A one-dimensional model of a heterogeneous material consisting of a matrix with embedded separated particles is considered, and the melting or solidification of the particles is investigated. The matrix is in imperfect contact with the particles, and the lumped capacity approximation applies to each individual particle. Heat is generated inside the particles or is transferred from the matrix to the particles coupled through a contact conductance. The matrix is not allowed to change phase and energy is either generated inside the matrix or transferred from the boundaries, which is initially conducted through the matrix material. The physical model of this coupled, two-step heat transfer process is solved using the energy method. The investigation is conducted in several phases using a building block approach. First, a lumped capacity system during phase transition is studied, then a one-dimensional homogeneous material during phase change is investigated, and finally the one-dimensional heterogeneous material is analyzed. A numerical solution based on the finite difference method is used to solve the model equations. This method allows for any kind of boundary conditions, any combination of material properties, particle sizes and contact conductance. In addition, computer programs, using Mathematica, are developed for the lumped capacity system, homogeneous material, and heterogeneous material. Results show the effects of control volume thickness, time step, contact conductance, material properties, internal sources, and external sources. / Master of Science

Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters. / Master of Science

Today, heterogeneous computing has truly reshaped the way scientists think and approach high-performance computing (HPC). Hardware accelerators such as general-purpose graphics processing units (GPUs) and Intel Many Integrated Core (MIC) architecture continue to make in-roads in accelerating large-scale scientific applications. These advancements, however, introduce new sets of challenges to the scientific community such as: selection of best processor for an application, effective performance optimization strategies, maintaining performance portability across architectures etc. In this thesis, we present our techniques and approach to address some of these significant issues. Firstly, we present a fully automated approach to project the relative performance of an OpenCL program over different GPUs. Performance projections can be made within a small amount of time, and the projection overhead stays relatively constant with the input data size. As a result, the technique can help runtime tools make dynamic decisions about which GPU would run faster for a given kernel. Usage cases of this technique include scheduling or migrating GPU workloads over a heterogeneous cluster with different types of GPUs. We then present our approach to accelerate a seismology modeling application that is based on the finite difference method (FDM), using MPI and CUDA over a hybrid CPU+GPU cluster. We describe the generic computational complexities involved in porting such applications to the GPUs and present our strategy of efficient performance optimization and characterization. We also show how performance modeling can be used to reason and drive the hardware-specific optimizations on the GPU. The performance evaluation of our approach delivers a maximum speedup of 23-fold with a single GPU and 33-fold with dual GPUs per node over the serial version of the application, which in turn results in a many-fold speedup when coupled with the MPI distribution of the computation across the cluster. We also study the efficacy of GPU-integrated MPI, with MPI-ACC as an example implementation, in a seismology modeling application and discuss the lessons learned. / Master of Science

For realistic predictions of vehicle performance in off-road conditions, it is critical to incorporate in the simulation accurate representations of the variability of the terrain profile. It is not practically feasible to measure the terrain at a sufficiently large number of points, or, if measured, to use such data directly in the simulation. Dedicated modeling techniques and computational methods that realistically and efficiently simulate off-road operating conditions are thus necessary. Many studies have been recently conducted to identify effective and appropriate ways to reduce experimental data in order to preserve only essential information needed to re-create the main terrain characteristics, for future use. This thesis focuses on modeling terrain profiles using the finite difference approach for solving linear second-order stochastic partial differential equations. We currently use this approach to model non-stationary terrain profiles in two dimensions (i.e., surface maps). Certain assumptions are made for the values of the model coefficients to obtain the terrain profile through the fast computational approach described, while preserving the stochastic properties of the original terrain topology. The technique developed is illustrated to recreate the stochastic properties of a sample of terrain profile measured experimentally. To further analyze off-road conditions, stochastic soil properties are incorporated into the terrain topology. Soil models can be developed empirically by measuring soil data at several points, or they can be created by using mathematical relations such as the Bekker's pressure-sinkage equation for homogeneous soils. In this thesis, based on a previously developed stochastic soil model, the polynomial chaos method is incorporated in the soil model. In a virtual proving ground, the wheel and soil interaction has to be simulated in order to analyze vehicle maneuverability over different soil types. Simulations have been created on a surface map for different case studies: stepping with a rigid plate, rigid wheel and flexible wheel, and rolling of a rigid wheel and flexible wheel. These case studies had various combinations of stochastic or deterministic terrain profile, stochastic or deterministic soil model, and an object to run across the surface (e.g., deterministic terrain profile, stochastic soil model, rolling rigid wheel). This thesis develops a comprehensive terrain and soil simulation environment for off-road mobility studies. Moreover, the technique developed to simulate stochastic terrain profile can be employed to simulate other stochastic systems modeled by PDEs. / Master of Science

