A Fast State-Based Peridynamic Numerical Model (Communications in Computational Physics, 2020)
The peridynamic (PD) theory is a reformulation of the classical theory ofcontinuum solid mechanics and is particularly suitable for the representation of discontinuities in displacement fields and the description of cracks and their evolutionin materials, which the classical partial differential equation (PDE) models tend to failto apply. However, the PD models yield numerical methods with dense stiffness matrices which requires O(N2) memory and O(N3) computational complexity where Nis the number of spatial unknowns. Consequently, the PD models are deemed to becomputationally very expensive especially for problems in multiple space dimensions.State-based PD models, which were developed lately, can be treated as a great improvement of the previous bond-based PD models. The state-based PD models havemore complicated structures than the bond-based PD models. In this paper we develop a fast collocation method for a state-based linear PD model by exploring thestructure of the stiffness matrix of the numerical method. The method has an O(N)memory requirement and computational complexity of O(NlogN) per Krylov subspace iteration. Numerical methods are presented to show the utility of the method.
Keywords: State-based peridynamic model; fast algorithm; collocation method; stiffness matrix.