System incorporated direct-splitting algorithm for periodic nonuniform metamaterial design in open regions

System incorporated (SI) direct-splitting (DS) algorithm is proposed to efficiently simulate periodic nonuniform structures in open regions. Based on the digital signal processing technique, the proposed algorithm cannot only maintain the calculation stability with the enlargement of time steps but also tighten the finite-difference time-domain (FDTD) implementation. An alternative periodic boundary condition (APBC) algorithm is proposed according to the unconditionally stable SIDS algorithm to analyze the periodic structures. To calculate multiscale nonuniform domains, domain decomposition (DD) method is proposed to discretize the entire computational domain into several sub-regions according to the SIDS algorithm. Furthermore, higher order perfectly matched layer (PML) is incorporated with the proposed algorithm for the boundary termination in open regions. Periodic nonuniform metamaterial structure is employed as an example to demonstrate the efficiency, absorption and accuracy. Through comparison with the other algorithms, the proposed algorithm can receive the most considerable performance from each aspect. By employing the proposed APBC algorithm, sparse matrix can be converted to tri-diagonal matrix which alleviates the time increment problem in periodic structures calculation. Through introducing the proposed domain decomposition method, size of nonuniform domains can be reduced compared with the uniform discretization which leads to the decrement of simulation duration and resources.