Normal directional NURBS arithmetic of conformal PML

Conformal Perfectly Matched Layer (PML) is a high-efficiency absorbing boundary condition for the finite element analysis of electromagnetic fields. Accurate calculation of normal direction of conformal PML is essential for the geometric modelling of conformal shell elements and constitutive parameters of conformal PML, especially for sophisticated and arbitrary shape scatterers. Consequently, a Non-Uniform Rational B-Splines (NURBS) arithmetic is proposed for describing the conformal surface accurately in this study. Based on the NURBS arithmetic, four weighted average formulas are presented for calculating the common normal direction of adjacent surface elements of conformal shell. Numerical experiments show the availability of NURBS arithmetic and precision of weighted average formulas in the geometrical modelling of conformal PML.