A Fast Unconditionally Stable FETD Algorithm Based on Local Eigenvalue solutions

A fast unconditionally stable time domain finite element (FUS-FETD) method based on local eigenvalue solutions is proposed in this paper. This method can reach unconditional stability for the explicit time marching, but it does not need to solve partial solutions of global eigenvalue problem. By strictly grouping and numbering, the unknowns in the computational domain are divided into two groups: the unknowns with fine grids and the unknowns without fine grids. The system matrix can be naturally divided into four different matrix blocks. By solving the eigenvalue problem of local matrix block related to fine grids, the unstable modes can be quickly and effectively obtained. Since the dimension of local matrix block is smaller than that of global matrix, the proposed method reduces the complexity of solving eigenvalue problem and improves the computational efficiency. Numerical results show the effectiveness of the proposed algorithm.