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VGFEM with perfectly matched layers

Vector generalized finite element (VGFEM) has been recently developed and applied to solve electromagnetic problems [1, 2, 3]. VGFEM is a powerful technique as it allows us to use a wide range of functions in the solution space. Moreover, one can easily use different type of basis functions or polynomial orders in any part of the problem domain, which yields better approximations, and perhaps, more efficient simulation. Since the introduction of the VGFEM, there have been some developments in the framework of it. Although the method was introduced as a meshless technique [1], it was later adapted to the polyhedral mesh structures, where the mesh elements are grouped to construct the partitions of unity (PU) domains [2]. In addition, a new set of vector basis space for representing discontinuous fields was developed based on the new framework [4]. These basis functions unlike the ones defined in [1] can handle the inhomogeneities in a PU domain. These developments were validated by solving the fields in closed domains filled with isotropic materials. In this paper, we further develop the VGFEM for solving the fields in open domains using the perfectly matched layers (PML). We use the anisotropic interpretation of the PML; therefore, we reformulate the VGFEM for anisotropic medium.