Introduction to the FDTD method and its application to implicit locally one-dimensional calculations

Abstract

This paper introduces the finite-difference time-domain (FDTD) method widely used for the analysis of electromagnetic problems. The original FDTD method is based an explicit formulation in time, allowing simple arithmetic operations without calculating simultaneous equations. However, at the cost of such a simple calculation, the FDTD method has a limitation on the choice of the time step size, known as the Courant-Friedrichs-Lewy (CFL) condition. To remove the CFL condition, the locally one-dimensional (LOD) scheme has been applied to the implicit FDTD formulation. Here, we review the formulation of the FDTD method and describe its application to implicit calculations, particularly with the use of the LOD scheme.