When the conventional FDTD method is applied to the high-frequency planar circuits, the time step must be very small due to the CFL stability criterion since the structural details of the circuits are usually very small. These results in a prohibitively high computation time since the simulation takes a long time to stabilize. This thesis will focus on implementing an ADI-FDTD algorithm suitable for the analysis and simulation of large-scale high-frequency planar circuits. Realization of the lumped elements befitting the ADI-FDTD algorithm will be developed. Furthermore, active devices will then be incorporated into the algorithm once the models for lumped elements are built up.

In recent years, the demand for portable radio communication has been increasing which requires low profile, light weight and small size antennas. Therefore, the size of the antenna is required to be as small as possible. In this thesis, some of the compact antennas will be analyzed and simulated. The early-stage PIFA antenna will be investigated first, and then the shorting pin characteristics to design compact and dual band antenna was utilized. Because the shorting pin will lead to the decrease of bandwidth, replacement of the shorting pin by using chip-resistor could improve this characteristic. The compactness of antennas will lead to the decrease of the gain. In order to improve the gain of antennas, the combination of substrate and superstrate configuration with very high permittivity material is used. For the consideration of Bluetooth system, we use the ACPS (Asymmetrical Co-planar Striplines) structure to design the antenna. Using this structure in the design will obtain a promotion in bandwidth compared with the conventional rectangular microstrip antenna. Because the size of the antenna is small, the time to simulate this structure by the FDTD (Finite Difference Time Domain) method is too long. In order to solve this problem, this thesis mainly study a new FDTD algorithm based on the Alternating-Direction Implicit method, and use this algorithm to simulate some simple structures.

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This thesis reports on the application of ground penetrating radar (GPR) as a non-destructive technique for the monitoring of ring separation in brick masonry arch bridges. In addition, research is reported on the assessment of the clay capping layer often used in construction as a waterproof backing to arches. The thrust of the research is numerical modelling, verified by large laboratory experiments. Due to the heterogeneity of these structures, the resultant signals from the interaction between the GPR system and the bridge are often complex and hence, hard to interpret. This highlighted the need to create a GPR numerical model that would allow the study of the attributes of reflected signals from various targets within the structure of the bridge. The GPR numerical analysis was undertaken using the finite-difference time-domain (FDTD) method. Since micro regions in the bridge structure need to be modelled, the introduction of subgrids of supporting finer spatial resolution into the standard FDTD method was considered essential in order to economise on the required computational resources. In the main part of this thesis, it is demonstrated how realistic numerical modelling of GPR using the FDTD method could greatly benefit from the implementation of subgrids into the conventional FDTD mesh. This is particularly important when (a) parts of the computational domain need to be modelled in detail (i.e., ring separation between the mortar layers and the brick units, which is the case studied in this thesis); and also (b) when there are features or regions in the overall computational mesh with values of high relative permittivity supporting propagation of waves at very short wavelengths. A scheme is presented that simplifies the process of implementing these subgrids into the traditional FDTD method. This scheme is based on the combination of the standard FDTD method and the unconditionally stable alternating-direction implicit (ADI) FDTD technique. Given that ADI-FDTD is unconditionally stable, its time-step can be set to any value that facilitates the accurate calculation of the electromagnetic fields. By doing so, the two grids can efficiently communicate information across their boundary without requiring to use a time-interpolation scheme. The performance of ADI-FDTD subgrids when implemented into the traditional FDTD method is discussed herein. The developed algorithm can handle cases where the subgrid crosses dielectrically inhomogeneous and/or conductive media. In addition, results from the comparison between the proposed scheme and a commonly employed purely FDTD subgridding technique are presented. After determination of the optimum ADI-FDTD scheme, numerical experiments were conducted and calibrated using GPR laboratory experiments. Good correlations were obtained between the numerical experiments and the actual GPR experiments. It was shown both numerically and experimentally that significant mortar loss between the masonry arch rings can be detected. Dry hairline delaminations between the mortar and the brick masonry are difficult to detect using standard GPR procedures. However, hairline faults containing water produce distinct and detectable GPR responses. In addition, the clay layer was successfully identified and its thickness calculated to a satisfactory accuracy.

The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. There has been no work on the Crank Nicolson FDTD (CN–FDTD) method for frequency dependent medium. In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debye materials is incorporated into the CN–FDTD method by means of an auxiliary differential formulation. In order to provide a convenient and straightforward algorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit. The proposed method yields a sparse system of linear equations which can be solved by direct or iterative methods, but numerical experiments demonstrate that for large problems of practical importance iterative solvers are to be used. The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorates with the increase of the time-step, making the solution time longer. Selection of the matrix solver to handle the FD–CN–FDTD sparse system is crucial to fully harness the advantages of using larger time-step, because the computational costs associated with the solver must be kept as low as possible. Two best–known iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), are extensively studied in terms of the number of iteration requirements for convergence, CPU time and memory requirements. BiCGStab outperforms GMRES in every aspect. Many of these findings do not match with the existing literature on frequency–independent CN–FDTD method and the possible reasons for this are pointed out. The proposed method is coded in Fortran and major implementation techniques of the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model of the human body is developed in the FD–CN–FDTD method and numerical simulation of the electromagnetic wave propagation inside the human head is shown. Finally, this thesis presents a new method modifying the frequency dependent alternating direction implicit FDTD (FD–ADI–FDTD) method. Although the ADI–FDTD method provides a computationally affordable approximation of the CN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTD method which may become severe for some practical applications. The modified FD–ADI–FDTD method can improve the accuracy of the normal FD–ADI–FDTD method without significantly increasing the computational costs.