Anisotropic materials in electromagnetic finite element analysis

Electromagnetic permeability, conductivity, and/or permittivity are anisotropic in many materials. The authors discuss how fully anisotropic tensors for these material properties may be used in 3D finite element analysis based on magnetic vector potential and the time integrated electric scalar potential. The tensors may have off-diagonal terms, not just diagonal terms. Besides real anisotropic tensors, complex anisotropic tensors for AC excitations are also discussed. In addition, a new method is presented for modeling nonlinear anisotropic permeability. An inductor serves as a test problem for static, complex, and nonlinear anisotropic cases; its fields calculated by finite element analysis are shown to agree with classical theory in all cases