A Nonlinear DG-FETD Scheme Based on Parametric Variational Principle

We propose a novel discontinuous Galerkin finite-element time-domain (DG-FETD) based on parametric variational principle to simulate nonlinear and multiscale electromagnetic problems. The nonlinear property of the material is reconstructed and solved based on the parametric quadratic programming method, and domain decomposition strategy with DG scheme is employed to deal with multiscale modeling. By solving the nonlinear constitutive relations as a series of linear complementary problems (LCP), this nonlinear DG-FETD scheme avoids updating the system matrices at each time step and presents a good convergence behavior. The DG method enables the non-conforming meshes between subdomains and also separate the nonlinear and electrically fine structure from other linear subdomains. Numerical examples demonstrate the efficiency and high flexibility of the nonlinear DG-FETD method.