The goal of this thesis is to introduce the finite difference method (FDM) adjusted for usage in modeling of sound propagation, and other approaches that are used together with this method. These approaches include selective filtering and time integration using the Runge-Kutta method, which has low computer memory requirements. An important topic in modeling sound propagation are boundary conditions. The thesis examines and verifies several types of boundary conditions. Included in the thesis are solutions to example problems implemented in Matlab.

The world population is expected to increase to approximately 11 billion by 2100. The ageing population (aged 60 and over) is projected to exceed the number of children in 2047. This will be a situation without precedent. The number of citizens with disorders of old age like Dementia will rise to 115 million worldwide by 2050. The estimated cost of Dementia will also increase, from $604 billion in 2010, to $1,117 billion by 2030. At the same time, medical expertise, evidence-driven policymaking and commissioning of services are increasingly evolving the definitive architecture of comprehensive long-term care to account for these changes. Technological advances, such as those provided by computational science and biomedical engineering, will allow for an expansion in our ability to model and simulate an almost limitless variety of complex problems that have long defied traditional methods of medical practice. Numerical methods and simulation offer the prospect of improved clinically relevant predictive information, and of course optimisation, enabling more efficient use of resources for designing treatment protocols, risk assessment and urgently needed management of a long term care system for a wide spectrum of brain disorders. Within this paradigm, the importance of the relationship of senescence of cerebrospinal fluid transport to dementia in the elderly make the cerebral environment notably worthy of investigation through numerical and computational modelling. Hydrocephalus can be succinctly described as the abnormal accumulation (imbalance between production and circulation) of cerebrospinal fluid (CSF) within the brain. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between cerebral fluid production, transport and drainage. The current state of knowledge about hydrocephalus, and more broadly integrative cerebral dynamics and its associated constitutive requirements, advocates that poroelastic theory provides a suitable framework to better understand the disease. In this work, Multiple-network poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement in various scales within the cerebral environment. The model is discretised in a variety of formats, through the established finite difference method, finite difference – finite volume coupling and also the finite element method. Both chronic and acute hydrocephalus was investigated in a variety of settings, and accompanied by emerging surgical techniques where appropriate. In the coupled finite difference – finite volume model, a key novelty was the amalgamation of anatomically accurate choroid plexuses with their feeding arteries and a simple relationship relaxing the constraint of a unique permeability for the CSF compartment. This was done in order to account for Aquaporin-4 sensitisation. This model is used to demonstrate the impact of aqueductal stenosis and fourth ventricle outlet obstruction. The implications of treating such a clinical condition with the aid of endoscopic third (ETV) and endoscopic fourth ventriculostomy (EFV) are considered. It was observed that CSF velocity in the aqueduct, along with ventricular displacement, CSF pressure, wall shear stress and pressure difference between lateral and fourth ventricles increased with applied stenosis. The application of ETV reduced the aqueductal velocity, ventricular displacement, CSF pressure, wall shear stress and pressure difference within nominal levels. The greatest reversal of the effects of atresia come by opting for ETV rather than the more complicated procedure of EFV. For the finite difference model incorporating nonlinear permeability, qualitatively similar results were obtained in comparison to the pertinent literature, however, there was an overall amplification of ventriculomegaly and transparenchymal pressure difference using this model. A quantitative and qualitative assessment is made of hydrocephalus cases involving aqueductal stenosis, along with the effects to CSF reabsorption in the parenchyma and subarachnoid space. The finite element discretisation template produced for the n^th- dimensional transient MPET system allowed for novel insight into hydrocephalus. In the 1D formulation, imposing the breakdown of the blood-CSF barrier responsible for clearance resulted in an increase in ventricular displacement, transparenchymal venous pressure gradient and transparenchymal CSF pressure gradient, whilst altering the compliance proved to markedly alter the rate of change of displacement and CSF pressure gradient. The influence of Poisson's ratio was investigated through the use of the dual-grid solver in order to distinguish between possible over or under prediction of the ventricular displacement. In the 2D model based on linear triangles, the importance of the MPET boundary conditions is acknowledged, along with the quality of the underlying mesh. Interesting results include that the fluid content is highest in the periventricular region and the skull, whilst after longer time scales, the peak CSF content becomes limited to the periventricular region. Venous fluid content is heavily influenced by the Biot-Willis constant, whilst both the venous and CSF/ISF compartments show to be strongly influenced by breakdown in the blood-CSF barrier. Increasing the venous compliance effects the arterial, capillary and venous compartments. Decreasing the venous compliance shows an accumulation of fluid, possibly helping to explain why the ventricles can be induced to compress rather than expand under decreased compliance. Finally, a successful application of the 3D-MPET template is shown for simple geometries. It is envisaged that future observations into the biology of cerebral fluid flow (such as perivascular CSF-ISF fluid exchange) and its interaction with the surrounding parenchyma, will demand the evolution of the MPET model to reach a level of complexity that could allow for an experimentally guided exploration of areas that would otherwise prove too intricate and intertwined under conventional settings.

