arXiv subjects

Adriano Festa

Publications and source records attributed to Adriano Festa.

24 records · Page 2Linked to original sources

arXiv2014

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.

math.NA↗

arXiv2014

Decomposition of Differential Games

This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a collection of target subsets; the decomposition consists of replacing the original target by each of the target subsets. The value of the original game is then obtained as the lower envelope of the values of the collection of games resulting from the decomposition, which can be much easier to solve than the original game. Criteria are given for the validity of the decomposition. The paper includes examples, illustrating the application of the technique to pursuit/evasion games, where the decomposition arises from considering the interaction of individual pursuer/evader pairs.

math.OC↗

arXiv2014

Domain decomposition based parallel Howard's algorithm

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.

math.NA↗

arXiv2013

A decomposition technique for pursuit evasion games with many pursuers

Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using some elements of Hamilton-Jacobi equations theory, we find a relation between the regularity of the solution and the possibility to decompose the problem. We use this technique to solve a pursuit evasion game with multiple agents.

math.OC↗

arXiv2013

An approximation scheme for an Eikonal Equation with discontinuous coefficient

We consider the stationary Hamilton-Jacobi equation where the dynamics can vanish at some points, the cost function is strictly positive and is allowed to be discontinuous. More precisely, we consider special class of discontinuities for which the notion of viscosity solution is well-suited. We propose a semi-Lagrangian scheme for the numerical approximation of the viscosity solution in the sense of Ishii and we study its properties. We also prove an a-priori error estimate for the scheme in an integral norm. The last section contains some applications to control and image processing problems.

math.NA↗

arXiv2012

An approximation scheme for an Hamilton-Jacobi equation defined on a network

In this paper we study an approximation scheme for an Hamilton-Jacobi equation of Eikonal type defined on a network. We introduce an appropriate notion of viscosity solution for this class of equations (see \cite{sc}) and we prove that an approximation scheme of semi-Lagrangian type converges to the unique solution of the problem.

math.AP↗