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Volumn 32, Issue 5, 2010, Pages 2853-2874

Some improvements for the fast sweeping method

Author keywords

Eikonal equation; Fast marching; Fast sweeping; Static Hamilton Jacobi equation

Indexed keywords

DATA STRUCTURES; GEOMETRICAL OPTICS; ITERATIVE METHODS; LOCKS (FASTENERS); NUMERICAL METHODS;

EID: 78149354082     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090749645     Document Type: Article
Times cited : (47)

References (27)
  • 1
    • 0001678817 scopus 로고    scopus 로고
    • Markov chain approximations for deterministic control problems with affine dynamics and quadratic costs in the control
    • M. Boue and P. Dupuis, Markov chain approximations for deterministic control problems with affine dynamics and quadratic costs in the control, SIAM J. Numer. Anal., 36 (1999), pp. 667-695.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 667-695
    • Boue, M.1    Dupuis, P.2
  • 2
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), pp. 1-42.
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 4
    • 33947097945 scopus 로고    scopus 로고
    • A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
    • Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, J. Comput. Phys., 223 (2007), pp. 398-415.
    • (2007) J. Comput. Phys. , vol.223 , pp. 398-415
    • Cheng, Y.1    Shu, C.-W.2
  • 5
    • 0030313072 scopus 로고    scopus 로고
    • Two new methods for simulating photolithography development in 3D
    • J. Helmsen, E. G. Puckett, P. Colella, and M. Dorr, Two new methods for simulating photolithography development in 3D, Proc. SPIE, 2736 (1996), pp. 253-261.
    • (1996) Proc. SPIE , vol.2736 , pp. 253-261
    • Helmsen, J.1    Puckett, E.G.2    Colella, P.3    Dorr, M.4
  • 6
    • 0021793358 scopus 로고
    • New polynomial bounded shortest path algorithm
    • F. Glover, D. Klingman, and N. Phillips, New polynomial bounded shortest path algorithm, Oper. Res., 33 (1985), pp. 65-73.
    • (1985) Oper. Res. , vol.33 , pp. 65-73
    • Glover, F.1    Klingman, D.2    Phillips, N.3
  • 7
    • 33751231737 scopus 로고    scopus 로고
    • Computational study of fast methods for the Eikonal equation
    • P. A. Gremaud and C. M. Kuster, Computational study of fast methods for the Eikonal equation, SIAM J. Sci. Comput., 27 (2006), pp. 1803-1816.
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1803-1816
    • Gremaud, P.A.1    Kuster, C.M.2
  • 8
    • 1942507479 scopus 로고    scopus 로고
    • Lax-Freidrichs sweeping schemes for static Hamilton- Jacobi equations
    • C. Y. Kao, S. J. Osher, and J. Qian, Lax-Freidrichs sweeping schemes 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.J.2    Qian, J.3
  • 9
    • 29144492874 scopus 로고    scopus 로고
    • Fast sweeping methods for static Hamilton-Jacobi equations
    • C. Y. Kao, S. J. 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.J.2    Tsai, Y.H.3
  • 10
    • 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
  • 11
    • 0001140342 scopus 로고    scopus 로고
    • Fast marching methods on triangulated domains
    • R. Kimmel and J. A. Sethian, Fast marching methods on triangulated domains, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 8341-8435.
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 8341-8435
    • Kimmel, R.1    Sethian, J.A.2
  • 12
    • 47049115993 scopus 로고    scopus 로고
    • A second order discontinuous Galerkin fast sweeping method for Eikonal equations
    • F. Li, C. W. Shu, Y. T. Zhang, and H. Zhao, A second order discontinuous Galerkin fast sweeping method for Eikonal equations, J. Comput. Phys., 227 (2008), pp. 8191-8208.
    • (2008) J. Comput. Phys. , vol.227 , pp. 8191-8208
    • Li, F.1    Shu, C.W.2    Zhang, Y.T.3    Zhao, H.4
  • 13
    • 34247359458 scopus 로고    scopus 로고
    • A fast sweeping method for static convex Hamilton-Jacobi equations
    • J. Qian, Y. 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.2    Zhao, H.3
  • 14
    • 34247377075 scopus 로고    scopus 로고
    • Fast sweeping methods for Eikonal equations on triangular meshes
    • J. Qian, Y. Zhang, and H. 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.2    Zhao, H.3
  • 16
    • 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
  • 17
    • 0032631799 scopus 로고    scopus 로고
    • Fast marching methods
    • J. A. Sethian, Fast marching methods, SIAM Rev., 41 (1999), pp. 199-235.
    • (1999) SIAM Rev. , vol.41 , pp. 199-235
    • Sethian, J.A.1
  • 19
    • 0034705102 scopus 로고    scopus 로고
    • Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes
    • J. A. Sethian and A. Vladimirsky, Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 5699-5703.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 5699-5703
    • Sethian, J.A.1    Vladimirsky, A.2
  • 20
    • 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
  • 22
    • 1942479348 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of Hamilton-Jacobi equations
    • R. Tsai, L. T. Cheng, S. J. Osher, and H. K. Zhao, Fast sweeping algorithms for a class of Hamilton-Jacobi equations, SIAM J. Numer. Anal., 41 (2003), pp. 673-1594
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 673-1594
    • Tsai, R.1    Cheng, L.T.2    Osher, S.J.3    Zhao, H.K.4
  • 23
    • 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
  • 24
    • 29144489240 scopus 로고    scopus 로고
    • O(N) implementation of the fast marching algorithm
    • L. Yatziv, A. Bartesaghi, and G. Sapiro, O(N) implementation of the fast marching algorithm, J. Comput. Phys., 212 (2005), pp. 393-399.
    • (2005) J. Comput. Phys. , vol.212 , pp. 393-399
    • Yatziv, L.1    Bartesaghi, A.2    Sapiro, G.3
  • 25
    • 47049130433 scopus 로고    scopus 로고
    • Fixed-point iterative sweeping methods for static Hamilton- Jacobi equations
    • Y. Zhang, H. Zhao, and S. Chen, Fixed-point iterative sweeping methods for static Hamilton- Jacobi equations, Methods Appl. Anal., 13 (2006), pp. 299-320.
    • (2006) Methods Appl. Anal. , vol.13 , pp. 299-320
    • Zhang, Y.1    Zhao, H.2    Chen, S.3
  • 26
    • 33750302668 scopus 로고    scopus 로고
    • High order fast sweeping methods for static Hamilton- Jacobi equations
    • Y.-T. Zhang, H.-K. Zhao, and J. Qian, High order fast sweeping methods for static Hamilton- Jacobi equations, J. Sci. Comput., 29 (2006), pp. 25-56.
    • (2006) J. Sci. Comput. , vol.29 , pp. 25-56
    • Zhang, Y.-T.1    Zhao, H.-K.2    Qian, J.3
  • 27
    • 14944383149 scopus 로고    scopus 로고
    • A fast sweeping method for Eikonal equations
    • H. Zhao, A fast sweeping method for Eikonal equations, Math. Comp., 74 (2004), pp. 603-627.
    • (2004) Math. Comp. , vol.74 , pp. 603-627
    • Zhao, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.