Reconstruction of independent sub-domains for a class of Hamilton–Jacobi equations and application to parallel computing
RICAM – Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences (ÖAW) Altenberger Straße 4040 Linz, Austria.
Received: 7 January 2015
Revised: 22 July 2015
Accepted: 28 August 2015
A previous knowledge of the domains of dependence of a Hamilton–Jacobi equation can be useful in its study and approximation. Information of this nature is, in general, difficult to obtain directly from the data of the problem. In this paper we formally introduce the concept of an independent sub-domain, discuss its main properties and provide a constructive implicit representation formula. Through these results, we propose an algorithm for the approximation of these sets that is shown to be relevant in the numerical resolution, via parallel computing.
Mathematics Subject Classification: 49L25 / 65N55 / 49M27
Key words: Hamilton–Jacobi equations / viscosity solutions / numerical approximation / parallel computing / domain decomposition
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