Este trabalho apresenta parte de um sistema de simulação integrado para escoamento de fluido incompressível bidimensional em malhas não estruturadas denominado UmFlow-2D. O sistema consiste de três módulos: um módulo modelador, um módulo simulador e um módulo visualizador. A parte do sistema apresentado neste trabalho é o módulo simulador. Este módulo, implementa as equações de Navier-Stokes. As equações governantes são discretizadas pelo método de diferenças finitas generalizadas e os termos convectivos pelo método semi-lagrangeano. Um método de projeção é empregado para desacoplar as componentes da velocidade e pressão. O gerenciamento da malha, não estruturada é feito pela estrutura de dados SHE. Os resultados numéricos obtidos pelo UmFlow-2D são comparados com soluções analíticas e soluções numéricas de outros trabalhos. / This work presents an integratc simulation system, called UmFlow-2D, wich aims a,t simulating two-dimensional íncompressible fluid flow using unstructed mesh. The system is divided three modules: modeling module, simulation module and visualization module. In this work we present the simulation module. The simulation module implements the Navier-Stokes equation. The governing equations are discretized by a generalized flnite dillerence method and the convective terms by semi-lagrangean method. A projection method is employed to uncouple the velocity componentes and pressure. The management at the unstructed mesh is ready using a data structure called SHE. The numérica! results are compared with analytical solutions and numerical simulations of other works.

Submitted by Maria Cristina (library@lncc.br) on 2017-08-14T19:07:20Z No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-08-14T19:07:34Z (GMT) No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) / Made available in DSpace on 2017-08-14T19:07:45Z (GMT). No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) Previous issue date: 2016-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes) / Wave propagation modeling is a challenging problem with many important practical applications in engineering and applied sciences. These applications include the modeling in acoustic, scattering, vibration, structural dynamic response, earthquake, seismic, electromagnetism, photonic, and so on. In fluid-structure modeling, the applications include, for example, simulations in aircraft, rockets, turbines, marine structures, storage tanks, dams, suspension bridges and noise reduction. Our interest is the development of numerical methods to accurately solving time-harmonic wave problems. In this thesis, we propose finite difference and finite element methods to solve the acoustic and elastic problems and a coupled acoustic fluid-structure problem. We also develop a numerical model to simulate hyperthermia therapy, based on topological derivatives and on a stabilized hybrid method. / Modelagem em propagação de ondas é um problema desafiador, com muitas aplicações práticas importantes em engenharia e ciências aplicadas. Estas aplicações incluem a modelagem em acústica, dispersão, vibração, resposta dinâmica estrutural, terremoto, sísmica, eletromagnetismo, fotônica, e assim por diante. Em modelagem de fluido-estrutura, as aplicações incluem simulações em aviões, foguetes, turbinas, estruturas marítimas, tanques de armazenamento, barragens e pontes suspensas, redução de ruído, por exemplo. Nosso interesse é o desenvolvimento de métodos numéricos para resolver precisamente problemas de ondas harmônicas no tempo. Nesta tese consideramos métodos de diferenças finitas e elementos finitos para resolver problemas acústicos e elásticos e um problema acoplado de fluido-estrutura acústica. Também desenvolvemos um modelo numérico para simular terapia por hipertermia, baseado em derivadas topológicas e um método híbrido estabilizado.

