Domain decomposition based parallel Howard's algorithm

TL;DR

This paper introduces a parallel domain decomposition approach to Howard's algorithm for solving discrete Hamilton-Jacobi equations, enhancing efficiency while maintaining convergence properties.

Contribution

It presents a novel parallelization method based on domain decomposition for Howard's algorithm, with proven convergence and improved performance.

Findings

Algorithm demonstrates good convergence properties.

Parallel implementation improves computational efficiency.

Test results confirm effectiveness of the approach.

Abstract

The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic 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 contribution 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 standard assumptions. The good features of the algorithm will be shown through some tests and examples.