Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

Finding optimal alternatives based on efficient comparative preference inference

Choosing the right or the best option is often a demanding and challenging task for the user (e.g., a customer in an online retailer) when there are many available alternatives. In fact, the user rarely knows which offering will provide the highest value. To reduce the complexity of the choice process, automated recommender systems generate personalized recommendations. These recommendations take into account the preferences collected from the user in an explicit (e.g., letting users express their opinion about items) or implicit (e.g., studying some behavioral features) way. Such systems are widespread; research indicates that they increase the customers' satisfaction and lead to higher sales. Preference handling is one of the core issues in the design of every recommender system. This kind of system often aims at guiding users in a personalized way to interesting or useful options in a large space of possible options. Therefore, it is important for them to catch and model the user's preferences as accurately as possible. In this thesis, we develop a comparative preference-based user model to represent the user's preferences in conversational recommender systems. This type of user model allows the recommender system to capture several preference nuances from the user's feedback. We show that, when applied to conversational recommender systems, the comparative preference-based model is able to guide the user towards the best option while the system is interacting with her. We empirically test and validate the suitability and the practical computational aspects of the comparative preference-based user model and the related preference relations by comparing them to a sum of weights-based user model and the related preference relations. Product configuration, scheduling a meeting and the construction of autonomous agents are among several artificial intelligence tasks that involve a process of constrained optimization, that is, optimization of behavior or options subject to given constraints with regards to a set of preferences. When solving a constrained optimization problem, pruning techniques, such as the branch and bound technique, point at directing the search towards the best assignments, thus allowing the bounding functions to prune more branches in the search tree. Several constrained optimization problems may exhibit dominance relations. These dominance relations can be particularly useful in constrained optimization problems as they can instigate new ways (rules) of pruning non optimal solutions. Such pruning methods can achieve dramatic reductions in the search space while looking for optimal solutions. A number of constrained optimization problems can model the user's preferences using the comparative preferences. In this thesis, we develop a set of pruning rules used in the branch and bound technique to efficiently solve this kind of optimization problem. More specifically, we show how to generate newly defined pruning rules from a dominance algorithm that refers to a set of comparative preferences. These rules include pruning approaches (and combinations of them) which can drastically prune the search space. They mainly reduce the number of (expensive) pairwise comparisons performed during the search while guiding constrained optimization algorithms to find optimal solutions. Our experimental results show that the pruning rules that we have developed and their different combinations have varying impact on the performance of the branch and bound technique.

System operational costs reduction with non-conventional reactive power sources

Wind energy installations are increasing in power systems worldwide and wind generation capacity tends to be located some distance from load centers. A conflict may arise at times of high wind generation when it becomes necessary to curtail wind energy in order to maintain conventional generators on-line for the provision of voltage control support at load centers. Using the island of Ireland as a case study and presenting commercially available reactive power support devices as possible solutions to the voltage control problems in urban areas, this paper explores the reduction in total generation costs resulting from the relaxation of the operational constraints requiring conventional generators to be kept on-line near load centers for reactive power support. The paper shows that by 2020 there will be possible savings of 87€m per annum and a reduction in wind curtailment of more than a percentage point if measures are taken to relax these constraints.

Cash or non-cash: that is the question - the story of e-payment for social welfare in Ireland part 2

E-Government in its various forms and extensions, notably T-Government, is often presented as the panacea for resolving such complex social problems as social exclusion, lack of governance transparency, poor value for money and other ailments of modern societies. Yet, E-Government has not been adopted up to predicted levels. Many case studies investigating success factors, maturity models, and the application of acceptance models have been presented over the last 15 years, but a deep understanding of the potential impact and consequences of E-Government is still lacking. This is especially true for those initiatives that involve socio-economic and cultural contexts, which makes their evaluation and the prediction of their impact difficult. This paper reports on an on-going E-Government initiative in Ireland aimed at implementing E-payments for G2C, notably in the social welfare area. Three sets of personal surveys have been carried out to understand the perceived impact of governmental plans of moving from an almost fully cash-based payment system to a fully electronic based solution. Early results indicate that perceived pre-requisites for the planned change may be misleading. The impact on recipients’ lives cannot solely be measured in terms of economic gains: the consequences of such implementation may well reach further than expected.