Extrapolation of the High Frequency and Late Time Response With Local Linear Basis Functions and Its Application in Evaluating Lightning Electric Field

To avoid numerical inaccuracy of the transient solution by the time-domain solvers or frequency-domain solvers, a simultaneous extrapolation approach reconstructing of the wide-band frequency spectrum using low-frequency and early-time data by the local linear basis functions is presented. The basic idea is transforming the transient integral equations into the analytical-form matrix equation, which can be solved using basis functions with a local support. By means of the early-time and low-frequency data, the matrix equation is solved by the method of singular value decomposition to obtain the wide-band spectrum. The proposed approach is validated by several numerical examples and applied in calculating the transient horizontal electric field of a lightning channel. The major advantage of the presented approach is an efficient and stable algorithm that can be generalized to apply to other transient scenarios when frequency- and time-domain-based transient analysis are involved.