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Volumn 45, Issue 1-3, 2010, Pages 514-536

Fast sweeping fifth order WENO scheme for static Hamilton-Jacobi equations with accurate boundary treatment

Author keywords

Boundary condition; Fast sweeping method; WENO scheme

Indexed keywords

BOUNDARY TREATMENT; CARTESIAN MESH; CPU TIME; DOMAIN BOUNDARY; ESSENTIALLY NON-OSCILLATORY; FAST SWEEPING METHOD; INFLOW BOUNDARY CONDITIONS; STATIC HAMILTON-JACOBI EQUATION; THIRD ORDER; WENO SCHEMES;

EID: 77956182473     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-010-9345-6     Document Type: Article
Times cited : (66)

References (20)
  • 1
    • 0030521036 scopus 로고    scopus 로고
    • Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes
    • 0870.65116 10.1002/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.0. CO;2-B 1414589
    • R. Abgrall 1996 Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes Commun. Pure Appl. Math. 49 1339 1373 0870.65116 10.1002/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.0. CO;2-B 1414589
    • (1996) Commun. Pure Appl. Math. , vol.49 , pp. 1339-1373
    • Abgrall, R.1
  • 3
    • 0001678817 scopus 로고    scopus 로고
    • Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control
    • 10.1137/S0036142997323521 1681057
    • M. Boué P. Dupuis 1999 Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control SIAM J. Numer. Anal. 36 667 695 10.1137/S0036142997323521 1681057
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 667-695
    • Boué, M.1    Dupuis, P.2
  • 4
    • 33947097945 scopus 로고    scopus 로고
    • A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
    • 1124.65090 10.1016/j.jcp.2006.09.012 2314396
    • Y. Cheng C.-W. Shu 2007 A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations J. Comput. Phys. 223 398 415 1124.65090 10.1016/j.jcp.2006.09.012 2314396
    • (2007) J. Comput. Phys. , vol.223 , pp. 398-415
    • Cheng, Y.1    Shu, C.-W.2
  • 5
    • 84966217981 scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • 744921
    • M. Crandall P.L. Lions 1984 Monotone difference approximations for scalar conservation laws Math. Comput. 34 1 19 744921
    • (1984) Math. Comput. , vol.34 , pp. 1-19
    • Crandall, M.1    Lions, P.L.2
  • 6
    • 0033296133 scopus 로고    scopus 로고
    • A discontinuous Galerkin finite element method for Hamilton-Jacobi equations
    • 0946.65090 10.1137/S1064827598337282 1718679
    • C. Hu C.-W. Shu 1999 A discontinuous Galerkin finite element method for Hamilton-Jacobi equations SIAM J. Sci. Comput. 21 666 690 0946.65090 10.1137/S1064827598337282 1718679
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 666-690
    • Hu, C.1    Shu, C.-W.2
  • 7
    • 45949093127 scopus 로고    scopus 로고
    • Numerical boundary conditions for the fast sweeping high order WENO methods for solving the Eikonal equation
    • 1174.76330 10.1016/j.cam.2007.06.009 2421885
    • L. Huang C.-W. Shu M. Zhang 2008 Numerical boundary conditions for the fast sweeping high order WENO methods for solving the Eikonal equation J. Comput. Math. 26 1 11 1174.76330 10.1016/j.cam.2007.06.009 2421885
    • (2008) J. Comput. Math. , vol.26 , pp. 1-11
    • Huang, L.1    Shu, C.-W.2    Zhang, M.3
  • 8
    • 55049132227 scopus 로고    scopus 로고
    • Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
    • 10.1016/j.trb.2008.06.003
    • L. Huang S.C. Wong M. Zhang C.-W. Shu W.H.K. Lam 2009 Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm Transp. Res. Part B, Methodol. 43 127 141 10.1016/j.trb.2008.06.003
    • (2009) Transp. Res. Part B, Methodol. , vol.43 , pp. 127-141
    • Huang, L.1    Wong, S.C.2    Zhang, M.3    Shu, C.-W.4    Lam, W.H.K.5
  • 9
    • 0034503787 scopus 로고    scopus 로고
    • Weighted ENO schemes for Hamilton-Jacobi equations
    • 0957.35014 10.1137/S106482759732455X 1762034
