  Perfectly matched layers (PMLs) are formulated and applied to numerically
solve nonlocal Helmholtz equations in one and two dimensions. In one dimension,
we present the PML modifications for the nonlocal Helmholtz equation with
general kernels and theoretically show its effectiveness in some sense. In two
dimensions, we give the PML modifications in both Cartesian coordinates and
polar coordinates. Based on the PML modifications, nonlocal Helmholtz equations
are truncated in one and two dimensional spaces, and asymptotic compatibility
schemes are introduced to discretize the resulting truncated problems. Finally,
numerical examples are provided to study the "numerical reflections" by PMLs
and demonstrate the effectiveness and validation of our nonlocal PML strategy.
