Accelerating Peridynamics Simulations on the GPU

Introduction

Peridynamics [2] is a recently developed non-local theory of continuum me- chanics that is useful in simulating multi-scale phenomena. Its formulation is based upon an integral equation of motion so that discontinuities may spontaneously form and propagate without special treatment, thus it is nat- urally well-suited to modeling fracture, dislocations, and phase boundaries.

The governing equations of peridynamics permit a ”mesh-free” solution method [3] that has the same computational structure as a molecular dy- namics simulation. Molecular dynamics [1] and other similar particle-based simulations have been seen large speedups and linear scaling when im- plemented on graphics processing units (GPUs), which excel at such data- parallel computational tasks.

In this work, we review a particle-based solution method for the governing equations of peridynamics, and detail our efforts to extend this method to the GPU using NVIDIA’s CUDA parallel computing architecture.