메뉴 건너뛰기




Volumn 45, Issue 5, 2007, Pages 1979-2011

Fast semi-Lagrangian schemes for the eikonal equation and applications

Author keywords

Eikonal equation; Fast marching methods; Finite differences; Front propagation; Semi Lagrangian schemes

Indexed keywords

ALGORITHMS; BENCHMARKING; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; GEOMETRICAL OPTICS; INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; OPTIMAL CONTROL SYSTEMS;

EID: 37049000150     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050637625     Document Type: Article
Times cited : (52)

References (39)
  • 1
    • 0034197010 scopus 로고    scopus 로고
    • High order numerical discretization for Hamilton-Jacobi equations on triangular meshes
    • S. AUGOULA AND R. ABGRALL, High order numerical discretization for Hamilton-Jacobi equations on triangular meshes, J. Sci. Comput., 15 (2000), pp. 197-229.
    • (2000) J. Sci. Comput , vol.15 , pp. 197-229
    • AUGOULA, S.1    ABGRALL, R.2
  • 3
    • 0025462851 scopus 로고
    • An approximation scheme for the minimum time function
    • M. BARDI AND M. FALCONE, An approximation scheme for the minimum time function, SIAM J. Control Optim., 28 (1990), pp. 950-965.
    • (1990) SIAM J. Control Optim , vol.28 , pp. 950-965
    • BARDI, M.1    FALCONE, M.2
  • 5
    • 2342496261 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations with measurable dependence on the state variable
    • F. CAMILLI AND A. SICONOLFI, Hamilton-Jacobi equations with measurable dependence on the state variable, Adv. Differential Equations, 8 (2003), pp. 733-768.
    • (2003) Adv. Differential Equations , vol.8 , pp. 733-768
    • CAMILLI, F.1    SICONOLFI, A.2
  • 6
    • 11144350063 scopus 로고    scopus 로고
    • An efficient algorithm for Hamilton-Jacobi equations in high dimension
    • E. CARLINI, M. FALCONE, AND R. FERRETTI, An efficient algorithm for Hamilton-Jacobi equations in high dimension, Comput. Vis. Sci., 7 (2004), pp. 15-29.
    • (2004) Comput. Vis. Sci , vol.7 , pp. 15-29
    • CARLINI, E.1    FALCONE, M.2    FERRETTI, R.3
  • 7
    • 0036210688 scopus 로고    scopus 로고
    • Some improvements of the fast marching method
    • D. L. CHOPP, Some improvements of the fast marching method, SIAM J. Sci. Comput., 23 (2001), pp. 230-244.
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 230-244
    • CHOPP, D.L.1
  • 8
    • 84966245867 scopus 로고
    • Two approximations of solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL AND P.-L. LIONS, Two approximations of solutions of Hamilton-Jacobi equations, Math. Comp., 43 (1984), pp. 1-19.
    • (1984) Math. Comp , vol.43 , pp. 1-19
    • CRANDALL, M.G.1    LIONS, P.-L.2
  • 10
    • 85055834413 scopus 로고    scopus 로고
    • E. CRISTIANI, M. FALCONE, AND A. SEGHINI, Numerical solution of the perspective shape from shading problem, in Proceedings of Control Systems: Theory, Numerics and Applications PoS (CSTNA2005) 008, http://pos.sissa.it/.
    • E. CRISTIANI, M. FALCONE, AND A. SEGHINI, Numerical solution of the perspective shape from shading problem, in Proceedings of Control Systems: Theory, Numerics and Applications PoS (CSTNA2005) 008, http://pos.sissa.it/.
  • 12
    • 0041980268 scopus 로고
    • The minimum time problem and its applications to front propagation
    • A. Visintin and G. Buttazzo, eds, de Gruyter, Berlin
    • M. FALCONE, The minimum time problem and its applications to front propagation, in Motion by Mean Curvature and Related Topics, A. Visintin and G. Buttazzo, eds., de Gruyter, Berlin, 1994, pp. 70-88.
    • (1994) Motion by Mean Curvature and Related Topics , pp. 70-88
    • FALCONE, M.1
  • 13
    • 55549148878 scopus 로고    scopus 로고
    • M. FALCONE, Numerical solution of dynamic programming equations, in Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, M. Bardi and I. Capuzzo Dolcetta, eds., Birkhäuser, Boston, 1997, Appendix A, pp. 471-504.
    • M. FALCONE, Numerical solution of dynamic programming equations, in Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, M. Bardi and I. Capuzzo Dolcetta, eds., Birkhäuser, Boston, 1997, Appendix A, pp. 471-504.
