In this thesis, we discuss the development, implementation and testing of a piecewise linear (PWL) continuous Galerkin finite element method applied to the threedimensional diffusion equation. This discretization is particularly interesting because it discretizes the diffusion equation on an arbitrary polyhedral mesh. We implemented our method in the KULL software package being developed at Lawrence Livermore National Laboratory. This code previously utilized Palmer's method as its diffusion solver, which is a finite volume method that can produce an asymmetric coefficient matrix. We show that the PWL method produces a symmetric positive definite coefficient matrix that can be solved more efficiently, while retaining the accuracy and robustness of Palmer's method. Furthermore, we show that in most cases Palmer's method is actually a non-Galerkin PWL finite element method. Because the PWL method is a Galerkin finite element method, it has a firm theoretical background to draw from. We have shown that the PWL method is a well-posed discrete problem with a second-order convergence rate. We have also performed a simple mode analysis on the PWL method and Palmer's method to compare the accuracy of each method for a certain class of problems. Finally, we have run a series of numerical tests to uncover more properties of both the PWL method and Palmer's method. These numerical results indicate that the PWL method, partially due to its symmetric matrix, is able to solve large-scale diffusion problems very efficiently.

In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiativetransfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

In Taiwan, a motorcycle is the most important and general transportation. It is no denying that wearing a motorcycle helmet could prevent the rider from head injuries in the accidents. However, the ventilation of helmets still has to be improved. This study aims to set several ventilation channels in the energy absorption liner. They apply the Venturi effect to increase the ventilation of helmets. But it may affect the protection performance of helmet. The purpose of this study is to estimate the protective ability of the ventilative helmet. Therefore, the various ventilative helmets are designed by the computer-aided design software SolidWorks, and simulations of the impact test of the helmet are investigated by the finite element analysis software ANSYS/LS-DYNA. In addition, the effect of using different foam material is also discussed in this study.

In the past ten years, various sewage treatment technologies have got extensive and profound studying in the field of water pollution control in Taiwan. In each unit apparatus of the sewage disposal system, a lamella separator as the sewage treatment facility, is an important link in the structure, has irreplaceable functions. This research investigated the lamella separator structure by means of the static analysis, add factors of earthquake, and typhoon. To achieve the purpose, the researcher used the computer-aided design software Solidworks to set up this structure model. After that, he used finite element analysis software, ANSYS, to analyze the structure. This research simulated in three situations. In static, earthquake, and typhoon analysis, the researcher found the stress of the original modal is over the yielding stress of materials. So, the researcher modified the support of a model to reduce the stress. Generally, the researcher hoped that this study could provide helpful references for designers¡¦ relevant studies on lamella separator structure in the future.

This research investigates the stress anslysis of a tower skirt support respectively by the earthquake and the wind pressure loading. The researcher used the computer-aided design software Solidworks to set up the tower model and he used finite element software ANSYS to analyze the structure. This study aims to analyze the safety of a tower support for different models. By the finite element analysis, this study found the largest displacement of tower, the von Mises stresses, and the safety factor for the skirt support. Among them, the butted-flared skirt support has the smallest displacement. According to the analysis result, the empty crate type design of skirt support revealed the safety factor of stress greater than two, which ensure that the equipment safety and material-savings. It is expected the study findings can provide a reference for designing or repairing a tower skirt support.

Thesis (M. Phil.)--University of Hong Kong, 1989.

Thesis--M. Phil., University of Hong Kong, 1984.

Thesis--Ph. D., University of Hong Kong, 1986.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 68-73).

Thesis (Ph. D.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 145-149).