Time-Domain Analysis of Photonic Band Gap Structure by a Finite-Element Tearing and Interconnecting Algorithm

Abstract

Based on the finite element approximation and nonoverlapping domain decomposition, an efficient parallel algorithm of the finite-element time-domain method is presented for the analysis of the photonic band gap structure. The unconditionally stable implicit Newmark-beta scheme is used in the time domain finite-element tearing and interconnecting algorithm. Through the use of Lagrange multipliers, the field continuity is enforced explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains. In this way, the direct sparse solver is used for each subdomain system and the large global problem is reduced to a much smaller interface problem. Thus, the final system matrix equation is solved by Krylov subspace solvers and a Neumann boundary condition is obtained at the interfaces between all the subdomains. Therefore, the fields inside each subdomain are then calculated by this Neumann boundary condition. Numerical results demonstrate that our proposed method is extremely efficient for the analysis of the photonic band gap structures.