We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions and computing them by fast Fourier transform (FFT), we reduce the computational complexity of PD models from O(N^2) to O(Nlog_2 N), with N being the total number of discretization nodes. Initial neighbor identification and storing neighbor information is not required, and, as a consequence, memory allocation scales with O(N) instead of O(N^2), common for existing methods. The method is applicable to bounded domains with arbitrary shapes and boundary conditions via an embedded constraint (EC) approach. We explain the FCBM-EC formulation for certain bond-based and state-based, linear and nonlinear PD models of elasticity and dynamic brittle fracture, as applications. We solve a 3D elastostatic problem and show that the FCBM reduces the computational time from days to hours and from years to days, compared with the original meshfree discretization for PD models. Large-scale computations of PD models are feasible with the new method, and we demonstrate its versatility by simulating, with ease, the difficult problem of multiple crack branching in a brittle plate.

翻译：我们为近地动力学(PD)采用了一种通用的快速革命法(FCBM)方法(FCBM ) 。通过快速Fleier变换(FFT)来表达PD组成部分,并用快速Freier变换(FFT)来计算,我们减少了PD模型的计算复杂性,从O(N)2到O(Nlog_2N),N是离散节节点的总数。我们不需要初步的邻居识别和储存邻居信息,因此,现有方法通常使用O(N)而不是O(N)的记忆分配尺度。该方法适用于带有任意形状和边界条件的封闭域。我们解释了FCBM-EC的公式,用于某些基于债券和基于国家、线性和非线性PD模型的弹性和动态软骨折的计算复杂性,作为应用。我们解决了3D弹性问题,并表明FCBM将计算时间从几天到几年不等,而与PD模型的原始的无线分解分解(EC)方法相比,大规模地计算PD模型的清晰度和多盘的易度,以多种方式展示。