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| We present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems . The main idea is to divide the domain of computation into subdomains following the dynamics of the control problem. This can result in a rather complex geometrical subdivision, but has the advantage that every subdomain is invariant with respect to the optimal dynamics. Exploiting this invariance speeds up the computation of the value function and also allows for an efficient parallelization, since the classical transmission conditions on the boundaries of the subdomains can be avoided. For this specific feature the subdomains are patches in the sense introduced by Ancona and Bressan. We present some properties of the method as well as several examples in dimension two and three. |
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