Document detail
ID
oai:arXiv.org:2404.10221
Topic
Mathematics - Numerical Analysis 34A08, 65F08, 65F10Author
She, Zi-Hang Zhang, Xue Gu, Xian-Ming Serra-Capizzano, StefanoCategory
Computer Science
Year
2024
listing date
4/24/2024
Keywords
riesz fractional numerical preconditionerAbstract
In the present study, we consider the numerical method for Toeplitz-like linear systems arising from the $d$-dimensional Riesz space fractional diffusion equations (RSFDEs).
We apply the Crank-Nicolson (CN) technique to discretize the temporal derivative and apply a quasi-compact finite difference method to discretize the Riesz space fractional derivatives.
For the $d$-dimensional problem, the corresponding coefficient matrix is the sum of a product of a (block) tridiagonal matrix multiplying a diagonal matrix and a $d$-level Toeplitz matrix.
We develop a sine transform based preconditioner to accelerate the convergence of the GMRES method.
Theoretical analyses show that the upper bound of relative residual norm of the preconditioned GMRES method with the proposed preconditioner is mesh-independent, which leads to a linear convergence rate.
Numerical results are presented to confirm the theoretical results regarding the preconditioned matrix and to illustrate the efficiency of the proposed preconditioner.
;Comment: 17 pages, 3 figures
She, Zi-Hang,Zhang, Xue,Gu, Xian-Ming,Serra-Capizzano, Stefano, 2024, On $\tau$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
Investigating the Serotonergic Modulation of Orientation Tuning of Neurons in Primary Visual Cortex of Anesthetized Mice
cortical tuning mean serotonin firing modulation rate neurons orientation visual activity system
