An accurate and efficient numerical method for solving linear peridynamic models

In this paper, we combine the recently developed localized radial basis functions-based pseudo-spectral method with the time-splitting technique to solve a linear wave equation arising from modelling the wave dynamics using peridynamic formulation in continuum mechanics. Specifically, we adopt this combined method for solving a Hamiltonian ordinary differential equation system, which is equivalent to the original linear peridynamic equation after introducing a new variable. The proposed approach inherits advantages of these two related methods in space and time: (1) offering high accuracy and efficiency in the solution of the problem under irregular domains for both uniform and non-uniform discretizations; (2) extending the applicability of the approach to multi-dimensions; and (3) maintaining a good approximation for problems at large time-step and long time integration. Numerical results indicate that the proposed method is simple, accurate, efficient, and stable for solving various linear peridynamic problems.