论文标题
在无界多尺度介质中的非局部波方程的完美匹配层上
On perfectly matched layers of nonlocal wave equations in unbounded multi-scale media
论文作者
论文摘要
在整个真实轴上为非局部波方程式制定了一个非本地匹配的层（PML），并设计了数值离散化，以求解有界域上的减少PML问题。非本地PML提出了PDE中不面临的挑战。例如，在非局部模型中没有衍生物，这使得无法用复杂的模型代替衍生。在这里，我们提供了一种为非局部模型构造PML的方法，该模型衰减了层中的波动，并在截断的边界处进行反射非常小。为了在数值上解决非局部PML问题，我们通过结合Talbot的轮廓和时间演变来设计用于空间非局部运算符的渐近兼容（AC）方案。各种数值示例说明了我们方法的准确性和有效性。
A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges not faced in PDEs. For example, there is no derivative in nonlocal models, which makes it impossible to replace derivates with complex ones. Here we provide a way of constructing the PML for nonlocal models, which decays the waves exponentially impinging in the layer and makes reflections at the truncated boundary very tiny. To numerically solve the nonlocal PML problem, we design the asymptotically compatible (AC) scheme for spatially nonlocal operator by combining Talbot's contour, and a Verlet-type scheme for time evolution. The accuracy and effectiveness of our approach are illustrated by various numerical examples.
