Modelling multi-scale problems in the transmission line modelling method

Abstract

Modern electromagnetic problems are becoming increasingly complex and their simulation must take into account geometrical features that are both large and small compared to the wavelength of interest. These multi-scale problems lead to a heavy computational burden in a discretised computational simulation approach since the small features require fine mesh to be used in the simulation, resulting in large run time and memory storage. To overcome such problems, this thesis presents an efficient and versatile method for embedding small features into an otherwise coarse mesh. The embedded model eliminates the need for discretising the small features and allows for a relative large mesh size to be used, thus saving the computational costs. The subject of the thesis is embedding a thin film as a small feature into the numerical Transmission Line Modelling (TLM) method, although any small feature with known analytical response can be implemented in practice. In the embedded model, the thin film is treated as a section of transmission line, whose admittance matrix is used to describe the frequency response of the thin film. The admittance matrix is manipulated by expanding the constituent cotangent and cosecant functions analytically, and then transforming them from the frequency domain to the time domain using the inverse Z transform and general digital filter theory. In this way the frequency responses of the thin film are successfully embedded into the TLM algorithm. The embedded thin film model can be applied to both single and multiple thin film layers. The embedded thin film model has been implemented in the one-dimensional (1D) and two-dimensional (2D) TLM method in the thesis. In the 1D TLM method, the embedded thin film model is used to investigate the reflection and transmission properties of lossy,anisotropic and lossless thin films, e.g. carbon fibre composite (CFC) panels, titanium panels, antireflection (AR) coatings and fibre Bragg gratings (FBG). The shielding performance of CFC panels is also discussed. In the 2D TLM method, the embedded thin film model is extended to model arbitrary excitations and curved thin films. The electromagnetic behaviour of infinitely long CFC panels with oblique incidence and a CFC panel of finite length with a point source excitation are studied using the embedded thin film model. The resonant effects of CFC circular and elliptical resonators and the shielding performance of a CFC airfoil with the profile of NACA2415 are investigated using the embedded curved thin film model. In addition, the effects of small gaps in the airfoil structure on the shielding performance are also reported. All the examples discussed in the thesis have validated the accuracy, stability, convergence and efficiency of the embedded thin film model developed. At the same time, the embedded thin film model has been proven to have the advantage of significantly saving computational overheads