  • 14
    • 33746012700 scopus 로고    scopus 로고
    • Some remarks on the synthesis of feedback controls via numerical methods
    • Equations, J. L. Menaldi, E. Rofman, and A. Sulem, eds, IOS Press, The Netherlands
    • M. FALCONE, Some remarks on the synthesis of feedback controls via numerical methods, in Optimal Control and Partial Differential Equations, J. L. Menaldi, E. Rofman, and A. Sulem, eds., IOS Press, The Netherlands, 2001, pp. 456-465.
    • (2001) Optimal Control and Partial Differential , pp. 456-465
    • FALCONE, M.1
  • 15
    • 21344488058 scopus 로고
    • Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations
    • M. FALCONE AND R. FERRETTI, Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations, Numer. Math., 67 (1994), pp. 315-344.
    • (1994) Numer. Math , vol.67 , pp. 315-344
    • FALCONE, M.1    FERRETTI, R.2
  • 16
    • 0037137981 scopus 로고    scopus 로고
    • Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods
    • M. FALCONE AND R. FERRETTI, Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods, J. Comput. Phys., 175 (2002), pp. 559-575.
    • (2002) J. Comput. Phys , vol.175 , pp. 559-575
    • FALCONE, M.1    FERRETTI, R.2
  • 17
    • 0028518326 scopus 로고
    • Level sets of viscosity solutions: Some applications to fronts and rendez-vous problems
    • M. FALCONE, T. GIORGI, AND P. LORETI, Level sets of viscosity solutions: Some applications to fronts and rendez-vous problems, SIAM J. Appl. Math., 54 (1994), pp. 1335-1354.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 1335-1354
    • FALCONE, M.1    GIORGI, T.2    LORETI, P.3
  • 18
    • 55549136840 scopus 로고    scopus 로고
    • M. FALCONE AND C. TRUINI, A Level-Set Algorithm for Front Propagation in the Presence of Obstacles, Technical Report, Dipartimento di Matematica, Università di Roma La Sapienza, Rome, Italy, 2003.
    • M. FALCONE AND C. TRUINI, A Level-Set Algorithm for Front Propagation in the Presence of Obstacles, Technical Report, Dipartimento di Matematica, Università di Roma "La Sapienza," Rome, Italy, 2003.
  • 20
    • 1942507479 scopus 로고    scopus 로고
    • Lax-Friedrichs sweeping scheme for static Hamilton- Jacobi equations
    • C.-Y. KAO, S. OSHER, AND J. QIAN, Lax-Friedrichs sweeping scheme for static Hamilton- Jacobi equations, J. Comput. Phys., 196 (2004), pp. 367-391.
    • (2004) J. Comput. Phys , vol.196 , pp. 367-391
    • KAO, C.-Y.1    OSHER, S.2    QIAN, J.3
  • 21
    • 29144492874 scopus 로고    scopus 로고
    • Fast sweeping methods for static Hamilton-Jacobi equations
    • C.-Y. KAO, S. OSHER, AND Y.-H. TSAI, Fast sweeping methods for static Hamilton-Jacobi equations, SIAM J. Numer. Anal., 42 (2005), pp. 2612-2632.
    • (2005) SIAM J. Numer. Anal , vol.42 , pp. 2612-2632
    • KAO, C.-Y.1    OSHER, S.2    TSAI, Y.-H.3
  • 22
    • 0035679975 scopus 로고    scopus 로고
    • An O(N) level set method for eikonal equations
    • S. KIM, An O(N) level set method for eikonal equations, SIAM J. Sci. Comput., 22 (2001), pp. 2178-2193.
    • (2001) SIAM J. Sci. Comput , vol.22 , pp. 2178-2193
    • KIM, S.1
  • 23
    • 0032555230 scopus 로고    scopus 로고
    • Computing geodesic paths on manifold
    • R. KIMMEL AND J. A. SETHIAN, Computing geodesic paths on manifold, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 8431-8435.
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 8431-8435
    • KIMMEL, R.1    SETHIAN, J.A.2
  • 24
    • 0035329048 scopus 로고    scopus 로고
    • Optimal algorithm for shape from shading and path planning
    • R. KIMMEL AND J. A. SETHIAN, Optimal algorithm for shape from shading and path planning, J. Math. Imaging Vision, 14 (2001), pp. 237-244.
    • (2001) J. Math. Imaging Vision , vol.14 , pp. 237-244
    • KIMMEL, R.1    SETHIAN, J.A.2
  • 26
    • 21144473929 scopus 로고
    • A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
    • S. OSHER, A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations, SIAM J. Math. Anal., 24 (1993), pp. 1145-1152.
    • (1993) SIAM J. Math. Anal , vol.24 , pp. 1145-1152
    • OSHER, S.1
