A hybrid finite-element/finite-difference method with an implicit–explicit time-stepping scheme for Maxwell's equations


Q. H. Liu, Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.

E-mail: qhliu@ee.duke.edu


This paper describes a hybrid technique in time domain that combines the explicit finite-difference time-domain (FDTD) method and the implicit finite-element time-domain (FETD) method based on the discontinuous Galerkin method to analyze transient electromagnetic problems. In the hybrid method, the FETD part uses the unconditionally stable Crank–Nicholson method with a triangular mesh, whereas the standard FDTD part employs a staggered Cartesian grid for spatial discretization and the leap-frog scheme for time stepping. Nonconforming meshes are allowed between the structured FDTD grid and unstructured FETD meshes. The hybrid method takes advantages of the modeling flexibility of the FETD method for complex structures and the efficiency of the FDTD method for simple structures. The hybrid implicit–explicit time-stepping scheme allows a time-step increment as large as the stability limit for the FDTD method, which can be much larger than the stability criterion of the explicit FETD scheme with small elements. The hybrid scheme has second-order accuracy. Numerical examples demonstrate the efficiency of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.