Fundamental Leapfrog ADI and CDI FDTD Methods

Abstract

This paper presents the fundamental leapfrog alternating direction implicit finite-difference time-domain (LF ADI FDTD) method, which simplifies the right-hand sides (RHS) of implicit update procedures following the principle of fundamental schemes. The leapfrog complying-divergence implicit (CDI) FDTD method is also presented, which comprises implicit update procedures with operator-free RHS while featuring complying divergence. When formulated in fundamental forms, both fundamental LF ADI and CDI FDTD methods are seen to be related by shifting certain RHS operators and operands in the update procedures. While addressing several issues of the LF ADI FDTD method, the LF CDI FDTD method features many advantages including unconditional stability, complying divergence, simplicity and efficient leapfrog update procedures.