  • 27
    • 34247377075 scopus 로고    scopus 로고
    • Fast sweeping methods for eikonal equations on triangular meshes
    • J. QIAN, Y.-T. ZHANG, AND H. K. ZHAO, Fast sweeping methods for eikonal equations on triangular meshes, SIAM J. Numer. Anal., 45 (2007), pp. 83-107.
    • (2007) SIAM J. Numer. Anal , vol.45 , pp. 83-107
    • QIAN, J.1    ZHANG, Y.-T.2    ZHAO, H.K.3
  • 28
    • 34247359458 scopus 로고    scopus 로고
    • A fast sweeping method for static convex Hamilton- Jacobi equations
    • J. QIAN, Y.-T. ZHANG, AND H. ZHAO, A fast sweeping method for static convex Hamilton- Jacobi equations, J. Sci. Comput., 31 (2007), pp. 237-271.
    • (2007) J. Sci. Comput , vol.31 , pp. 237-271
    • QIAN, J.1    ZHANG, Y.-T.2    ZHAO, H.3
  • 29
    • 0026880997 scopus 로고
    • A viscosity solutions approach to shape-from-shading
    • E. ROUY AND A. TOURIN, A viscosity solutions approach to shape-from-shading, SIAM J. Numer. Anal., 29 (1992), pp. 867-884.
    • (1992) SIAM J. Numer. Anal , vol.29 , pp. 867-884
    • ROUY, E.1    TOURIN, A.2
  • 30
    • 55549140262 scopus 로고    scopus 로고
    • M. SAGONA, Numerical Methods for Degenerate Eikonal Type Equation and Applications, Ph.D. thesis, Dipartimento di Matematica, Universita di Napoli Federico II, Naples, Italy, 2001.
    • M. SAGONA, Numerical Methods for Degenerate Eikonal Type Equation and Applications, Ph.D. thesis, Dipartimento di Matematica, Universita di Napoli "Federico II," Naples, Italy, 2001.
  • 31
    • 11144316551 scopus 로고    scopus 로고
    • An adaptive scheme for the shape from shading problem
    • M. Falcone and Ch. Makridakis, eds, World Scientific, Singapore
    • M. SAGONA AND A. SEGHINI, An adaptive scheme for the shape from shading problem, in Numerical Methods for Viscosity Solutions and Applications, M. Falcone and Ch. Makridakis, eds., World Scientific, Singapore, 2001, pp. 197-219.
    • (2001) Numerical Methods for Viscosity Solutions and Applications , pp. 197-219
    • SAGONA, M.1    SEGHINI, A.2
  • 33
    • 0029966538 scopus 로고    scopus 로고
    • A fast marching level set method for monotonically advancing fronts
    • J. A. SETHIAN, A fast marching level set method for monotonically advancing fronts, Proc. Natl. Acad. Sci. USA, 93 (1996), pp. 1591-1595.
    • (1996) Proc. Natl. Acad. Sci. USA , vol.93 , pp. 1591-1595
    • SETHIAN, J.A.1
  • 34
    • 1842511489 scopus 로고    scopus 로고
    • Ordered upwind methods for static Hamilton-Jacobi equations: Theory and algorithms
    • J. A. SETHIAN AND A. VLADIMIRSKY, Ordered upwind methods for static Hamilton-Jacobi equations: Theory and algorithms, SIAM J. Numer. Anal., 41 (2003), pp. 325-363.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 325-363
    • SETHIAN, J.A.1    VLADIMIRSKY, A.2
  • 35
    • 0036059914 scopus 로고    scopus 로고
    • Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian
    • P. SORAVIA, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian, Indiana Univ. Math. J., 51 (2002), pp. 451-477.
    • (2002) Indiana Univ. Math. J , vol.51 , pp. 451-477
    • SORAVIA, P.1
  • 37
    • 1942479348 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of Hamilton-Jacobi equations
    • Y.-H. R. TSAI, L.-T. CHENG, S. OSHER, AND H.-K. ZHAO, Fast sweeping algorithms for a class of Hamilton-Jacobi equations, SIAM J. Numer. Anal., 41 (2003), pp. 673-694.
    • (2003) SIAM J. Numer. Anal , vol.41 , pp. 673-694
    • TSAI, Y.-H.R.1    CHENG, L.-T.2    OSHER, S.3    ZHAO, H.-K.4
  • 38
    • 0029373106 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • J. N. TSITSIKLIS, Efficient algorithms for globally optimal trajectories, IEEE Trans. Automat. Control, 40 (1995), pp. 1528-1538.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 1528-1538
    • TSITSIKLIS, J.N.1
  • 39
    • 14944383149 scopus 로고    scopus 로고
    • A fast sweeping method for eikonal equations
    • H. ZHAO, A fast sweeping method for eikonal equations, Math. Comp., 74 (2005), pp. 603-627.
    • (2005) Math. Comp , vol.74 , pp. 603-627
    • ZHAO, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.