The finite-difference time-domain (FDTD) method is one of most widely used computational electromagnetics (CEM) methods to solve the Maxwell's equations for modern engineering problems. In biomedical applications, like the microwave imaging for early disease detection and treatment, the human tissues are considered as lossy and dispersive materials. The most popular model to describe the material properties of human body is the Debye model. In order to simulate the computational domain as an open region for biomedical applications, the complex-frequency-shifted perfectly matched layers (CFS-PML) are applied to absorb the outgoing waves. The CFS-PML is highly efficient at absorbing the evanescent or very low frequency waves. This thesis investigates the stability of the CFS-PML and presents some conditions to determine the parameters for the one dimensional and two dimensional CFS-PML.The advantages of the FDTD method are the simplicity of implementation and the capability for various applications. However the Courant-Friedrichs-Lewy (CFL) condition limits the temporal size for stable FDTD computations. Due to the CFL condition, the computational efficiency of the FDTD method is constrained by the fine spatial-temporal sampling, especially in the simulations with the electrically small objects or dispersive materials. Instead of modifying the explicit time updating equations and the leapfrog integration of the conventional FDTD method, the spatial filtered FDTD method extends the CFL limit by filtering out the unstable components in the spatial frequency domain. This thesis implements filtered FDTD method with CFS-PML and one-pole Debye medium, then introduces a guidance to optimize the spatial filter for improving the computational speed with desired accuracy.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.