Symmetry and TLM method in nonlinear magnetostatics

Exploitation of geometrical symmetry in magnetostatic problems with asymmetry in excitation is generally solved by using a symmetric decomposition technique derived from group theory. However, the nonlinearity makes this method invalid since the material property no longer shares this symmetry. A method that makes the exploitation of symmetry feasible is proposed. It consists of replacing the nonlinear material by a linear and homogeneous one, the nonlinearity is expressed as fictitious sources in an iterative algorithm via the transmission line modeling (TLM) method. The symmetric decomposition of the problem may then be performed at each step of the process. Large computational cost savings are obtained as demonstrated by numerical results