Dissertation (Ph.D.)--Worcester Polytechnic Institute. / Keywords: PIC, unstructured grid, plasma simulation. Includes bibliographical references (p.129-135).

This thesis considers the application of the type II third order WENO finite volume reconstruction for unstructured tetrahedral meshes proposed by Zhang and Shu in (CCP, 2009) and the third order multirate Runge-Kutta time-stepping to the solution of Maxwell's equations. The dependance of accuracy of the third order WENO scheme on the small parameter in the definition of non-linear weights is studied in detail for one-dimensional uniform meshes and numerical results confirming the theoretical analysis are presented for the linear advection equation. This analysis is found to be crucial in the design of the efficient three-dimensional WENO scheme, full details of which are presented. Several multirate Runge-Kutta (MRK) schemes which advance the solution with local time-steps assigned to different multirate groups are studied. Analysis of accuracy of three different MRK approaches for linear problems based on classic order-conditions is presented. The most flexible and efficient multirate schemes based on works by Tang and Warnecke (JCM, 2006) and Liu, Li and Hu (JCP, 2010) are implemented in three-dimensional finite volume time-domain (FVTD) method. The main characteristics of chosen MRK schemes are flexibility in defining the time-step ratios between multirate groups and consistency of the scheme. Various approaches to partition the three-dimensional computational domain into multirate groups to maximize the achievable speedup are discussed. Numerical experiments with three-dimensional electromagnetic problems are presented to validate the performance of the proposed FVTD method. Three-dimensional results agree with theoretical and numerical accuracy analysis performed for the one-dimensional case. The proposed implementation of multirate schemes demonstrates greater speedup than previously reported in literature. / February 2016

In today’s society, movies and videogames with a great deal of visual effects that contain objects that break, shatter or explode are popular. They are created from a number of different kinds of 3D programs and plugins. This time Autodesk Mayas nCloth is compared with the new built-in Digital Molecular Matter (DMM) Plugin to see which technique is easiest to use, as well as delivers the best result. A modeled sculpture was shattered using both nCloth and DMM and a set of predefined areas were studied. The results reveals that both techniques can be employed however the DMM technology has several advantages where less time consumption is one of them.

The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.

<p>  </p> <p>The development of a novel technique employing the use of a linear quadrupole ion trap mass spectrometer coupled to a Nd:YAG laser and a home-built fast reagent-mixing apparatus is detailed and used to detect the short-lived tetrahedral reaction intermediate of the reaction of acetyl chloride with ethanol in microdroplets. Additionally, tandem and high-resolution mass spectrometry is used to characterize potential precursors for solution-processed metal selenide semiconductors in order to determine a synthetic route to sulfur-free thin films. Lastly, Raman MCR (multivariate curve resolution) spectroscopy is used to study the binding-induced conformational change of 1-bromopropane upon binding to α-cyclodextrin as a model system to examine guest conformational changes upon binding to a host molecule.</p>

In this thesis, we present a simple and efficient \emph{a posteriori} error estimation procedure for a discontinuous finite element method applied to scalar first-order hyperbolic problems on structured and unstructured tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin orthogonality condition for the leading term of the discretization error and find basis functions spanning the error for several finite element spaces. We describe an implicit error estimation procedure for the leading term of the discretization error by solving a local problem on each tetrahedron. Numerical computations show that the implicit \emph{a posteriori} error estimation procedure yields accurate estimates for linear and nonlinear problems with smooth solutions. Furthermore, we show the performance of our error estimates on problems with discontinuous solutions. We investigate pointwise superconvergence properties of the discontinuous Galerkin (DG) method using enriched polynomial spaces. We study the effect of finite element spaces on the superconvergence properties of DG solutions on each class and type of tetrahedral elements. We show that, using enriched polynomial spaces, the discretization error on tetrahedral elements having one inflow face, is O(h^{p+2}) superconvergent on the three edges of the inflow face, while on elements with one inflow and one outflow faces the DG solution is O(h^{p+2}) superconvergent on the outflow face in addition to the three edges of the inflow face. Furthermore, we show that, on tetrahedral elements with two inflow faces, the DG solution is O(h^{p+2}) superconvergent on the edge shared by two of the inflow faces. On elements with two inflow and one outflow faces and on elements with three inflow faces, the DG solution is O(h^{p+2}) superconvergent on two edges of the inflow faces. We also show that using enriched polynomial spaces lead to a simpler{a posterior error estimation procedure. Finally, we extend our error analysis for the discontinuous Galerkin method applied to linear three-dimensional hyperbolic systems of conservation laws with smooth solutions. We perform a local error analysis by expanding the local error as a series and showing that its leading term is O( h^{p+1}). We further simplify the leading term and express it in terms of an optimal set of polynomials which can be used to estimate the error. / Ph. D.

