Solving large systems arising from fractional models by preconditioned methods
Publish Year: 1394
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CMDE-3-4_003
تاریخ نمایه سازی: 15 اسفند 1401
Abstract:
This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee 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 further 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.
Authors
Reza Khoshsiar Ghaziani
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box ۱۱۵, Shahrekord, Iran
Mojtaba Fardi
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box ۱۱۵, Shahrekord, Iran
Mehdi Ghasemi
Faculty of Mathematical Sciences, Shahrekord University, P. O. Box ۱۱۵, Shahrekord, Iran