A time-domain finite element method for seakeeping and wave resistance problems

El objetivo de la tesis es la investigación de algoritmos numéricos para el desarrollo de herramientas numéricas para la simulación de problemas tanto de comportamiento en la mar como de resistencia al avance de buques y estructuras flotantes. La primera herramienta desarrollada resuelve el problema de difracción y radiación de olas. Se basan en el método de los elementos finitos (MEF) para la resolución de la ecuación de Laplace, así como en esquemas basados en MEF, integración a lo largo de líneas de corriente, y en diferencias finitas desarrollados para la condición de superficie libre. Se han desarrollado herramientas numéricas para la resolución de la dinámica de sólido rígido en sistemas multicuerpos con ligaduras. Estas herramientas han sido integradas junto con la herramienta de resolución de olas difractadas y radiadas para la resolución de problemas de interacción de cuerpos con olas. También se han diseñado algoritmos de acoplamientos con otras herramientas numéricas para la resolución de problemas multifísica. En particular, se han realizado acoplamientos con una herramienta numérica basada de cálculo de estructuras con MEF para problemas de interacción fluido-estructura, otra de cálculo de líneas de fondeo, y con una herramienta numérica de cálculo de flujos en tanques internos para problemas acoplados de comportamiento en la mar con “sloshing”. Se han realizado simulaciones numéricas para la validación y verificación de los algoritmos desarrollados, así como para el análisis de diferentes casos de estudio con aplicaciones diversas en los campos de la ingeniería naval, oceánica, y energías renovables marinas. ABSTRACT The objective of this thesis is the research on numerical algorithms to develop numerical tools to simulate seakeeping problems as well as wave resistance problems of ships and floating structures. The first tool developed is a wave diffraction-radiation solver. It is based on the finite element method (FEM) in order to solve the Laplace equation, as well as numerical schemes based on FEM, streamline integration, and finite difference method tailored for solving the free surface boundary condition. It has been developed numerical tools to solve solid body dynamics of multibody systems with body links across them. This tool has been integrated with the wave diffraction-radiation solver to solve wave-body interaction problems. Also it has been tailored coupling algorithms with other numerical tools in order to solve multi-physics problems. In particular, it has been performed coupling with a MEF structural solver to solve fluid-structure interaction problems, with a mooring solver, and with a solver capable of simulating internal flows in tanks to solve couple seakeeping-sloshing problems. Numerical simulations have been carried out to validate and verify the developed algorithms, as well as to analyze case studies in the areas of marine engineering, offshore engineering, and offshore renewable energy.

Estudio de una metodología de software para la predicción y análisis del balance paramétrico de buques para su aplicación en los criterios de estabilidad de segunda generación

El objetivo de ésta tesis es estudiar cómo desarrollar una aplicación informática que implemente algoritmos numéricos de evaluación de características hidrodinámicas de modelos geométricos representativos de carenas de buques. Se trata de especificar los requisitos necesarios que debe cumplir un programa para informático orientado a dar solución a un determinado problema hidródinámico, como es simular el comportamiento en balance de un buque sometido a oleaje, de popa o proa. una vez especificada la aplicación se realizará un diseño del programa; se estudiarán alternativas para implementar la aplicación; se explicará el proceso que ha de seguirse para obtener la aplicación en funcionamiento y se contrastarán los resultados obtenidos en la medida que sea posible. Se pretende sistematizar y sintetizar todo el proceso de desarrollo de software, orientado a la simulación del comportamiento hidrodinámico de un buque, en una metodología que se pondrá a disposición de la comunidad académica y científica en la forma que se considere más adecuada. Se trata, por tanto, de proponer una metodología de desarrollo de software para obetener una aplicación que facilite la evaluación de diferentes alternativas de estudio variando parámetros relativos al problema en estudio y que sea capaz de proporcionar resultados para su análisis. Así mismo se incide en cómo ha de conducirse en el proceso para que dicha aplicación pueda crecer, incorporando soluciones existentes no implementadas o nuevas soluciones que aparezcan en este ámbito de conocimiento. Como aplicación concreta de la aplicación se ha elegido implementar los algoritmos necesarios para evaluar la aparición del balance paramétrico en un buque. En el análisis de éste problema se considera de interés la representación geométrica que se hace de la carena del buque. Además de la carena aparecen otros elementos que tienen influencia determinante en éste estudio, como son las situación de mar y las situaciones de carga. Idealmente, el problema sería resuelto si se consiguiera determinar el ángulo de balance que se produce al enfrentar un buque a las diferentes condiciones de mar. Se pretende preparar un programa utilizando el paradigma de la orientación a objetos. Considero que es la más adecuada forma de modularizar el programa para poder utilizar diferentes modelos de una misma carena y así comparar los resultados de la evaluación del balance paramétrico entre sí. En una etapa posterior se podrían comparar los resultados con otros obtenidos empíricamente. Hablo de una nueva metodología porque pretendo indicar cómo se ha de construir una aplicación de software que sea usable y sobre la que se pueda seguir desarrollando. Esto justifica la selección del lenguaje de programación C++. Se seleccionará un núcleo geométrico de software que permita acoplar de forma versátil los distintos componentes de software que van a construir el programa. Este trabajo pretende aplicar el desarrollo de software a un aspecto concreto del área de conocimiento de la hidrodinámica. No se pretende aportar nuevos algoritmos para resolver problemas de hidrodinámica, sino diseñar un conjunto de objetos de software que implementen soluciones existentes a conocidas soluciones numéricas a dichos problemas. Se trata fundamentalmente de un trabajo de software, más que de hidrodinámica. Lo que aporta de novedad es una nueva forma de realizar un programa aplicado a los cálculos hidrodinámicos relativos a la determinación del balance paramétrico, que pueda crecer e incorporar cualquier novedad que pueda surgir más adelante. Esto será posible por la programación modular utilizada y los objetos que representan cada uno de los elementos que intervienen en la determinación del balance paramétrico. La elección de aplicar la metodología a la predicción del balance paramétrico se debe a que este concepto es uno de los elementos que intervienen en la evaluación de criterios de estabilidad de segunda generación que estan en estudio para su futura aplicación en el ámbito de la construcción naval. Es por tanto un estudio que despierta interés por su próxima utilidad. ABSTRACT The aim of this thesis is to study how to develop a computer application implementing numerical algorithms to assess hydrodynamic features of geometrical models of vessels. It is therefore to propose a methodology for software development applied to an hydrodynamic problem, in order to evaluate different study alternatives by varying different parameters related to the problem and to be capable of providing results for analysis. As a concrete application of the program it has been chosen to implement the algorithms necessary for evaluating the appearance of parametric rolling in a vessel. In the analysis of this problem it is considered of interest the geometrical representation of the hull of the ship and other elements which have decisive influence in this phenomena, such as the sea situation and the loading condition. Ideally, the application would determine the roll angle that occurs when a ship is on waves of different characteristics. It aims to prepare a program by using the paradigm of object oriented programming. I think it is the best methodology to modularize the program. My intention is to show how face the global process of developing an application from the initial specification until the final release of the program. The process will keep in mind the spefici objetives of usability and the possibility of growing in the scope of the software. This work intends to apply software development to a particular aspect the area of knowledge of hydrodynamics. It is not intended to provide new algorithms for solving problems of hydrodynamics, but designing a set of software objects that implement existing solutions to these problems. This is essentially a job software rather than hydrodynamic. The novelty of this thesis stands in this work focuses in describing how to apply the whole proccess of software engineering to hydrodinamics problems. The choice of the prediction of parametric balance as the main objetive to be applied to is because this concept is one of the elements involved in the evaluation of the intact stability criteria of second generation. Therefore, I consider this study as relevant usefull for the future application in the field of shipbuilding.

