The finite difference time domain (FDTD) and finite element numerical methods are two popular time domain computational methods in electromagnetics, but the two numerical methods have certain tradeoffs. FDTD is a fast explicit method with second order accuracy, but the method’s accuracy is reduced when analyzing structures that are not conforming to a Cartesian grid. The finite element method on the other hand excels at examining domains with non-conforming structures, but its method of solution usually requires a matrix inverse operation, which is computationally expensive. Fortunately, research in hybrid methods have shown that the FDTD method for isotropic materials can be viewed upon as a subset of finite elements, and from this viewpoint, the FDTD and finite element method in the time domain can be hybridized together to the advantages of both methods while mitigating the disadvantages.
With the recent rise in the study of metamaterials, which contain anisotropic media, having a hybridized method to study anisotropic media is a desirable tool as, for example, the effects of these materials combined with antennas are being examined. However, the hybridization approach combining the FDTD and finite element method for isotropic media does not extend to anisotropic media since the anisotropic FDTD equation cannot be recovered from the finite element formulation in this fashion. In this dissertation, a hybridized FDTD/finite element method for anisotropic materials will be developed. In the derivation of the hybridized method, a new finite element method will be formulated which incorporates the constitutive relation in a finite element point of view. This new finite element method will also be used to construct new anisotropic FDTD stencils in a systematic manner for certain interface and boundary conditions that the traditional anisotropic FDTD update fails to handle. Numerical tests will be performed to demonstrate the accuracy of the both the hybridized anisotropic FDTD/finite element method as well as the new FDTD stencils that are derived from the new finite element method.