Efficient implementation of unconditionally stable FDTD with the local eigenvalue solution

Due to the explicit and unconditionally stable finite difference time domain (US-FDTD) method has a high computational cost of solving eigenvalues of the global matrix and field iteration when there are a large number of unknown fields or unstable modes. To solve this problem, an efficient implementation scheme of US-FDTD based on the local eigenvalue solution (USL-FDTD) is given.All unstable modes in the entire system can be obtained accurately and efficiently without solving the eigenvalue problem of the global matrix by this scheme. In the implementation, first, the computational domain is divided into two parts.Region I contains all fine grids and the adjacent coarse grids.Region Ⅱ consists of the remaining coarse grids. Then the original global system matrix can be divided naturally into four local matrix blocks. These four small matrices contain the grid information on region I and region Ⅱ respectively, and the coupling relationship between region I and region Ⅱ.Since the unstable modes only exist in fine grids and the adjacent coarse grids, all unstable modes can be obtained by solving the eigenvalue problem of the local matrix corresponding to region I.Finally, the fields in region I and region Ⅱ can be calculated respectively. The fields of these two regions are associated by two coupling matrix blocks. In addition, there is no unstable mode in coupling matrix blocks.USL-FDTD not only decreases the dimension of the matrix to be solved, but also reduces the computational complexity and improves the computational efficiency.Numerical results show the accuracy and efficiency of this implementation. © 2022, Editorial Department of Journal of Xidian University. All right reserved.