners for the coarse problems of BDDC, SIAM J. Sci. Comput., 41 (2019), no. 5, A3021-A3044. https://doi.org/10.1137/19m1237557
- C. R. Dohrmann and O. B. Widlund, An overlapping Schwarz algorithm for almost incompressible elasticity, SIAM J. Numer. Anal., 47 (2009), no. 4, 2897-2923. https://doi.org/10.1137/080724320
- C. R. Dohrmann and O. B. Widlund, On the design of small coarse spaces for domain decomposition algorithms, SIAM J. Sci. Comput., 39 (2017), no. 4, A1466-A1488. https://doi.org/10.1137/17M1114272
- A. Heinlein, C. Hochmuth, and A. Klawonn, Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems, Internat. J. Numer. Methods Engrg., 121 (2020), no. 6, 1101-1119. https://doi.org/10.1002/nme.6258
- R. Hiptmair, Multigrid method for H(div) in three dimensions, Electron. Trans. Numer. Anal., 6 (1997), no. Dec., 133-152.
- R. Hiptmair and A. Toselli, Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions, in Parallel solution of partial differential equations, Springer, New York, 2000, 181-208.
- R. Hiptmair and J. Xu, Nodal auxiliary space preconditioning in H(curl) and H(div) spaces, SIAM J. Numer. Anal., 45 (2007), no. 6, 2483-2509. https://doi.org/10.1137/060660588
- T. V. Kolev and P. S. Vassilevski, Parallel auxiliary space AMG solver for H(div) problems, SIAM J. Sci. Comput., 34 (2012), no. 6, A3079-A3098. https://doi.org/10.1137/110859361
- J. H. Lee, Overlapping domain decomposition methods for numerically thin Reissner-Mindlin plates approximated with the Falk-Tu elements, SIAM J. Numer. Anal., 51 (2013), no. 1, 24-46. https://doi.org/10.1137/110837516
- P. Lin, A sequential regularization method for time-dependent incompressible Navier-Stokes equations, SIAM J. Numer. Anal., 34 (1997), no. 3, 1051-1071. https://doi.org/10.1137/S0036142994270521
- D.-S. Oh, An alternative coarse space method for overlapping Schwarz preconditioners for Raviart-Thomas vector fields, in Domain decomposition methods in science and engineering XX, Heidelberg, 2013, 361-367.
- D.-S. Oh, An overlapping Schwarz algorithm for Raviart-Thomas vector fields with discontinuous coefficients, SIAM J. Numer. Anal., 51 (2013), no. 1, 297-321. https://doi.org/10.1137/110838868
- D.-S. Oh, A BDDC preconditioner for problems posed in H(div) with deluxe scaling, in Domain decomposition methods in science and engineering XXII, Springer, Cham, 2016, 355-361.
- D.-S. Oh, O. B. Widlund, S. Zampini, and C. R. Dohrmann, BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields, Math. Comp., 87 (2018), no. 310, 659-692. https://doi.org/10.1090/mcom/3254
- A. Toselli and O. Widlund, Domain decomposition methods-algorithms and theory, Springer-Verlag, Berlin, 2005.
- P. S. Vassilevski and U. Villa, A block-diagonal algebraic multigrid preconditioner for the Brinkman problem, SIAM J. Sci. Comput., 35 (2013), no. 5, S3-S17. https://doi.org/10.1137/120882846
- B. I. Wohlmuth, A. Toselli, and O. B. Widlund, An iterative substructuring method for Raviart-Thomas vector fields in three dimensions, SIAM J. Numer. Anal., 37 (2000), no. 5, 1657-1676. https://doi.org/10.1137/S0036142998347310