Part I. Improved handling to geometry details in finite difference time domain method. Part II. Method of circuit extraction using finite difference frequency domain matrix formulation with application to power bus modeling

In the first half of this work, a subgridding algorithm with separate spatial and temporal subgridding interfaces is proposed, which makes it possible to analyze and test the spatial and temporal algorithms separately and may also provide additional flexibility.; The spatial subgridding method is based on the linear interpolation of the electric and magnetic current densities. The forward and backward coupling schemes are designed to be symmetric, which ensures the stability of the subgridding algorithm. The temporal subgridding method is based on a simple assumption that the field values at the temporal subgridding interface keep constant during one coarse time step. The stability of this scheme is illustrated by using a one-dimensional FDTD model. The full subgridding algorithm combining the two sub-algorithms is also implemented. The stability and accuracy of the subgridding method are tested numerically.; The second part of the dissertation proposes a procedure to generate an equivalent circuit network from the Finite Difference Time Domain (FDTD) model. A matrix equation that has the same form of Kirchhoff Current Law (KCL) is derived from the formulation of the Finite Difference Frequency Domain (FDFD) method. Based on the matrix equation, an equivalent circuit can be generated, and the extracted circuit model can be simulated in a SPICE-like solver. Although the generated circuit model does not reduce the complexity of its 3-D full wave counterpart, it provides the possibility of an easy combination of the SPICE circuit and full wave models.; The subgridding method is well-suited for the DC power bus modeling. The example models show that the accuracy and efficiency of the proposed method are comparable to the cavity model.