Perfectly matched layers for peridynamic scalar waves and the numerical discretization on real coordinate space

Nonlocal perfectly matched layers (nonlocal PMLs) for nonlocal wave equations and the corresponding numerical discretization to solve the reduced PML problems on bounded domains are studied. The nonlocal PMLs are derived by combining the Laplace transform and the analytical continuation into the complex plane. The discrete scheme defined on the complex space may lead to a spurious imaginary part of the numerical solution and has a large computational cost. Here we design some new nonlocal PMLs and numerical schemes and prove that they are on the real space, which is much efficient comparing with the complex space. The accuracy and effectiveness of our approaches are illustrated by some numerical examples.