A hybrid approach for resolving the electromagnetic fields inside a waveguide loaded with a lossy medium

In this work a novel hybrid approach is presented that uses a combination of both time domain and frequency domain solution strategies to predict the power distribution within a lossy medium loaded within a waveguide. The problem of determining the electromagnetic fields evolving within the waveguide and the lossy medium is decoupled into two components, one for computing the fields in the waveguide including a coarse representation of the medium (the exterior problem) and one for a detailed resolution of the lossy medium (the interior problem). A previously documented cell-centred Maxwell’s equations numerical solver can be used to resolve the exterior problem accurately in the time domain. Thereafter the discrete Fourier transform can be applied to the computed field data around the interface of the medium to estimate the frequency domain boundary condition in-formation that is needed for closure of the interior problem. Since only the electric fields are required to compute the power distribution generated within the lossy medium, the interior problem can be resolved efficiently using the Helmholtz equation. A consistent cell-centred finite-volume method is then used to discretise this equation on a fine mesh and the underlying large, sparse, complex matrix system is solved for the required electric field using the iterative Krylov subspace based GMRES iterative solver. It will be shown that the hybrid solution methodology works well when a single frequency is considered in the evaluation of the Helmholtz equation in a single mode waveguide. A restriction of the scheme is that the material needs to be sufficiently lossy, so that any penetrating waves in the material are absorbed.

A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

Exploring the role of the governing body (board) in information technology governance : a study of Australian universities

In this thesis, I advance the understanding of information technology (IT) governance research and corporate governance research by considering the question “How do boards govern IT?” The importance of IT to business has increased over the last decade, but there has been little academic research which has focused on boards and their role in the governance of IT (Van Grembergen, De Haes and Guldentops, 2004). Most of the research on information technology governance (ITG) has focused on advancing the understanding and measurement of the components of the ITG model (Buckby, Best & Stewart, 2008; Wilkin & Chenhall, 2010), a model recommended by the IT Governance Institute (2003) as ‘best practice’ for boards to use in governing IT. IT governance is considered to be the responsibility of the board and is said to form an important subset of an organisation’s corporate governance processes (Borth & Bradley, 2008). Boards need to govern IT as a result of the large capital investment in IT resources and high dependency on IT by organisations. Van Grembergen, De Haes and Guldentops (2004) and De Haes & Van Grembergen (2009) indicate that corporate governance matters are not able to be effectively discharged unless IT is being governed properly, and call for further specific research on the role of the board in ITG. Researchers also indicate that the link between corporate governance and IT governance has been neglected (Borth & Bradley, 2008; Musson & Jordan, 2005; Bhattacharjya & Chang, 2008). This thesis will address this gap in the ITG literature by providing the bridge between the ITG and corporate governance literatures. My thesis uses a critical realist epistemology and a mixed method approach to gather insights into my research question. In the first phase of my research I develop a survey instrument to assess whether boards consider the components of the ITG model in governing IT. The results of this first study indicated that directors do not conceptualise their role in governing IT using the elements of the ITG model. Thus, I moved to focus on whether prominent corporate governance theories might elucidate how boards govern IT. In the second phase of the research, I used a qualitative inductive case based study to assess whether agency, stewardship and resource dependence theories explain how boards govern IT in Australian universities. As the first in-depth study of university IT governance processes, my research contributes to the ITG research field by revealing that Australian university board governance of IT is characterized by a combination of agency theory and stewardship theory behaviours and processes. The study also identified strong links between a university’s IT structure and evidence of agency and stewardship theories. This link provides insight into the structures element of the emerging enterprise governance of IT framework (Van Grembergen, De Haes & Guldentops, 2004; De Haes & Van Grembergen, 2009; Van Grembergen & De Haes, 2009b; Ko & Fink, 2010). My research makes an important contribution to governance research by identifying a key link between corporate and ITG literatures and providing insight into board IT governance processes. The research conducted in my thesis should encourage future researchers to continue to explore the links between corporate and IT governance research.

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.