Domain decomposition based parallel Howard's algorithm

The Howard’s algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for itshigh efficiency and good performances. A useful characteristic of the method is the superlinear convergence which, in presenceof a finite number of controls, is reached in finite time. Performances of the method can be significantly improved using parallelcomputing. Building a parallel version of the method is not trivial because of the hyperbolic nature of the problem. In this paperwe propose a parallel version of the Howard’s algorithm driven by an idea of domain decomposition. This permits to derive someimportant properties and to prove the convergence under standard assumptions. The good features of the algorithm are shownthrough some tests and examples.