A Local Ordered Upwind Method for Hamilton-Jacobi and Isaacs Equations

Simone Cacace 1 Emiliano Cristiani 2 Maurizio Falcone 3
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : We present a generalization of the Fast Marching (FM) method for the numerical solution of a class of Hamilton-Jacobi equations, including Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. The method is able to compute an approximation of the viscosity solution concentrating the computations only in a small evolving trial region, as the original FM method. The main novelty is that the size of the trial region does not depend on the dynamics. We compare the new method with the standard iterative algorithm and the FM method, in terms of accuracy and order of computations on the grid nodes.
Type de document :
Communication dans un congrès
18th IFAC World Congress, Aug 2012, Milano, Italy. 18, 2012, World Congress. 〈10.3182/20110828-6-IT-1002.02473〉
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https://hal.inria.fr/hal-00724748
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 22 août 2012 - 14:57:57
Dernière modification le : jeudi 11 janvier 2018 - 06:22:33

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Simone Cacace, Emiliano Cristiani, Maurizio Falcone. A Local Ordered Upwind Method for Hamilton-Jacobi and Isaacs Equations. 18th IFAC World Congress, Aug 2012, Milano, Italy. 18, 2012, World Congress. 〈10.3182/20110828-6-IT-1002.02473〉. 〈hal-00724748〉

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