In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions.

翻译：本文针对黏性介质中的近场动力学标量波型问题，提出了一种离散完美匹配层（PML）。为非局部模型构建PML通常具有挑战性，这主要源于非局部算子通常与多种核函数相关联。我们首先采用基于求积的有限差分格式将连续模型转化为空间半离散形式，随后通过离散解析延拓从半离散方程推导出PML方程。该PML层能够无反射地吸收半离散方程的谐波指数基本解（平面波模式），并使其呈指数衰减。通过与精确吸收边界条件的对比数值实验，验证了离散PML优异的吸收效率与数值稳定性。