Processing and rendering of Fourier domain optical coherence tomography images at a line rate over 524 kHz using a graphics processing unit

In Fourier domain optical coherence tomography (FD-OCT), a large amount of interference data needs to be resampled from the wavelength domain to the wavenumber domain prior to Fourier transformation. We present an approach to optimize this data processing, using a graphics processing unit (GPU) and parallel processing algorithms. We demonstrate an increased processing and rendering rate over that previously reported by using GPU paged memory to render data in the GPU rather than copying back to the CPU. This avoids unnecessary and slow data transfer, enabling a processing and display rate of well over 524,000 A-scan/s for a single frame. To the best of our knowledge this is the fastest processing demonstrated to date and the first time that FD-OCT processing and rendering has been demonstrated entirely on a GPU.

Key Agreement Protocol (KAP) Based on Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Asymmetric Cipher Protocol Using Decomposition Problem

The asymmetric cipher protocol based on decomposition problem in matrix semiring M over semiring of natural numbers N is presented. The security parameters are defined and preliminary security analysis is presented.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.

Modeling of a Heat-Induced Buckling of Plates Using the Mesh-free Method

In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.

The SUGAR Toolbox - Version 7

The SUGAR Toolbox contains scripts coded in MATLAB for calculating various thermodynamic, kinetic, and geologic properties of substances occurring in the marine environment, particularly gas hydrate and seep systems. Brief descriptions of the toolbox scripts and some notes on the underlying basic theory as well as tables of additional property values can be found in the accompanying documentation.

Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Optimal impulsive collision avoidance in low earth orbit

This paper presents a high-accuracy fully analytical formulation to compute the miss distance and collision probability of two approaching objects following an impulsive collision avoidance maneuver. The formulation hinges on a linear relation between the applied impulse and the objects? relative motion in the b-plane, which allows one to formulate the maneuver optimization problem as an eigenvalue problem coupled to a simple nonlinear algebraic equation. The optimization criterion consists of minimizing the maneuver cost in terms of delta-V magnitude to either maximize collision miss distance or to minimize Gaussian collision probability. The algorithm, whose accuracy is verified in representative mission scenarios, can be employed for collision avoidance maneuver planning with reduced computational cost when compared with fully numerical algorithms.

Meshfree Method for Prediction of Thermal Properties of Porous Ceramic Materials

In the presented thesis work, meshfree method with distance fields is applied to create a novel computational approach which enables inclusion of the realistic geometric models of the microstructure and liberates Finite Element Analysis(FEA) from thedependance on and limitations of meshing of fine microstructural feature such as splats and porosity.Manufacturing processes of ceramics produce materials with complex porosity microstructure.Geometry of pores, their size and location substantially affect macro scale physical properties of the material. Complex structure and geometry of the pores severely limit application of modern Finite Element Analysis methods because they require construction of spatial grids (meshes) that conform to the geometric shape of the structure. As a result, there are virtually no effective tools available for predicting overall mechanical and thermal properties of porous materials based on their microstructure. This thesis is a separate handling and controls of geometric and physical computational models that are seamlessly combined at solution run time. Using the proposedapproach we will determine the effective thermal conductivity tensor of real porous ceramic materials featuring both isotropic and anisotropic thermal properties. This work involved development and implementation of numerical algorithms, data structure, and software.

Parallel algorithms of the Purcell method for direct solution of linear systems

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.