The extended method of approximate particular solutions to simulate two-dimensional electromagnetic scattering from arbitrary shaped anisotropic objects

The numerical simulation of electromagnetic scattering problem by cylinders of arbitrary cross-section made of homogeneous and anisotropic material is carried out. The anisotropic materials are characterized by symmetric and positive definite magnetic permeability tensors. An efficient and powerful meshfree strong form technique based on the particular solutions of anisotropic radial basis functions (A-RBFs) is extended to deal with anisotropic problem directly. The A-RBFs are constructed by introducing a special norm associated to the appearing anisotropic tensor and replacing it with the standard Euclidean norm in RBFs. The particular solutions for the anisotropic Laplace operator are approximated explicitly by using the anisotropic radial basis functions. Because of material discontinuity at the interface of anisotropic and free regions, two different sets of basis functions, the approximate particular solutions of the anisotropic generalized multiquadric (A-GMQ) and the standard generalized multiquadric (GMQ) functions are employed to approximate the total electric field inside and the scattered field outside the anisotropic scatterer respectively. Some numerical simulations are implemented to confirm the accuracy and efficiency of the method for anisotropic scatterer with arbitrary cross-sections.