"Material property estimation method is developed with 1-D heat conduction model and bounding exercise for Fire Dynamics Simulator (FDS) analysis. The purpose of this study is to develop an unsophisticated tool to convert small scale cone calorimeter data into input data that can be used in computational fluid dynamics (CFD) models to predict flame spread. Specific interests of input data for FDS in this study include thermal conductivity, specific heat, pre exponential factor, activation energy, heat of vaporization. The tool consists of two objects; 1-D model and bounding exercise. Main structure of the model is based on one of the thermal boundary conditions in the FDS, named as “Pyrolysis Model, Thermally-Thick Solid”, in which pyrolysis flux occurs on the surface of the object under radiant heat flux. This boundary condition is adopted because it has the best characteristics in the dynamics of modeling which are subject to our interests. The structure of the model is simple and concise. For engineering point of view, a practical model ought to have such simplicity that saves time and effort. Pyrolysis model in FDS meets this requirement. It is also a part of reason that this study is to develop a computational model which converts a set of data from the cone calorimeter test to a set of input data for FDS. A pyrolysis term on a surface of an object in this boundary condition will be playing an important role regarding a surface temperature and a mass loss rate of the object. Bounding exercise is introduced to guide proper outcome out of the modeling. Prediction of the material properties from the simulation is confirmed by the experimental data in terms of surface temperature history and mass loss rate under the bounding exercise procedure. For the cone calorimeter, thirteen different materials are tested. Test materials vary with their material composition such as thermoplastics, fiber reinforced plastics (FRP), and a wood. Throughout the modeling fed by a set of the cone calorimeter test data, estimated material properties are provided. So called “Bounding Exercise” is introduced here to draw the estimated material properties. Bounding exercise is a tool in order to guide the material property estimation procedure. Three sets of properties (Upper, Standard and Lower) are derived from the boundary exercise as recommended material properties. From the modeling results, PMMA shows the best agreement regarding the estimated material properties compared with already known results from the references. Wood indicates, however, somewhat different results, in which the mass loss rate takes a peak around the ignition and decreases sharply. This burning behavior can not be predicted using the “Pyrolysis Model”. The model in this study does not account so called “Charring Behavior” that a charring layer toward a surface or difference between a charred density in a charring layer and a normal density in a virgin layer of a wood. These factors result in a discrepancy of the estimated material properties with the reference data. Unlike PMMA and wood, FRP materials show a unique ignition characteristic. Mass loss rate history from some FRP materials indicate more a thermoplastic burning behavior and other materials tend to char. In addition there are few known material property data for theses materials and it is difficult to verify the results from this study with pre-existing data. Some plastic samples also indicate difficulties of the modeling. Because some samples melt and disfigure during the test, one dimensional heat transfer boundary condition is no longer applicable. Each bounding exercise results are fully examined and analyze in Chapter 6. Some of limitations contain model’s structural limitation, in which the model is too simple for certain cases, as well as limitations of bounding exercise. Finally, recommendations are made for future work including upgraded model accountable for the pyrolysis of charring material and FRP materials, data comparison with FDS results, and improved bounding exercise method."

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply. In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.