Hybrid Staggered Perfectly Matched-layers in Non-Staggered Meshless Time-Domain Vector Potential Technique

Authors: Zahra Shaterian, Thomas Kaufmann, and Christophe Fumeaux

Source: FERMAT, Volume 02, Communication 8, Mar_Apr, 2014

Abstract: 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.

Index Terms: Radial point interpolation, meshless methods, magnetic vector potential, wave equation, perfectly matched layer.

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Hybrid Staggered Perfectly Matched-layers in Non-Staggered Meshless Time-Domain...