메뉴 건너뛰기




Volumn 230, Issue 9, 2011, Pages 3302-3330

Optimal mass transport for higher dimensional adaptive grid generation

Author keywords

Adaptive grid generation; L2 Monge Kantorovich problem; Parabolic Monge Amp re equation

Indexed keywords

MESH GENERATION; NUMERICAL METHODS;

EID: 79952444448     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.01.025     Document Type: Article
Times cited : (52)

References (28)
  • 1
    • 0000105971 scopus 로고
    • Moving mesh methods based on moving mesh partial differential equations
    • Huang W., Ren Y., Russell R.D. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys. 1994, 113(2):279-290.
    • (1994) J. Comput. Phys. , vol.113 , Issue.2 , pp. 279-290
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 2
    • 0028446372 scopus 로고
    • Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
    • Huang W., Ren Y., Russell R.D. Moving mesh partial differential equations (MMPDES) based on the equidistribution principle. SIAM J. Numer. Anal. 1994, 31(3):709-730.
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.3 , pp. 709-730
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 3
    • 0000448909 scopus 로고    scopus 로고
    • Analysis of moving mesh partial differential equations with spatial smoothing
    • Huang W., Russell R.D. Analysis of moving mesh partial differential equations with spatial smoothing. SIAM J. Numer. Anal. 1997, 34(3):1106-1126.
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.3 , pp. 1106-1126
    • Huang, W.1    Russell, R.D.2
  • 4
    • 0000458449 scopus 로고    scopus 로고
    • Moving mesh methods for problems with blow-up
    • Budd C.J., Huang W., Russell R.D. Moving mesh methods for problems with blow-up. SIAM J. Sci. Comput. 1996, 17(2):305-327.
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.2 , pp. 305-327
    • Budd, C.J.1    Huang, W.2    Russell, R.D.3
  • 5
    • 0030081518 scopus 로고    scopus 로고
    • A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math. workshop on the method of lines for time-dependent problems (Lexington, KY, 1995).
    • W. Huang, R.D. Russell, A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math. 20 (1-2) (1996) 101-116, workshop on the method of lines for time-dependent problems (Lexington, KY, 1995).
    • (1996) , vol.20 , Issue.1-2 , pp. 101-116
    • Huang, W.1    Russell, R.D.2
  • 6
    • 0032226429 scopus 로고    scopus 로고
    • Moving mesh strategy based on a gradient flow equation for two-dimensional problems
    • (electronic)
    • Huang W., Russell R.D. Moving mesh strategy based on a gradient flow equation for two-dimensional problems. SIAM J. Sci. Comput. 1999, 20(3):998-1015. (electronic).
    • (1999) SIAM J. Sci. Comput. , vol.20 , Issue.3 , pp. 998-1015
    • Huang, W.1    Russell, R.D.2
  • 7
    • 0035922234 scopus 로고    scopus 로고
    • An efficient dynamically adaptive mesh for potentially singular solutions
    • Ceniceros H.D., Hou T.Y. An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys. 2001, 172:609-639.
    • (2001) J. Comput. Phys. , vol.172 , pp. 609-639
    • Ceniceros, H.D.1    Hou, T.Y.2
  • 8
    • 0037252816 scopus 로고    scopus 로고
    • A moving mesh method based on the geometric conservation law
    • (electronic)
    • Cao W., Huang W., Russell R.D. A moving mesh method based on the geometric conservation law. SIAM J. Sci. Comput. 2002, 24(1):118-142. (electronic).
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.1 , pp. 118-142
    • Cao, W.1    Huang, W.2    Russell, R.D.3
  • 9
    • 33646255211 scopus 로고    scopus 로고
    • Parabolic Monge-Ampère methods for blow-up problems in several spatial dimensions
    • Budd C.J., Williams J.F. Parabolic Monge-Ampère methods for blow-up problems in several spatial dimensions. J. Phys. A 2006, 39(19):5425-5444.
    • (2006) J. Phys. A , vol.39 , Issue.19 , pp. 5425-5444
