A novel higher order finite difference time domain method based on the Castillo-Grone mimetic curl operator with applications concerning the time-dependent Maxwell equations
This thesis presents an extension of the mimetic Castillo-Grone operators to include the curl operator. Specifically, a family of one- and two-dimensional curl operators will be developed that are globally fourth order. These operators are then used, within the context of the Finite Difference Time Domain (FDTD) framework, to approximate solutions to one- and two-dimensional problems in electromagnetics involving Maxwell's Equations, where the analytic solutions are known. A three-way comparison is made between two of the Castillo-Grone curl operators and an existing fourth order solution technique and it is shown that one of the mimetic Castillo-Grone operators outperforms the other two.