No / The need for greater energy efficiency has garnered increasing support for the use of fuel-cell technology, a prime example being the solid-oxide fuel cell1, 2. A crucial requirement for such devices is a good ionic (O2- or H+) conductor as the electrolyte3, 4. Traditionally, fluorite- and perovskite-type oxides have been targeted3, 4, 5, 6, although there is growing interest in alternative structure types for intermediate-temperature (400¿700 °C) solid-oxide fuel cells. In particular, structures containing tetrahedral moieties, such as La1-xCaxMO4-x/2(M=Ta,Nb,P) (refs 7,8), La1-xBa1+xGaO4-x/2 (refs 9,10) and La9.33+xSi6O26+3x/2 (ref. 11), have been attracting considerable attention recently. However, an atomic-scale understanding of the conduction mechanisms in these systems is still lacking; such mechanistic detail is important for developing strategies for optimizing the conductivity, as well as identifying next-generation materials. In this context, we report a combined experimental and computational modelling study of the La1-xBa1+xGaO4-x/2 system, which exhibits both proton and oxide-ion conduction9, 10. Here we show that oxide-ion conduction proceeds via a cooperative 'cog-wheel'-type process involving the breaking and re-forming of Ga2O7 units, whereas the rate-limiting step for proton conduction is intra-tetrahedron proton transfer. Both mechanisms are unusual for ceramic oxide materials, and similar cooperative processes may be important in related systems containing tetrahedral moieties.

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes such estimators are known but they fail when applied to anisotropic meshes. Rectangular (or cuboidal) anisotropic meshes were already investigated. In this paper an error estimator is presented for tetrahedral or triangular meshes which offer a much greater geometrical flexibility.

Many architecure, medical and engineering applications need a spacial support for various numerical computations (i.e. FEM simulations). Tetrahedral meshes are one of perspective spatial representations for them. In this thesis, several possibilities of effective tetrahedral mesh representation for its generating and processing are described. A computer library for the mesh processing is proposed which can be characterized by memory  efficient imposition of the mesh while preserving the ability to apply topological and geometric algorithms effectively. The library is implemented in C++ language using templates. Time and space complexity of typical mesh operations is compared with CGAL library and according to measurements the proposed library has lower memory requirements than CGAL.

