Free Access
Volume 36, Number 5, September/October 2002
Special issue on Programming
Page(s) 883 - 905
Published online 15 October 2002
  1. R. Abgrall and J.-D. Benamou, Big ray tracing and eikonal solver on unstructured grids: Application to the computation of a multi-valued travel-time field in the marmousi model. Geophysics 64 (1999) 230-239. [CrossRef] [Google Scholar]
  2. V.I. Arnol'd, Mathematical methods of Classical Mechanics. Springer-Verlag (1978). [Google Scholar]
  3. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag (1994). [Google Scholar]
  4. J.-D. Benamou, Big ray tracing: Multi-valued travel time field computation using viscosity solutions of the eikonal equation. J. Comput. Phys. 128 (1996) 463-474. [CrossRef] [Google Scholar]
  5. J.-D. Benamou, Direct solution of multi-valued phase-space solutions for Hamilton-Jacobi equations. Comm. Pure Appl. Math. 52 (1999). [Google Scholar]
  6. J.-D. Benamou and P. Hoch, GO++: A modular Lagrangian/Eulerian software for Hamilton-Jacobi equations of Geometric Optics type. INRIA Tech. Report RR. [Google Scholar]
  7. Y. Brenier and L. Corrias, A kinetic formulation for multi-branch entropy solutions of scalar conservation laws. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 169-190. [CrossRef] [MathSciNet] [Google Scholar]
  8. M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1-42. [CrossRef] [MathSciNet] [Google Scholar]
  9. J.J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities. Comm. Pure Appl. Math. 27 (1974) 207-281. [CrossRef] [MathSciNet] [Google Scholar]
  10. B. Engquist, E. Fatemi and S. Osher, Numerical resolution of the high frequency asymptotic expansion of the scalar wave equation. J. Comput. Phys. 120 (1995) 145-155. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Engquist and O. Runborg, Multi-phase computation in geometrical optics. Tech report, Nada KTH (1995). [Google Scholar]
  12. S. Izumiya, The theory of Legendrian unfoldings and first order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 517-532. [MathSciNet] [Google Scholar]
  13. G. Lambare, P. Lucio and A. Hanyga, Two dimensional multi-valued traveltime and amplitude maps by uniform sampling of a ray field. Geophys. J. Int 125 (1996) 584-598. [CrossRef] [Google Scholar]
  14. B. Merryman S. Ruuth and S.J. Osher, A fixed grid method for capturing the motion of self-intersecting interfaces and related PDEs. Preprint (1999). [Google Scholar]
  15. S.J. Osher and C.W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM J. Numer. Anal. 83 (1989) 32-78. [Google Scholar]
  16. J. Steinhoff, M. Fang and L. Wang, A new eulerian method for the computation of propagating short acoustic and electromagnetic pulses. J. Comput. Phys. 157 (2000) 683-706. [CrossRef] [MathSciNet] [Google Scholar]
  17. W. Symes, A slowness matching algorithm for multiple traveltimes. TRIP report (1996). [Google Scholar]
  18. V. Vinje, E. Iversen and H. Gjoystdal, Traveltime and amplitude estimation using wavefront construction. Geophysics 58 (1993) 1157-1166. [CrossRef] [Google Scholar]
  19. L.C. Young, Lecture on the Calculus of Variation and Optimal Control Theory. Saunders, Philadelphia (1969). [Google Scholar]

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