Solving nonlinear Maxwell´s equations with finite-element time-domain method and parametric variational principle

A novel method for nonlinear Maxwell´s equations is proposed in this paper. This method is based on the parametric variational principle and finite-element time-domain scheme. Unlike conventional nonlinear methods based on iteration, the proposed method treats the nonlinear constitutive relations as a set of linear complementary problems. This method is effective in handling nonlinear constitutive laws in electromagnetics, such as Kerr medium, ferroelectric and ferromagnetic hysteresis.