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. © 2011 IFAC.
A local ordered upwind method for Hamilton-Jacobi and Isaacs equations / Cacace, S.; Cristiani, E.; Falcone, M.. - 44:1(2011), pp. 6800-6805. (Intervento presentato al convegno 18th IFAC World Congress tenutosi a Milan; Italy) [10.3182/20110828-6-IT-1002.02473].
A local ordered upwind method for Hamilton-Jacobi and Isaacs equations
Cacace S.;Falcone M.
2011
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. © 2011 IFAC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