    • Budd, C.J.1    Williams, J.F.2
  • 10
    • 75749125433 scopus 로고    scopus 로고
    • Moving mesh generation using the parabolic Monge-Ampère equation
    • Budd C.J., Williams J.F. Moving mesh generation using the parabolic Monge-Ampère equation. SIAM J. Sci. Comput. 2009, 31(5):3438-3465.
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.5 , pp. 3438-3465
    • Budd, C.J.1    Williams, J.F.2
  • 11
    • 53349146583 scopus 로고    scopus 로고
    • An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization
    • Delzanno G.L., Chacón L., Finn J.M., Chung Y., Lapenta G. An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization. J. Comput. Phys. 2008, 227(23):9841-9864.
    • (2008) J. Comput. Phys. , vol.227 , Issue.23 , pp. 9841-9864
    • Delzanno, G.L.1    Chacón, L.2    Finn, J.M.3    Chung, Y.4    Lapenta, G.5
  • 12
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J.-D., Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 2000, 84(3):375-393.
    • (2000) Numer. Math. , vol.84 , Issue.3 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 13
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 1991, 44(4):375-417.
    • (1991) Commun. Pure Appl. Math. , vol.44 , Issue.4 , pp. 375-417
    • Brenier, Y.1
  • 14
    • 0021421774 scopus 로고
    • On the optimal mapping of distributions
    • Knott M., Smith C.S. On the optimal mapping of distributions. J. Optim. Theory Appl. 1984, 43(1):39-49.
    • (1984) J. Optim. Theory Appl. , vol.43 , Issue.1 , pp. 39-49
    • Knott, M.1    Smith, C.S.2
  • 15
    • 0018529022 scopus 로고
    • Geometric conservation law and its application to flow computations on moving grids
    • Thomas P.D., Lombard C.K. Geometric conservation law and its application to flow computations on moving grids. AIAA J. 1979, 17(10):1030-1037.
    • (1979) AIAA J. , vol.17 , Issue.10 , pp. 1030-1037
    • Thomas, P.D.1    Lombard, C.K.2
  • 16
    • 85190225870 scopus 로고    scopus 로고
    • F.M. Beg, Volumetric image registration methods based on solving the Monge-Ampère equation, in: The Canadian Applied Mathematics Quarterly Special Edition to Celebrate the 30th Anniversary of the Canadian Applied and Industrial Mathematics Society, in press
    • M.H. Sulman, J. Williams, R.D. Russell, F.M. Beg, Volumetric image registration methods based on solving the Monge-Ampère equation, in: The Canadian Applied Mathematics Quarterly Special Edition to Celebrate the 30th Anniversary of the Canadian Applied and Industrial Mathematics Society, in press, 17 (4).
    • , vol.17 , Issue.4
    • Sulman, M.H.1    Williams, J.2    Russell, R.D.3
  • 17
    • 78650885435 scopus 로고    scopus 로고
    • An efficient approach for the numerical solution of the Monge-Ampere equation
    • Sulman M.H., Williams J., Russell R. An efficient approach for the numerical solution of the Monge-Ampere equation. Appl. Numer. Math. 2011, 61(3):298-307.
    • (2011) Appl. Numer. Math. , vol.61 , Issue.3 , pp. 298-307
    • Sulman, M.H.1    Williams, J.2    Russell, R.3
  • 18
    • 0346724414 scopus 로고    scopus 로고
    • Neumann and second boundary value problems for Hessian and Gauss curvature flows
    • Schnürer O.C., Smoczyk K. Neumann and second boundary value problems for Hessian and Gauss curvature flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 2003, 20(6):1043-1073.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.6 , pp. 1043-1073
    • Schnürer, O.C.1    Smoczyk, K.2
  • 19
    • 1342309948 scopus 로고    scopus 로고
    • Translating solutions for Gauss curvature flows with Neumann boundary conditions
    • Schnürer O.C., Schwetlick H.R. Translating solutions for Gauss curvature flows with Neumann boundary conditions. Pacific J. Math. 2004, 213(1):89-109.
    • (2004) Pacific J. Math. , vol.213 , Issue.1 , pp. 89-109
    • Schnürer, O.C.1    Schwetlick, H.R.2
  • 20
