Optimization of perfectly matched layer for 2D Poisson's equation with antisymmetrical or symmetrical boundary conditions

Parameters of the perfectly matched layer (PML) for 2D magnetic field in a region bounded by circular boundary are rigorously calculated for the case of symmetrical or antisymmetrical boundary conditions. The PML consists of a single or double layer of elements, whose artificial parameters are calculated by minimizing an error function of potential difference between the nodal potentials of the PML and of the original grid expanding to infinity.