On meshless methods : a novel interpolatory method and a GPU-accelerated implementation
- Authors: Hamed, Maien Mohamed Osman
- Date: 2013
- Subjects: Engineering mathematics , Numerical analysis
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10509 , http://hdl.handle.net/10948/d1018227
- Description: Meshless methods have been developed to avoid the numerical burden imposed by meshing in the Finite Element Method. Such methods are especially attrac- tive in problems that require repeated updates to the mesh, such as problems with discontinuities or large geometrical deformations. Although meshing is not required for solving problems with meshless methods, the use of meshless methods gives rise to different challenges. One of the main challenges associated with meshless methods is imposition of essential boundary conditions. If exact interpolants are used as shape functions in a meshless method, imposing essen- tial boundary conditions can be done in the same way as the Finite Element Method. Another attractive feature of meshless methods is that their use involves compu- tations that are largely independent from one another. This makes them suitable for implementation to run on highly parallel computing systems. Highly par- allel computing has become widely available with the introduction of software development tools that enable developing general-purpose programs that run on Graphics Processing Units. In the current work, the Moving Regularized Interpolation method has been de- veloped, which is a novel method of constructing meshless shape functions that achieve exact interpolation. The method is demonstrated in data interpolation and in partial differential equations. In addition, an implementation of the Element-Free Galerkin method has been written to run on a Graphics Processing Unit. The implementation is described and its performance is compared to that of a similar implementation that does not make use of the Graphics Processing Unit.
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- Date Issued: 2013
User experience metrics for Dr Math
- Authors: Ngaye, Zonke
- Date: 2012
- Subjects: Mathematics -- Data processing , Mathematical models , Mathematics -- Study and teaching , Numerical analysis
- Language: English
- Type: Thesis , Masters , MTech
- Identifier: vital:9799 , http://hdl.handle.net/10948/d1012036 , Mathematics -- Data processing , Mathematical models , Mathematics -- Study and teaching , Numerical analysis
- Description: The purpose of this research study is to propose guidelines for providing a positive user experience for pupils using Dr Math®. User experience was found to have a positive impact on the acceptance and adoption of a product. Thus the proposed guidelines contribute in maximizing the adoption and acceptance of Dr Math® among pupils. This study begins with an introductory chapter that describes the problem that forms the basis for this research. The chapter defines the objectives that this study is intended to achieve in order to accomplish its ultimate goal. The methodology followed to conduct this research study as well as its scope are also defined here. The results from a preliminary survey revealed that despite its potential accessibility, Dr Math® has a low adoption rate. However, when compared to other mobile learning (m-learning) applications for mathematics learning, Dr Math® is more popular. Thus Dr Math® was selected as a case for study. Chapter 2 of this study provides a detailed description of Dr Math® as a local mobile application for mathematics learning. It was found that the affordability and accessibility of Dr Math® did not necessarily imply a high adoption rate. There are various possible barriers to its low adoption. User experience (UX), which is the focus of this study, is one of them. Thus, a subsequent chapter deals with UX. Chapter 3 discusses UX, its scope, components and definition and places particular emphasis on its significance in the success of any product. The chapter also highlights the characteristics of a positive UX and the importance of designing for this outcome. In Chapter 4, a discussion and justification of the methodology used to conduct this research is discussed. This study primarily employs a qualitative inductive approach within an interpretivism paradigm. An exploratory single case study was used to obtain an in-depth analysis of the case. Data was collected using Dr Math® log files as a documentary source. Gathered data was then analysed and organized into themes and categories using qualitative content analysis as outlined in Chapter 5. Also the findings obtained from the results, which are mainly the factors that were found to have an impact on the user interaction with Dr Math®, are presented here. The identified factors served as a basis from which the guidelines presented in Chapter 6 were developed. Chapter 7 presents the conclusions and recommendations of the research. From both theoretical and empirical work, it was concluded that Dr Math® has the potential to improve mathematics learning in South Africa. Its adoption rate, however, is not satisfying: hence, the investigation of the factors impacting on the user interaction with Dr Math®, from which the proposed guidelines are based.
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- Date Issued: 2012