Abstract

In this paper, we investigate an acceleration of the discrete Green's function (DGF) formulation of the FDTD method (DGF-FDTD) with the use of recurrence schemes. The DGF-FDTD method allows one to compute FDTD solutions as a convolution of the excitation with the DGF kernel. Hence, it does not require to execute a leapfrog time-stepping scheme in a whole computational domain for this purpose. Until recently, the DGF generation has been the limiting step of DGF-FDTD due to large computational resources, in terms of processor time and memory, required for these computations. Hence, we have derived the no-neighbours recurrence scheme for one-dimensional FDTD-compatible DGF using solely properties of the Gauss hypergeometric function (GHF). Using known properties of GHF, the recurrence scheme is obtained for arbitrary stable time-step size. In this paper, we show that using the recurrence scheme, computations of 1-D FDTD solutions with the use of the DGF-FDTD method can be around an order of magnitude faster than those based on the direct FDTD method. Although 2- and 3-D recurrence schemes for DGF (valid not only for the magic time-step size) still need to be derived, the 1-D case remains the starting point for any research in this area.

Authors (2)