关键词: 精细时程积分, Krylov子空间法, 培德级数近似

Abstract: An efficient precise time-step integration algorithm to solve large-scale transient problems is presented. The Krylov subspace method, the Pad\'{e} approximations and the dimensional expanding method of ordinary excitations are applied to modify the original precise time-step integration algorithm in order to improve the computational efficiency. The problems of arbitrary complex excitations can also be solved. For a large-scale system, the efficiency of the algorithm would be influenced because the dimension of system extended by the dimension expanding method becomes higher, especially, for the complex excitations. The present algorithm can solve the large-scale system without difficulty by using the decreasing dimension analysis of the Krylov subspace method. The efficiency of the new algorithm can be improved by analyzing the exponentional matrix in a subspace instead of the original large space. More computational cost can be saved by selecting the parameter $N$ carefully.

Key words: Precise time-step integration (PTI) algorithm, Krylov subspace method, Padé approximations