ABSTRACT An efficient locally implicit discontinuous Galerkin finite element method is proposed for time domain analysis of 3D layered problems. The vector mixed finite elements with discontinuous Galerkin method are employed for spatial discretization, and the singly diagonally implicit Runge–Kutta scheme is used for time stepping. The block Thomas algorithm is utilized during time integration to eliminate the subdomain‐based iteration. Numerical examples demonstrate the proposed method is efficient in simulating 3D layered structures containing electrically small components. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1912–1916, 2013