@Article{NMTMA-11-827,
author = {Xuelei Lin, Michael K. Ng and Haiwei Sun},
title = {A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2018},
volume = {11},
number = {4},
pages = {827--853},
abstract = {<p style="text-align: justify;">In this paper, we study linear systems arising from time-space fractional
Caputo-Riesz diffusion equations with time-dependent diffusion coefficients. The coefficient
matrix is a summation of a block-lower-triangular-Toeplitz matrix (temporal component)
and a block-diagonal-with-diagonal-times-Toeplitz-block matrix (spatial component).
The main aim of this paper is to propose separable preconditioners for solving
these linear systems, where a block ϵ-circulant preconditioner is used for the temporal
component, while a block diagonal approximation is used for the spatial variable. The
resulting preconditioner can be block-diagonalized in the temporal domain. Furthermore,
the fast solvers can be employed to solve smaller linear systems in the spatial
domain. Theoretically, we show that if the diffusion coefficient (temporal-dependent
or spatial-dependent only) function is smooth enough, the singular values of the preconditioned
matrix are bounded independent of discretization parameters. Numerical
examples are tested to show the performance of proposed preconditioner.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2018.s09},
url = {http://global-sci.org/intro/article_detail/nmtma/12475.html}
}