ANALYSIS OF CURVED AND ANGLED SURFACES ON A CARTESIAN MESH USING A NOVEL FINITE-DIFFERENCE TIME-DOMAIN ALGORITHM

The widely accepted finite-difference time-domain algorithm, based on a Cartesian mesh, is unable to rigorously model the curved surfaces wh ich arise in many engineering applications, while more rigorous soluti on algorithms are inevitably considerably more computationally intensi ve. A nonintensive, but still rigorous, alternative to this approach h as been to incorporate a priori knowledge of the behavior of the field s (their asymptotic static field solutions) into the FDTD algorithm, U nfortunately, until now, this method has often resulted in instability . In this contribution an algorithm (denoted 'SFDTD' for second-order finite difference time domain) is presented which uses the static fiel d solution technique to accurately characterize curved and angled meta llic boundaries. A hitherto unpublished stability theory for this algo rithm, relying on principles of energy conservation, is described and it is found that for the first time a priori knowledge of the field di stribution can be incorporated into the algorithm with no possibility of instability. The accuracy of the SFDTD algorithm is compared to tha t of the standard FDTD method by means of two test structures for whic h analytic results are available.