论文标题
1D半滴定植物动力学的确切人工边界条件
Exact artificial boundary conditions of 1D semi-discretized peridynamics
论文作者
论文摘要
Peridyannic理论根据不差的方程而不是部分微分方程来重新制定连续力学的方程式。直接在人工边界条件下直接应用幼稚的方法来使连续素质进行植入动力学建模并不微不足道，因为它通常涉及半差异方案。在本文中，我们提出了一种使用内核函数和递归关系来构建半稀释性植入动力学的确切边界条件的新方法。特别是，内核函数用于表征一个单一源以构建确切的边界条件。提出了内核函数之间的递归关系，因此可以通过高精度的普通微分系统和积分系统来计算内核函数。数值结果表明边界条件具有很高的精度。所提出的方法可以应用于其他非本地理论和高维情况的波传播的建模。
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.
