Constructing nonstandard and high order FDTD schemes in cylindrical coordinates using spectral domain and modified equation methodologies–1-D case

One of the major drawbacks of the original Yee’s algorithm is “staircasing.” In an attempt to overcome this flaw, especially when trying to solve electromagnetic problems involving cylindrical geometries, an FDTD scheme was formulated in cylindrical coordinates. The vast majority of works published describe an algorithm with a (2, 2) order of accuracy. In this work, we use a recently introduced methodology, that of constructing finite difference schemes in the spectral domain, combined with the well-established one known as the “modified equation” to analyze existing cylindrical FDTD schemes and synthesize new nonstandard and high-order ones.