کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
518624 867605 2013 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A circulant preconditioner for fractional diffusion equations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A circulant preconditioner for fractional diffusion equations
چکیده انگلیسی

The implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is employed to discretize fractional diffusion equations. The resulting systems are Toeplitz-like and then the fast Fourier transform can be used to reduce the computational cost of the matrix–vector multiplication. The preconditioned conjugate gradient normal residual method with a circulant preconditioner is proposed to solve the discretized linear systems. The spectrum of the preconditioned matrix is proven to be clustered around 1 if diffusion coefficients are constant; hence the convergence rate of the proposed iterative algorithm is superlinear. Numerical experiments are carried out to demonstrate that our circulant preconditioner works very well, even though for cases of variable diffusion coefficients.


► The coefficient matrix of the fractional diffusion equation is Toeplitz-like.
► The PCGRN method with a circulant preconditioner is proposed to solve the resulting Toeplitz-like system.
► The superlinear convergence rate for the proposed method has been theoretically proven under some conditions.
► Numerical results show the robustness and efficiency of our circulant preconditioner.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 242, 1 June 2013, Pages 715–725
نویسندگان
, ,