A fast-convolution based space-time Chebyshev spectral method for peridynamic models

TL;DR

This paper introduces a fast-convolution spectral method using Chebyshev polynomials for efficiently solving one-dimensional nonlinear peridynamic models, achieving high accuracy and demonstrating convergence through simulations.

Contribution

It presents a novel two-dimensional spectral method based on Chebyshev polynomials tailored for peridynamic models, improving computational efficiency and accuracy.

Findings

Method converges reliably in simulations

Achieves high spatial and temporal accuracy

Demonstrates efficiency in nonlinear peridynamic problems

Abstract

Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral operator. As a consequence, it finds applications in the framework of the development and evolution of fractures and damages in elastic materials. In this paper we consider a one-dimensional nonlinear model of peridynamics and propose a suitable two-dimensional fast-convolution spectral method based on Chebyshev polynomials to solve the model. This choice allows us to gain the same accuracy both in space and time. We show the convergence of the method and perform several simulations to study the performance of the spectral scheme.