    • 0035995727 scopus 로고    scopus 로고
    • Translating solutions to the second boundary value problem for curvature flows
    • Schnürer O.C. Translating solutions to the second boundary value problem for curvature flows. Manuscripta Math. 2002, 108(3):319-347.
    • (2002) Manuscripta Math. , vol.108 , Issue.3 , pp. 319-347
    • Schnürer, O.C.1
  • 21
    • 77952426648 scopus 로고    scopus 로고
    • Grid generation and adaptation by Monge-Kantorovich optimization in two and three dimensions
    • Springer, Berlin, Heidelberg, R.V. Garimella (Ed.)
    • Finn J.M., Delzanno G.L., Chacón L. Grid generation and adaptation by Monge-Kantorovich optimization in two and three dimensions. Proceedings of the 17th International Meshing Roundtable 2008, 551-568. Springer, Berlin, Heidelberg. R.V. Garimella (Ed.).
    • (2008) Proceedings of the 17th International Meshing Roundtable , pp. 551-568
    • Finn, J.M.1    Delzanno, G.L.2    Chacón, L.3
  • 22
    • 4544232505 scopus 로고    scopus 로고
    • An adaptive mesh redistribution algorithm for convection-dominated problems
    • Zhang Z.-R., Tang T. An adaptive mesh redistribution algorithm for convection-dominated problems. Commun. Pure Appl. Anal. 2002, 1(3):341-357. http://dx.doi.org/10.3934/cpaa.2002.1.341. 10.3934/cpaa.2002.1.341.
    • (2002) Commun. Pure Appl. Anal. , vol.1 , Issue.3 , pp. 341-357
    • Zhang, Z.-R.1    Tang, T.2
  • 23
    • 85190222461 scopus 로고    scopus 로고
    • Interpreting moving mesh methods and transformation techniques from various applications in terms of the mass transport problem, Master's Thesis, Simon Fraser University, October
    • M.H.M. Sulman, Interpreting moving mesh methods and transformation techniques from various applications in terms of the mass transport problem, Master's Thesis, Simon Fraser University, October 2003.
    • (2003)
    • Sulman, M.H.M.1
  • 24
    • 85190185346 scopus 로고
    • Augmented Lagrangian Methods, of Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D.C. Spicer.
    • M. Fortin, R. Glowinski, Augmented Lagrangian Methods, vol. 15 of Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam, 1983, applications to the numerical solution of boundary value problems, Translated from the French by B. Hunt and D.C. Spicer.
    • (1983) , vol.15
    • Fortin, M.1    Glowinski, R.2
  • 25
    • 0344463965 scopus 로고    scopus 로고
    • On the time-continuous mass transport problem and its approximation by augmented Lagrangian techniques
    • (electronic)
    • Guittet K. On the time-continuous mass transport problem and its approximation by augmented Lagrangian techniques. SIAM J. Numer. Anal. 2003, 41(1):382-399. (electronic).
    • (2003) SIAM J. Numer. Anal. , vol.41 , Issue.1 , pp. 382-399
    • Guittet, K.1
  • 26
    • 25444533561 scopus 로고    scopus 로고
    • Measuring mesh qualities and application to variational mesh adaptation
    • (electronic)
    • Huang W. Measuring mesh qualities and application to variational mesh adaptation. SIAM J. Sci. Comput. 2005, 26(5):1643-1666. (electronic).
    • (2005) SIAM J. Sci. Comput. , vol.26 , Issue.5 , pp. 1643-1666
    • Huang, W.1
  • 27
    • 0000802396 scopus 로고
    • A new approach to grid generation
    • Liao G., Anderson D. A new approach to grid generation. Appl. Anal. 1992, 44(3-4):285-297.
    • (1992) Appl. Anal. , vol.44 , Issue.3-4 , pp. 285-297
    • Liao, G.1    Anderson, D.2
  • 28
    • 77249155146 scopus 로고    scopus 로고
    • An efficient numerical method for solution of L2 optimal mass transfer problem
    • Haber E., Rehman T., Tannenbaum A. An efficient numerical method for solution of L2 optimal mass transfer problem. SIAM J. Sci. Comput. 2010, 32(1):197-211.
    • (2010) SIAM J. Sci. Comput. , vol.32 , Issue.1 , pp. 197-211
    • Haber, E.1    Rehman, T.2    Tannenbaum, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.