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

TL;DR

This paper introduces the concept of independent sub-domains for Hamilton-Jacobi equations, providing a constructive representation and an algorithm that enhances parallel computing efficiency.

Contribution

It formally defines independent sub-domains, offers a constructive implicit representation, and proposes an algorithm for their approximation to improve parallel solution computation.

Findings

The concept of independent sub-domains is formally introduced.

A constructive implicit representation formula is provided.

An algorithm for approximating these sub-domains is proposed and shown to be effective.

Abstract

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.