Reconstruction of Independent Sub-domains for a class of Hamilton Jacobi Equations and its Application to Parallel Computing

A previous knowledge of the domains of dependence of an Hamilton Jacobi equation can be useful in its study and approximation. Information of this nature are, in general, difficult to obtain directly from the data of the problem. In this paper we introduce formally the concept of independent sub-domains discussing their main properties and we provide a constructive implicit representation formula. Using such results we propose an algorithm for the approximation of these sets that will be shown to be relevant in parallel computing of the solution.