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.
Accepté le :
DOI : 10.1051/m2an/2015070
Mots clés : Hamilton–Jacobi equations, viscosity solutions, numerical approximation, parallel computing, domain decomposition
@article{M2AN_2016__50_4_1223_0,
author = {Festa, Adriano},
title = {Reconstruction of independent sub-domains for a class of {Hamilton{\textendash}Jacobi} equations and application to parallel computing},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1223--1240},
publisher = {EDP-Sciences},
volume = {50},
number = {4},
year = {2016},
doi = {10.1051/m2an/2015070},
mrnumber = {3535237},
zbl = {1347.49044},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015070/}
}
TY - JOUR AU - Festa, Adriano TI - Reconstruction of independent sub-domains for a class of Hamilton–Jacobi equations and application to parallel computing JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1223 EP - 1240 VL - 50 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015070/ DO - 10.1051/m2an/2015070 LA - en ID - M2AN_2016__50_4_1223_0 ER -
%0 Journal Article %A Festa, Adriano %T Reconstruction of independent sub-domains for a class of Hamilton–Jacobi equations and application to parallel computing %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1223-1240 %V 50 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015070/ %R 10.1051/m2an/2015070 %G en %F M2AN_2016__50_4_1223_0
Festa, Adriano. Reconstruction of independent sub-domains for a class of Hamilton–Jacobi equations and application to parallel computing. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1223-1240. doi : 10.1051/m2an/2015070. http://www.numdam.org/articles/10.1051/m2an/2015070/
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