Generalized Monge-Kantorovich optimization for grid generation and adaptation in Lp

SIAM Journal on Scientific Computing

Volumn 32, Issue 6, 2010, Pages 3524-3547

  Delzanno, G L ^a   Finn, J M ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Adaptive grid generation; Equidistribution; Monge Amp ; Monge Kantorovich optimization; Moving meshes; Multigrid preconditioning; Newton Krylov; Re equation

Indexed keywords

MESH GENERATION;

ADAPTIVE GRID GENERATION; EQUIDISTRIBUTION; GRID GENERATION; MONGE-AMPÉ; MONGE-KANTOROVICH OPTIMIZATION; MOVING MESH; MULTIGRID PRECONDITIONING; NEWTON-KRYLOV; OPTIMISATIONS; RE EQUATION;

VARIATIONAL TECHNIQUES;

EID: 79251515006     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090749785     Document Type: Article

References (21)

1. G. L. Delzanno, L. Chacón, J. M. Finn, Y. Chung, and G. Lapenta, An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization, J. Comput. Phys., 227 (2008), pp. 9841-9864.
2. J. M. Finn, G. L. Delzanno, and L. Chacón, Grid generation and adaptation by Monge-Kantorovich optimization in two and three dimensions, in Proceedings of the 17th International Meshing Roundtable, Pittsburgh, PA, 2008, p. 551.
3. C. J. Budd and J. F. Williams, Parabolic Monge-Ampére methods for blow-up problems in several spatial dimensions, J. Phys. A, 39 (2006), p. 5425.
4. L. Chacón, G. L. Delzanno, and J. M. Finn, Robust, multidimensional mesh motion based on Monge-Kantorovich equidistribution, J. Comput. Phys., 230 (2011), pp. 87-103.
5. G. Lapenta, Variational grid adaptation based on the minimization of local truncation error: Time independent problems, J. Comput. Phys., 193 (2004), p. 159.
6. L. Caffarelli, L. Nirenberg, and J. Spruck, The Dirichlet problem for nonlinear 2ndorder elliptic equations I. Monge-Ampére equation, Comm. Pure Appl. Math., 37 (1984),pp. 369-402.
7. D. A. Knoll and W. J. Rider, Multigrid preconditioned Newton-Krylov method, SIAMJ. Sci. Comput., 21 (1999), pp. 691-710.
8. L. Chacón, D. C. Barnes, D. A. Knoll, and G. H. Miley, An implicit energy-conservative 2D Fokker-Planck algorithm. II. Jacobian-free Newton-Krylov solver, J. Comput. Phys., 157 (2000), pp. 654-682.
9. G. Monge, Mèmoire sur la thèorie des dèblais at des remblais, Histoire de l'Acadèmie Royale des Sciences de Paris, (1781), pp. 666-704.
10. L. C. Evans, Partial differential equations and Monge-Kantorovich mass transfer, in Current Developments in Mathematics, R. Bott, A. Jaffe, D. Jerison, G. Lusztig, I. Singer, and S. T. Yau, eds., International Press Incorporated Boston, Cambridge, MA, 1997.
11. L. C. Evans and W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc., 137 (1999), p. 1.
12. S. Angenent, S. Haker, and A. Tannenbaum, Minimizing flows for the Monge-Kantorovich problem, SIAM J. Math. Anal., 35 (2003), pp. 61-97.
13. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, Optimal mass transport for registration and warping, Internat. J. Comput. Vision, 60 (2004), pp. 225-240.
14. L. Zhu, Y. Yang, S. Haker, and A. Tannenbaum, An image morphing technique based on optimal mass preserving mapping, IEEE Trans. Image Process., 16 (2007), pp. 1481-1495. (Pubitemid 46804334)
15. L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, 1999.
16. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, 1995.
17. J. U. Brackbill and H. M. Ruppel, FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions, J. Comput. Phys., 65 (1986), pp. 314-343.
18. J. U. Brackbill, FLIP MHD: A particle-in-cell method for magnetohydrodynamics, J. Comput. Phys., 96 (1991), pp. 163-192.
19. D. Sulsky and J. U. Brackbill, A numerical method for suspension flow, J. Comput. Phys., 96 (1991), pp. 339-368.
20. G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal., 44 (1992), pp. 285-297.
21. G. L. Delzanno and J. M. Finn, The fluid dynamic approach to equidistribution methods for grid adaptation, Comput. Phys., to appear.