L'objectif principal de ce travail était l'étude systématique de plusieurs groupes de matériaux conducteurs protoniques: Gd₃₋ₓMeₓGaO₆₋₅ (Me = Ca²+, Sr²+), Ba₂Nb₁₋ₓY₁₊ₓO₆₋₅, et BaZr₀.₈₅Y₀.₁₅O₃₋₅ (BZY15). Nous avons développé une voie de synthèse pour chaque groupe de matériaux tels que le procédé de combustion sol-gel, la synthèse lyophilisation et le procédé de complexation de citrate-EDTA modifié des nanopoudres pures et des céramiques denses ont été obtenus après ces synthèses suives d'un processus de frittage classique. La structure et la composition des produits obtenues ont été caractérisées par diffraction des rayons X (XRD) et microscopie électronique à balayage (MEB). La variation de la conductivité en fonction de la température a été étudiée par spectroscopie d'impédance, ainsi que la dépendance en fonction de pO₂ et pH₂O. Pour la famille de Gd₃₋ₓMeₓGaO₆₋₅ (Me = Ca²+, Sr²+), nous avons étudié l'influence de la nature et la quantité de dopant sur les propriétés structurales et électriques. Les résultats indiquent une solution solide possible jusqu'à 10% de taux du substituant. Selon les observations au MEB, la taille des grains est augmente le taux de substitution. En ce qui concerne les propriétés électriques, nous avons constaté une augmentation de la conduction avec le taux de substitution. Tous les composés présentent une bonne stabilité en milieu humide, sous hydrogène et CO₂. Dans le cas des matériaux Ba₂Y₁₊ₓNb₁₋ₓO₆₋₅, les propriétés physico-chimiques des matériaux synthétisés ont été caractérisées par la diffraction des rayons X et par MEB. La taille moyenne des grains a considérablement augmenté avec l'augmentation du taux de Y³⁺. Les propriétés de conduction ont été légèrement améliorées avec la substitution partielle de niobium par l'yttrium. La stabilité de Ba₂Y₁₊ₓNb₁₋ₓO₆₋₅ composés a été étudiée sous différentes atmosphères et conditions. Les propriétés de conduction ionique restent modestes ce qui a été explique par des simulations de dynamique moléculaire. Enfin, nous avons étudié l'influence d'emploi d'un additif ZnO et NiO lors de la synthèse de BZY15, les adjuvants de frittage pouvant être utilisés pour abaisser la température de frittage. L'oxyde de zinc comme un adjuvant de frittage permet de diminuer de 300 °C la température de frittage et d'augmenter légèrement la conduction ionique. / The main objective of the present work was the systematic study of several groups of materials: Gd₃₋ₓMeₓGaO₆₋₅ (Me = Ca²+, Sr²+), Ba₂Nb₁₋ₓY₁₊ₓO₆₋₅, and BaZr₀.₈₅Y₀.₁₅O₃₋₅ (BZY15) as proton conductors. We developed a synthesis route for each group of materials such as sol-gel combustion method, freeze-drying synthesis and modified citrate-EDTA complexing method. Pure nanopowders and dense ceramics were obtained after these syntheses plus a classical sintering process. The structure and composition of the obtained products were characterized by X-ray diffraction (XRD) and scanning electron microscope (SEM). The temperature dependences of the conductivity were investigated by impedance spectroscopy as a function of pO₂ and pH₂O. For the family of Gd₃₋ₓMeₓGaO₆₋₅ (Me = Ca²+, Sr²+), we studied the influence of dopant nature and content on the structural and electrical properties. Results indicate that the substitution possible till 10 % of doping content. According to the SEM observations, the grain size is increased with increasing dopant content. Concerning electrical properties, we found an increase of conduction with increasing dopant content. All compounds present a good stability in humid, hydrogen and CO₂ containing atmosphere. In case of Ba₂Y₁₊ₓNb₁₋ₓO₆₋₅ materials, the physico-chemical properties of synthesized materials have been characterized by the XRD and SEM techniques. The average grain size increased significantly with increasing amount of Y³⁺. Conduction properties were slightly improved with the partial substitution of niobium by yttrium. The stability of Ba₂Y₁₊ₓNb₁₋ₓO₆₋₅ compounds was investigated under different atmospheres and conditions. The ionic conduction in this case is quite low, which has been explained by futher molecular dynamics simulations. Finally, we studied the influence of an ZnO and NiO additives on the sintering of BZY15, being these sintering aids used to lower the sintering temperature. Zinc oxide as a sintering aid lowers the sintering temperature by 300 °C and slightly increases the bulk and total conductivity of BZY15.