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.
Mots-clés : Hamilton-Jacobi, hamiltonian system, ray tracing, viscosity solution, upwind scheme, geometric optics, C++
@article{M2AN_2002__36_5_883_0, author = {Benamou, Jean-David and Hoch, Philippe}, title = {GO++ : a modular lagrangian/eulerian software for {Hamilton} {Jacobi} equations of geometric optics type}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {883--905}, publisher = {EDP-Sciences}, volume = {36}, number = {5}, year = {2002}, doi = {10.1051/m2an:2002037}, mrnumber = {1955540}, zbl = {1023.78001}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2002037/} }
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: Modélisation mathématique et analyse numérique PY - 2002 SP - 883 EP - 905 VL - 36 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2002037/ DO - 10.1051/m2an:2002037 LA - en ID - M2AN_2002__36_5_883_0 ER -
%0 Journal Article %A Benamou, Jean-David %A Hoch, Philippe %T GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 883-905 %V 36 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2002037/ %R 10.1051/m2an:2002037 %G en %F M2AN_2002__36_5_883_0
Benamou, Jean-David; Hoch, Philippe. GO++ : a modular lagrangian/eulerian software for Hamilton Jacobi equations of geometric optics type. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Programming, Tome 36 (2002) no. 5, pp. 883-905. doi : 10.1051/m2an:2002037. http://archive.numdam.org/articles/10.1051/m2an:2002037/
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