Solving large systems arising from fractional model by preconditioned methods
Reza Khoshsiar Ghaziani, Mojtaba Fardi and Mehdi Ghasemi* Author for corresponding; e-mail address: Rkhoshsiar@gmail.com
Volume: Vol.44 No.4 (October 2017)
Research Article
DOI:
Received: 20 March 2015, Revised: -, Accepted: 26 September 2016, Published: -
Citation: Ghaziani R.K., Fardi M. and Ghasemi M., Solving large systems arising from fractional model by preconditioned methods, Chiang Mai Journal of Science, 2017; 44(4): 1769-1780.
Abstract
This study develops and analyzes preconditioned Krylov subspace methods for solving discretization of the time-independent space-fractional models. First we apply a shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we apply two preconditioned iterative methods, namely, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient for normal residual (preconditioned CGN) method, to solve the corresponding discritized systems. We make comparisons between the preconditioners commonly used in the parallelization of the preconditioned Krylov subspace methods. The results suggest that preconditioning technique is a promising candidate for solving large-scale linear systems arising from fractional models.