A Lagrangian approach for the handling of curved boundaries in the finite-difference in 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.