一维半离散周波方程的精确人工边界条件
Exact artificial boundary conditions of 1D semi-discretized peridynamics
摘要：
周期理论将连续介质力学方程从偏微分方程转化为积分微分方程。直接将连续介质人工边界条件中的朴素方法应用于周期性流体动力学建模并不容易，因为它通常涉及半离散化方案。本文提出了一种利用核函数和递归关系构造半离散周期动力学精确边界条件的新方法。特别地，核函数被用来表征一个单一的源被结合起来，以构造精确的边界条件。提出了核函数之间的递推关系，使核函数可以通过常微分系统和常积分系统进行高精度计算。数值结果表明，该边界条件具有较高的精度.该方法可用于其他非局部理论和高维情况下的波传播建模。
英文摘要：
The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not trivial to directly apply naive approach in artificial boundary conditions for continua to peridynamics modeling, because it usually involves semi-discretization scheme. In this paper, we present a new way to construct exact boundary conditions for semi-discretized peridynamics using kernel functions and recursive relations. Specially, kernel functions are used to characterize one single source are combined to construct the exact boundary conditions. The recursive relationships between the kernel functions are proposed, therefore the kernel functions can be computed through the ordinary differential system and integral system with high precision. The numerical results demonstrate that the boundary condition has high accuracy. The proposed method can be applied to modeling of wave propagation of other nonlocal theories and high dimensional cases.
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