论文标题
二阶双曲方程的边界含量等几何分析
A boundary-penalized isogeometric analysis for second-order hyperbolic equations
论文作者
论文摘要
明确的时间衡量方案很受欢迎，可用于解决时间依赖的偏微分方程。这些方法遭受的最大挑战之一是增加了保证数值稳定性的关键时间级步长。通常，有两种增加临界步长的方法。一种是降低空间离散化系统的刚度，而另一个是设计具有较大稳定性区域的时间紧迫方案。在本文中，我们专注于最近提出的二阶双曲方程的显式广义 - $α$方法，并通过降低同几年差异化系统的刚度来增加临界步长。特别是，我们应用边界惩罚来降低系统的刚度。对于$ p $ -th顺序$ c^{p-1} $ isoemetric元素，我们从数字上显示，关键步长增加了$ \ sqrt {\ frac {\ frac {p^2-3p+6} {4} {4}}} $，这表明使用提出的方法的优势，尤其是用于高级订购的优势，尤其是用于高级订购的元素。一个，二维和三个维度的各种示例验证了所提出的技术的性能。
Explicit time-marching schemes are popular for solving time-dependent partial differential equations; one of the biggest challenges these methods suffer is increasing the critical time-marching step size that guarantees numerical stability. In general, there are two ways to increase the critical step size. One is to reduce the stiffness of the spatially discretized system, while the other is to design time-marching schemes with larger stability regions. In this paper, we focus on the recently proposed explicit generalized-$α$ method for second-order hyperbolic equations and increase the critical step size by reducing the stiffness of the isogeometric-discretized system. In particular, we apply boundary penalization to lessen the system's stiffness. For $p$-th order $C^{p-1}$ isogeometric elements, we show numerically that the critical step size increases by a factor of $\sqrt{\frac{p^2-3p+6}{4}}$, which indicates the advantages of using the proposed method, especially for high-order elements. Various examples in one, two, and three dimensions validate the performance of the proposed technique.
