A Block Fast Regularized Hermitian Splitting Preconditioner for Two-Dimensional Discretized Almost Isotropic Spatial Fractional Diffusion Equations
Year: 2022
Author: Yao-Ning Liu, Galina V. Muratova
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 213–232
Abstract
Block fast regularized Hermitian splitting preconditioners for matrices arising in approximate solution of two-dimensional almost-isotropic spatial fractional diffusion equations are constructed. The matrices under consideration can be represented as the sum of two terms, each of which is a nonnegative diagonal matrix multiplied by a block Toeplitz matrix having a special structure. We prove that excluding a small number of outliers, the eigenvalues of the preconditioned matrix are located in a complex disk of radius $r<1$ and centered at the point $z_0=1$. Numerical experiments show that such structured preconditioners can significantly improve computational efficiency of the Krylov subspace iteration methods such as the generalized minimal residual and bi-conjugate gradient stabilized methods. Moreover, if the corresponding equation is almost isotropic, the methods constructed outperform many other existing preconditioners.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.070621.300821
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 213–232
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Preconditioning spatial fractional diffusion equation Toeplitz matrix two-dimensional problem.