Open AccessBlock splitting preconditioner for time-space fractional diffusion equations
Author(s) -
Jun Luo,
Hong Li,
Weibo Wei
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022041
Subject(s) - preconditioner , krylov subspace , mathematics , identity matrix , toeplitz matrix , triangular matrix , coefficient matrix , generalized minimal residual method , iterative method , matrix (chemical analysis) , block (permutation group theory) , matrix norm , norm (philosophy) , rank (graph theory) , mathematical analysis , algorithm , combinatorics , pure mathematics , eigenvalues and eigenvectors , invertible matrix , physics , materials science , quantum mechanics , composite material , political science , law
For solving a block lower triangular Toeplitz linear system arising from the time-space fractional diffusion equations more effectively, a single-parameter two-step split iterative method (TSS) is introduced, its convergence theory is established and the corresponding preconditioner is also presented. Theoretical analysis shows that the original coefficient matrix after preconditioned can be expressed as the sum of the identity matrix, a low-rank matrix, and a small norm matrix. Numerical experiments show that the preconditioner improve the calculation efficiency of the Krylov subspace iteration method.