Domain decomposition based parallel Howard’s algorithm

The Classic Howard’s algorithm, a technique of resolution for dis-crete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial character-istic of the method is the superlinear convergence which, in presence of a finite number of controls, is reached in finite time. Performances of the method can be significantly improved by using parallel computing; how to build a parallel version of method is not a trivial point, the difficulties come from the strict relation between various values of the solution, even related to distant points of the domain. In this contri-bution we propose a parallel version of the Howard’s algorithm driven by an idea of domain decomposition. This permits to derive some important properties and to prove the convergence under quite stan-dard assumptions. The good features of the algorithm will be shown through some tests and examples