Hybrid staggered perfectly matched layers in non-staggered meshless time-domain vector potential technique

In this paper a hybrid algorithm for the implementation of Perfectly Matched Layers (PMLs) in the meshless magnetic vector potential technique is proposed. Solving the wave equation in time-domain, the magnetic vector potential technique avoids using staggered node distributions which are needed for calculating the E and H fields when directly solving Maxwell´s equations. However, implementing PMLs with stretched coordinate formulation requires auxiliary variables on a staggered (dual) node distribution. To avoid defining staggered nodes in the whole computational domain, a hybrid algorithm is proposed in this paper: The algorithm keeps a single set of nodes for the magnetic vector potential A inside the free space while it uses staggered nodes for A and auxiliary variables inside the PML. The hybrid algorithm is validated in a 2D rectangular waveguide and numerical reflection coefficients are compared for different thicknesses of the PML and for different orders of a polynomial conductivity profile inside the PML. A good agreement between theoretical results and converged solutions validates the approach, with best performance using a polynomial order m = 3.