Hybrid FDTD algorithm for electromagnetic analysis of fine structures

A new hybrid Finite-Difference Time-Domain (hybrid FDTD) algorithm is proposed in this paper. This hybrid FDTD method combines the superiorities of explicit unconditionally stable FDTD (US-FDTD) and traditional FDTD methods to achieve unconditional stability and high calculation efficiency. US-FDTD is used in fine grids and the adjacent coarse grids subdomain and it breaks the Courant-Friedrich-Levy (CFL) condition. Traditional FDTD is used in the remaining coarse grids subdomain and it is a matrix free method. A compensation scheme is used on the subdomain boundary without compromising accuracy. Hybrid FDTD makes the explicit time marching with a uniform time step determined by the size of coarse grid in whole domain, which reduces the iteration time. In addition, because US-FDTD is only used in one of the subdomains, compared with global US-FDTD method, the matrix dimension of hybrid FDTD is reduced, which saves the time for eigenvalue solution. Numerical results show high efficiency and accuracy of the proposed method.