3-D Domain Decomposition Based Hybrid Finite-Difference Time-Domain/Finite-Element Time-Domain Method With Nonconformal Meshes

Abstract

A new 3-D domain decomposition based hybrid finite-difference time-domain (FDTD)/finite-element time-domain (FETD) method is introduced to facilitate electromagnetic modeling by exploiting both the computational efficiency of FDTD and the meshing flexibility of FETD. The proposed hybrid method allows the FETD mesh and the FDTD grid to be nonconformal based on domain decomposition technique. It implements the hybridization with a buffer zone, which functions as a transition region between FDTD and FETD. The buffer zone helps the proposed hybrid method obviate the interpolation approach for field coupling of the nonconformal mesh and hence overcome the late-time instability issue. The discontinuous Galerkin method is utilized to couple different regions, thus improving the coupling accuracy compared with that using the Dirichlet boundary condition. Moreover, the hybrid method allows further division of the FETD region into multiple subdomains when the degrees of freedom in this region are large. For temporal discretization, a global leapfrog time integration scheme is implemented to sequentially update the fields in the FDTD, buffer, and FETD regions. The numerical results are shown to demonstrate the meshing flexibility and computational efficiency of the proposed hybrid method inherited from FETD and FDTD methods.