GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type

Jean-David Benamou; Philippe Hoch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 5, page 883-905
  • ISSN: 0764-583X

Abstract

top
We describe both the classical lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.

How to cite

top

Benamou, Jean-David, and Hoch, Philippe. "GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.5 (2002): 883-905. <http://eudml.org/doc/245984>.

@article{Benamou2002,
abstract = {We describe both the classical lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.},
author = {Benamou, Jean-David, Hoch, Philippe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Hamilton–Jacobi; hamiltonian system; ray tracing; viscosity solution; upwind scheme; geometric optics; C++; Hamilton-Jacobi equations; Hamiltonian system},
language = {eng},
number = {5},
pages = {883-905},
publisher = {EDP-Sciences},
title = {GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type},
url = {http://eudml.org/doc/245984},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Benamou, Jean-David
AU - Hoch, Philippe
TI - GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 5
SP - 883
EP - 905
AB - We describe both the classical lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
LA - eng
KW - Hamilton–Jacobi; hamiltonian system; ray tracing; viscosity solution; upwind scheme; geometric optics; C++; Hamilton-Jacobi equations; Hamiltonian system
UR - http://eudml.org/doc/245984
ER -

References

top
  1. [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. 
  2. [2] V.I. Arnol’d, Mathematical methods of Classical Mechanics. Springer-Verlag (1978). Zbl0386.70001
  3. [3] G. Barles, Solutions de viscosité des équations de Hamilton–Jacobi. Springer-Verlag (1994). Zbl0819.35002
  4. [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. Zbl0860.65052
  5. [5] J.-D. Benamou, Direct solution of multi-valued phase-space solutions for Hamilton–Jacobi equations. Comm. Pure Appl. Math. 52 (1999). Zbl0935.35032
  6. [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. Zbl1023.78001
  7. [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. Zbl0893.35068
  8. [8] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton–Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. Zbl0599.35024
  9. [9] J.J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities. Comm. Pure Appl. Math. 27 (1974) 207–281. Zbl0285.35010
  10. [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. Zbl0836.65099
  11. [11] B. Engquist and O. Runborg, Multi-phase computation in geometrical optics. Tech report, Nada KTH (1995). Zbl0947.78001MR1430373
  12. [12] S. Izumiya, The theory of Legendrian unfoldings and first order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 517–532. Zbl0786.35033
  13. [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. 
  14. [14] B. MerrymanS. Ruuth and S.J. Osher, A fixed grid method for capturing the motion of self-intersecting interfaces and related PDEs. Preprint (1999). 
  15. [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. Zbl0674.65061
  16. [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. Zbl1043.78556
  17. [17] W. Symes, A slowness matching algorithm for multiple traveltimes. TRIP report (1996). 
  18. [18] V. Vinje, E. Iversen and H. Gjoystdal, Traveltime and amplitude estimation using wavefront construction. Geophysics 58 (1993) 1157–1166. 
  19. [19] L.C. Young, Lecture on the Calculus of Variation and Optimal Control Theory. Saunders, Philadelphia (1969). Zbl0177.37801MR259704

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.