**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 Maxwellâ€™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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