GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type
Jean-David Benamou; Philippe Hoch
- Volume: 36, Issue: 5, page 883-905
- ISSN: 0764-583X
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topBenamou, 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] 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] V.I. Arnol’d, Mathematical methods of Classical Mechanics. Springer-Verlag (1978). Zbl0386.70001
- [3] G. Barles, Solutions de viscosité des équations de Hamilton–Jacobi. Springer-Verlag (1994). Zbl0819.35002
- [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] J.-D. Benamou, Direct solution of multi-valued phase-space solutions for Hamilton–Jacobi equations. Comm. Pure Appl. Math. 52 (1999). Zbl0935.35032
- [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] 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] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton–Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. Zbl0599.35024
- [9] J.J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities. Comm. Pure Appl. Math. 27 (1974) 207–281. Zbl0285.35010
- [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] B. Engquist and O. Runborg, Multi-phase computation in geometrical optics. Tech report, Nada KTH (1995). Zbl0947.78001MR1430373
- [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] 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] 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] 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] 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] W. Symes, A slowness matching algorithm for multiple traveltimes. TRIP report (1996).
- [18] V. Vinje, E. Iversen and H. Gjoystdal, Traveltime and amplitude estimation using wavefront construction. Geophysics 58 (1993) 1157–1166.
- [19] L.C. Young, Lecture on the Calculus of Variation and Optimal Control Theory. Saunders, Philadelphia (1969). Zbl0177.37801MR259704
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