论文标题
基于快速卷积的时空Chebyshev光谱方法
A fast-convolution based space-time Chebyshev spectral method for peridynamic models
论文作者
论文摘要
Peridynanic是对连续力学理论的非局部概括，它在不使用部分衍生物并由整体操作员替换其替代的情况下，适应不连续的问题。结果，它在弹性材料中裂缝和损坏的发展和进化框架中找到了应用。 在本文中，我们考虑了一种基于Chebyshev多项式的一维非线性非线性模型，并提出了一种合适的二维快速卷积光谱方法来解决该模型。这种选择使我们能够在时空和时间上获得相同的精度。我们显示了该方法的收敛性，并执行了几个模拟以研究光谱方案的性能。
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.
