On the late-time instability of perfectly matched layers in the meshless radial point interpolation method

The time-domain behavior of the Uniaxial Perfectly Matched Layer (UPML) in the 3D meshless Radial Point Interpolation Method (RPIM) is investigated in this paper. It is theoretically shown that the UPML will become unstable after a very long time when the energy in the computational domain almost completely vanishes. A timed introduction of loss terms in the equations inside the UPMLs, i.e. at a time after absorption of most of the energy, can significantly delay or even remove the occurrence of this instability without compromising the accuracy of the solution.