Factorization‐splitting algorithm based on system incorporated method for periodic nonuniform domains in open regions

Abstract

The original Factorization‐Splitting (FS) algorithm solves large number of coefficients and components in each iteration cycle which significantly affects the computational resources and calculation efficiency. Meanwhile, it can merely solve problems in uniform domains due to the limitation of discretized mesh sizes. In order alleviate these drawbacks, system incorporated factorization‐splitting algorithm is proposed to efficiently solve problems in nonuniform domains. The finite‐difference time‐domain (FDTD) domain is terminated by the higher order perfectly matched layer (PML) formulation which shows advantages in improving the absorbing performance. As the employment of the original domain decomposition method results in the algorithm unstable, an alternative domain decomposition method is proposed which can split the entire nonuniform domain into several sub‐regions. Metamaterial structure is introduced to demonstrate the performance of the proposed algorithms. Through results, the proposed algorithm can decrease memory consumption and simulation duration due to the calculation prevention of repeated components and coefficients. The absorption can be further improved especially in the low‐frequency band due to the enhanced absorption of propagation waves. In addition, the alternative domain decomposition method shows considerable advantages in the simulation of nonuniform domains.