A discrete Perfectly Matched Layer for peridynamic scalar waves in two-dimensional viscous media

TL;DR

This paper introduces a novel discrete perfectly matched layer (PML) for simulating scalar wave problems in viscous media within peridynamics, effectively absorbing waves without reflection and demonstrating high efficiency and stability.

Contribution

The paper develops a discrete PML tailored for nonlocal peridynamic models, using semi-discretization and discrete analytic continuation to improve wave absorption in viscous media.

Findings

PML effectively absorbs plane wave modes without reflection.

Numerical tests show high efficiency and stability of the proposed PML.

Comparison with exact boundary conditions confirms PML's effectiveness.

Abstract

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.