    • G. Jiang D.P. Peng 2000 Weighted ENO schemes for Hamilton-Jacobi equations SIAM J. Sci. Comput. 21 2126 2143 0957.35014 10.1137/S106482759732455X 1762034
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 2126-2143
    • Jiang, G.1    Peng, D.P.2
  • 10
    • 47049115993 scopus 로고    scopus 로고
    • A second order discontinuous Galerkin fast sweeping method for Eikonal equations
    • 1151.65092 10.1016/j.jcp.2008.05.018 2442450
    • F. Li C.-W. Shu Y.-T. Zhang H. Zhao 2008 A second order discontinuous Galerkin fast sweeping method for Eikonal equations J. Comput. Phys. 227 8191 8208 1151.65092 10.1016/j.jcp.2008.05.018 2442450
    • (2008) J. Comput. Phys. , vol.227 , pp. 8191-8208
    • Li, F.1    Shu, C.-W.2    Zhang, Y.-T.3    Zhao, H.4
  • 11
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • 0659.65132 10.1016/0021-9991(88)90002-2 965860
    • S. Osher J. Sethian 1988 Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys. 79 12 49 0659.65132 10.1016/0021-9991(88)90002-2 965860
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 12
    • 0026204106 scopus 로고
    • High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations
    • 0736.65066 10.1137/0728049 1111446
    • S. Osher C.-W. Shu 1991 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations SIAM J. Numer. Anal. 28 907 922 0736.65066 10.1137/0728049 1111446
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.-W.2
  • 13
    • 0026880997 scopus 로고
    • A viscosity solutions approach to shape-from-shading
    • 0754.65069 10.1137/0729053 1163361
    • E. Rouy A. Tourin 1992 A viscosity solutions approach to shape-from-shading SIAM J. Numer. Anal. 29 867 884 0754.65069 10.1137/0729053 1163361
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 867-884
    • Rouy, E.1    Tourin, A.2
  • 16
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • 0653.65072 10.1016/0021-9991(88)90177-5 954915
    • C.-W. Shu S. Osher 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes J. Comput. Phys. 77 439 471 0653.65072 10.1016/0021-9991(88)90177-5 954915
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 17
    • 57849162805 scopus 로고    scopus 로고
    • An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model
    • 10.1002/nme.2329 2458530
    • Y. Xia S.C. Wong M. Zhang C.-W. Shu W.H.K. Lam 2008 An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model Int. J. Numer. Methods Eng. 76 337 350 10.1002/nme.2329 2458530
    • (2008) Int. J. Numer. Methods Eng. , vol.76 , pp. 337-350
    • Xia, Y.1    Wong, S.C.2    Zhang, M.3    Shu, C.-W.4    Lam, W.H.K.5
  • 18
    • 0038070190 scopus 로고    scopus 로고
    • High order WENO schemes for Hamilton-Jacobi equations on triangular meshes
    • 1034.65051 10.1137/S1064827501396798 1950522
    • Y.-T. Zhang C.-W. Shu 2003 High order WENO schemes for Hamilton-Jacobi equations on triangular meshes SIAM J. Sci. Comput. 24 1005 1030 1034.65051 10.1137/S1064827501396798 1950522
    • (2003) SIAM J. Sci. Comput. , vol.24 , pp. 1005-1030
    • Zhang, Y.-T.1    Shu, C.-W.2
  • 19
    • 33750302668 scopus 로고    scopus 로고
    • High order fast sweeping methods for static Hamilton-Jacobi equations
    • 10.1007/s10915-005-9014-3 2266807
    • Y.-T. Zhang H.-K. Zhao J. Qian 2006 High order fast sweeping methods for static Hamilton-Jacobi equations J. Sci. Comput. 29 25 56 10.1007/s10915-005- 9014-3 2266807
    • (2006) J. Sci. Comput. , vol.29 , pp. 25-56
    • Zhang, Y.-T.1    Zhao, H.-K.2    Qian, J.3
  • 20
    • 14944383149 scopus 로고    scopus 로고
    • A fast sweeping method for Eikonal equations
    • 1070.65113
    • H.-K. Zhao 2005 A fast sweeping method for Eikonal equations Math. Comput. 74 603 627 1070.65113
    • (2005) Math. Comput. , vol.74 , pp. 603-627
    • Zhao, H.-K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.