Treatment of non-Cartesian sharp metal edges in the FDTD algorithm.

摘要

The Finite Difference Time Domain (FDTD) algorithm performs a brute force solution of discretized versions of Maxwell's equations of classical electromagnetics for the purpose of examining electromagnetic phenomena in realistic situations. The algorithm is second order accurate in its derivation, however certain model geometries exhibit spatial field behaviour that changes much faster than this implied second-order approximation. In particular, sharp metal edges have a field singularity at the edge due to electrical charge being compressed into a small space. Thus, analysis of these types of sharp edged metal structures is inaccurately represented in typical FDTD formulations. Several techniques have been proposed to make use of the knowledge of this singular field for enhancement of FDTD simulation accuracy, however all of these treatment methods make an assumption with regards to the direction in which the edge runs through the FDTD mesh. Some techniques assume a cartesian metal edge coincident with the FDTD mesh, while other techniques assume a perfectly diagonal edge with respect to the mesh. A new technique is presented in this thesis, in an attempt to model metal structures which have sharp edges that are not aligned with the cartesian FDTD mesh. Numerical tests on several different structures containing sharp metal edges have been performed and it has been determined that this new technique is not particularly effective in simulating 3D geometries, however, the approximation introduced can be used to increase accuracy of certain 2D geometries.