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

Abstract

Abstract 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.

Keywords

• Nonlocal models
• Peridynamic model
• Preconditioner
• Fast collocation method