A preconditioned fast collocation method for a linear bond-based peridynamic model

Advances in Difference Equations

article

Zhang, Xuhao¹  Li, Xiao²  Cheng, Aijie²  Wang, Hong³ 

[1] School of Mathematics and Statistics, Qilu University of Technology;School of Mathematics, Shandong University;Department of Mathematics, University of South Carolina

关键词: Nonlocal models;    Peridynamic model;    Preconditioner;    Fast collocation method;   

DOI  :  10.1186/s13662-020-02700-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We develop a fast collocation method for a static bond-based peridynamic model. Based on the analysis of the structure of the stiffness matrix, a fast matrix-vector multiplication technique was found, which can be used in the Krylov subspace iteration method. In this paper, we also present an effective preconditioner to accelerate the convergence of the Krylov subspace iteration method. Using the block-Toeplitz–Toeplitz-block (BTTB)-type structure of the stiffness matrix, we give a block-circulant-circulant-block (BCCB)-type preconditioner. The numerical experiments show the utility of the preconditioned fast collocation method.

【 授权许可】

CC BY