Geodesic
Parallel two-grids algorithms for solution of anomalous diffusion equations of fractional order
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 83-98

Voir la notice de l'article provenant de la source Math-Net.Ru

New parallel algorithms are proposed for solving the initial-boundary value problems for anomalous diffusion equations with the Riemann-Liouville spatial- and/or timefractional derivatives. A two-grid technique is employed to construct these algorithms. Spline-approximation on a coarse grid is used to compute the spatial and time long-range effects, and a fine grid is used for finite-difference discretization of the fractional diffusion equations. The parallel algorithms with a spatial and a time domain decomposition are discussed separately. The approach originally developed for the Parareal algorithm is used for time domain decomposition. The theoretical estimates of the speed-up and efficiency of the proposed algorithms are given. It has been shown that the algorithms have a superlinear speed-up in comparison with a classical sequential finite-difference algorithm, and have the same accuracy if the size of a fine grid is agreed with the size of a coarse grid. Some computational results are also presented to verify the efficiency of the proposed algorithms.
Keywords: parallel two-grid algorithm, fractional differential equation.
Mots-clés : anomalous diffusion 
@article{VYURV_2012_2_a7,
     author = {S. Yu. Lukashchuk},
     title = {Parallel two-grids algorithms for solution of anomalous diffusion equations of fractional order},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {83--98},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2012_2_a7/}
}
TY  - JOUR
AU  - S. Yu. Lukashchuk
TI  - Parallel two-grids algorithms for solution of anomalous diffusion equations of fractional order
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
PY  - 2012
SP  - 83
EP  - 98
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURV_2012_2_a7/
LA  - ru
ID  - VYURV_2012_2_a7
ER  - 
%0 Journal Article
%A S. Yu. Lukashchuk
%T Parallel two-grids algorithms for solution of anomalous diffusion equations of fractional order
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
%D 2012
%P 83-98
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURV_2012_2_a7/
%G ru
%F VYURV_2012_2_a7
S. Yu. Lukashchuk. Parallel two-grids algorithms for solution of anomalous diffusion equations of fractional order. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, no. 2 (2012), pp. 83-98. http://geodesic.mathdoc.fr/item/VYURV_2012_2_a7/