Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios.

Ground penetrating radar (GPR) systems are increasingly being used for the detection and location of buried objects within the upper regions of the earth’s surface. The antenna is the most critical component of such a system. This thesis presents a comprehensive study of resistor-loaded planar dipole antennas for GPR applications using both theory and experiments. The theoretical analysis is performed using the finite difference time domain (FDTD) technique. The analysis starts with the most popular planar dipole, the bow-tie. A parametric study is done to find out how the flare angle, length, and lumped resistors of the antenna should be selected to achieve broadband properties and good target detection with less clutter. The screening of the antenna and the position of transmitting and receiving antennas with respect to each other and ground surface are also studied. A number of other planar geometrical shapes are considered and compared with the bow-tie in order to find what geometrical shape gives the best performance. The FDTD simulations are carried out for both lossless and lossy, dispersive grounds. Also simulations are carried out including surface roughness and natural clutter like rocks and twigs to make the modeling more realistic. Finally, a pair of resistor-loaded bow-tie antennas is constructed and both indoor and outdoor measurements are carried out to validate the simulation results. / <p>QC 20100923</p>