A Lagrangian Approach for the Handling of Curved Boundaries in the Finite-Difference Time-Domain Method

A methodology is proposed for the systematic and accurate modeling of electromagnetic field interactions in geometries with curved boundaries using the Finite-Difference Time-Domain method. The methodology utilizes a Lagrangian approach to solve a modified set of Maxwell´s equations on a map of the physical domain, for which all boundaries are parallel to a Cartesian coordinate system. Hence, a rectangular Yee´s lattice can be used for the spatial discretization of Maxwell´s equations. The proposed scheme avoids the need for the staircase approximation of curved boundaries and provides for enhanced accuracy in a systematic manner. The proposed methodology is validated through its application to the modeling of wave propagation through the two-dimensional geometry of a non-uniform section of a parallel-plate waveguide formed by the cascading of two exponential tapers.