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Title of Journal: Comput Visual Sci

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Abbravation: Computing and Visualization in Science

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Springer Berlin Heidelberg

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DOI

10.1016/0022-328x(93)83023-o

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1433-0369

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An efficient algorithm for Hamilton–Jacobi equatio

Authors: Elisabetta Carlini Maurizio Falcone Roberto Ferretti
Publish Date: 2004/06/01
Volume: 7, Issue: 1, Pages: 15-29
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Abstract

In this paper we develop a new version of the semiLagrangian algorithm for first order Hamilton–Jacobi equations This implementation is well suited to deal with problems in high dimension ie in Rm with m≥3 which typically arise in the study of control problems and differential games Our model problem is the evolutive Hamilton–Jacobi equation related to the optimal control finite horizon problem We will give a stepbystep description of the algorithm focusing our attention on two critical routines the interpolation in high dimension and the search for the global minimum We present some numerical results on test problems which range from m=3 to m=5 and deal with applications to front propagation aerospace engineering ecomomy and biology

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