论文标题
用于求解空间网络上波动方程的多尺度方法
Multiscale methods for solving wave equations on spatial networks
论文作者
论文摘要
我们介绍并分析了在空间网络上提出的波传播问题的多尺度方法。通过使用插值在网络上的有限元空间引入粗尺度，我们使用局部正交分解（LOD）方法构建了离散的多尺度空间。然后将空间离散化与能源保存的时间方案结合使用，以形成所提出的方法。在预先准备的初始数据的假设下，我们在空间和时间离散化方面得出了最佳顺序的先验误差。在分析中，我们结合了用于空间网络上固定椭圆问题的理论与经典的有限元有关双曲线问题的结果。最后，我们提出了证实我们理论发现的数值实验。
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using the localized orthogonal decomposition (LOD) methodology. The spatial discretization is then combined with an energy conserving temporal scheme to form the proposed method. Under the assumption of well-prepared initial data, we derive an a priori error bound of optimal order with respect to the space and time discretization. In the analysis, we combine the theory derived for stationary elliptic problems on spatial networks with classical finite element results for hyperbolic problems. Finally, we present numerical experiments that confirm our theoretical findings.
