Block splitting preconditioner for time-space fractional diffusion equations

Jia-Min Luo; Hou-Biao Li; Wei-Bo Wei; Jia-Min Luo; Hou-Biao Li; Wei-Bo Wei

doi:10.3934/era.2022041

Electronic Research Archive

2022, Volume 30, Issue 3: 780-797. doi: 10.3934/era.2022041

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Block splitting preconditioner for time-space fractional diffusion equations

1.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2.
College of Computer Science & Technology, Qingdao University, Qingdao 266071, China

Academic Editor: Xian-Ming Gu

Received: 24 December 2021 Revised: 17 February 2022 Accepted: 20 February 2022 Published: 01 March 2022

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.
- time-space fractional diffusion equation,
- splitting iteration method,
- Kronecker product,
- Krylov subspace method
Citation: Jia-Min Luo, Hou-Biao Li, Wei-Bo Wei. Block splitting preconditioner for time-space fractional diffusion equations[J]. Electronic Research Archive, 2022, 30(3): 780-797. doi: 10.3934/era.2022041

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Abstract

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.

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