The main goal of this article is to study computationally the controllability of a diffusion process on the surface of a sphere in . To achieve this goal, we employ a methodology combining finite differences for the time discretization, finite elements for the space approximation, and a conjugate gradient algorithm for the iterative solution of the discrete control problems. The results of numerical experiments, obtained using the above methodology, will be presented. Furthermore, the null-controllability properties of the diffusion model under consideration will be also studied computationally.
Accepté le :
DOI : 10.1051/cocv/2016045
Keywords: Diffusion process, surface of a shere, conjugate gradient, null-controlability, approximate controllability, Laplace−Beltrami operator
Assaely León Velasco, D. 1 ; Glowinski, Roland 2, 3 ; Héctor Juárez Valencia, L. 1
@article{COCV_2016__22_4_1054_0,
author = {Assaely Le\'on Velasco, D. and Glowinski, Roland and H\'ector Ju\'arez Valencia, L.},
title = {On the controllability of diffusion processes on a sphere: {A} numerical study},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1054--1077},
year = {2016},
publisher = {EDP Sciences},
volume = {22},
number = {4},
doi = {10.1051/cocv/2016045},
mrnumber = {3570494},
zbl = {1353.49042},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016045/}
}
TY - JOUR AU - Assaely León Velasco, D. AU - Glowinski, Roland AU - Héctor Juárez Valencia, L. TI - On the controllability of diffusion processes on a sphere: A numerical study JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1054 EP - 1077 VL - 22 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016045/ DO - 10.1051/cocv/2016045 LA - en ID - COCV_2016__22_4_1054_0 ER -
%0 Journal Article %A Assaely León Velasco, D. %A Glowinski, Roland %A Héctor Juárez Valencia, L. %T On the controllability of diffusion processes on a sphere: A numerical study %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1054-1077 %V 22 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016045/ %R 10.1051/cocv/2016045 %G en %F COCV_2016__22_4_1054_0
Assaely León Velasco, D.; Glowinski, Roland; Héctor Juárez Valencia, L. On the controllability of diffusion processes on a sphere: A numerical study. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1054-1077. doi: 10.1051/cocv/2016045
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