Recurrence scheme for FDTD-compatible discrete Green's function derived based on properties of Gauss hypergeometric function

ABSTRACT

In this paper, the formulation of one-dimensional FDTD (Finite-difference time-domain)-compatible discrete Green's function (DGF) is derived based on the Gauss hypergeometric function (GHF). The properties of GHF make it possible to derive the recurrence scheme only in the time domain for the DGF generation. Furthermore, this recurrence scheme is valid for any stable time-step size and can be implemented using standard numerical precision of computations. The proposed derivation is obtained without processing in any symbolic mathematics software and relies on the application of known properties of GHF. The difference between the developed recurrence scheme and the direct FDTD simulation is approximately at the level of numerical noise, which confirms the correctness of our derivation. The results obtained should be useful for the development of computational techniques employing FDTD and the diakoptic approach.

KEYWORDS:

• Finite-difference time-domain methods
• Green's function
• discrete Green's function
• Gauss hypergeometric function

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jacek Gulgowski  http://orcid.org/0000-0002-7706-9263

Tomasz P. Stefański  http://orcid.org/0000-0002-3952-5731