Integrating-factor-based 2-additive Runge-Kutta methods for advection-reaction-diffusion equations

There are three distinct processes that are predominant in models of flowing media with interacting components: advection, reaction, and diffusion. Collectively, these processes are typically modelled with partial differential equations (PDEs) known as advection-reaction-diffusion (ARD) equations. To solve most PDEs in practice, approximation methods known as numerical methods are used. The method of lines is used to approximate PDEs with systems of ordinary differential equations (ODEs) by a process known as semi-discretization. ODEs are more readily analysed and benefit from well-developed numerical methods and software. Each term of an ODE that corresponds to one of the processes of an ARD equation benefits from particular mathematical properties in a numerical method. These properties are often mutually exclusive for many basic numerical methods. A limitation to the widespread use of more complex numerical methods is that the development of the appropriate software to provide comparisons to existing numerical methods is not straightforward. Scientific and numerical software is often inflexible, motivating the development of a class of software known as problem-solving environments (PSEs). Many existing PSEs such as Matlab have solvers for ODEs and PDEs but lack specific features, beyond a scripting language, to readily experiment with novel or existing solution methods. The PSE developed during the course of this thesis solves ODEs known as initial-value problems, where only the initial state is fully known. The PSE is used to assess the performance of new numerical methods for ODEs that integrate each term of a semi-discretized ARD equation. This PSE is part of the PSE pythODE that uses object-oriented and software-engineering techniques to allow implementations of many existing and novel solution methods for ODEs with minimal effort spent on code modification and integration. The new numerical methods use a commutator-free exponential Runge-Kutta (CFERK) method to solve the advection term of an ARD equation. A matrix exponential is used as the exponential function, but CFERK methods can use other numerical methods that model the flowing medium. The reaction term is solved separately using an explicit Runge-Kutta method because solving it along with the diffusion term can result in stepsize restrictions and hence inefficiency. The diffusion term is solved using a Runge-Kutta-Chebyshev method that takes advantage of the spatially symmetric nature of the diffusion process to avoid stepsize restrictions from a property known as stiffness. The resulting methods, known as Integrating-factor-based 2-additive Runge-Kutta methods, are shown to be able to find higher-accuracy solutions in less computational time than competing methods for certain challenging semi-discretized ARD equations. This demonstrates the practical viability both of using CFERK methods for advection and a 3-splitting in general

Англійська мова для студентів електромеханічних спеціальностей

Навчальний посібник розрахований на студентів напряму підготовки 6.050702 Електромеханіка. Містить уроки, що структуровані за тематичними розділами, граматичний коментар, короткі англо-український і українсько- англійський словники та додатки, які спрямовані на закріплення загальних навичок володіння англійською мовою. Акцентований на ɨсобливості термінології, що застосовується у науково-технічній галузі, зокрема, в електромеханіці та виконання запропонованих завдань, що буде сприяти формуванню навичок перекладу з англійської та української мов, сприйняттю письмової та усної англійської мови, вмінню письмового викладення англійською мовою науково-технічних та інших текстів під час професійної діяльності, спілкуванню з професійних та загальних питань тощо

Computationally-efficient visual inertial odometry for autonomous vehicle

This thesis presents the design, implementation, and validation of a novel nonlinearfiltering based Visual Inertial Odometry (VIO) framework for robotic navigation in GPSdenied environments. The system attempts to track the vehicle’s ego-motion at each time instant while capturing the benefits of both the camera information and the Inertial Measurement Unit (IMU). VIO demands considerable computational resources and processing time, and this makes the hardware implementation quite challenging for micro- and nanorobotic systems. In many cases, the VIO process selects a small subset of tracked features to reduce the computational cost. VIO estimation also suffers from the inevitable accumulation of error. This limitation makes the estimation gradually diverge and even fail to track the vehicle trajectory over long-term operation. Deploying optimization for the entire trajectory helps to minimize the accumulative errors, but increases the computational cost significantly. The VIO hardware implementation can utilize a more powerful processor and specialized hardware computing platforms, such as Field Programmable Gate Arrays, Graphics Processing Units and Application-Specific Integrated Circuits, to accelerate the execution. However, the computation still needs to perform identical computational steps with similar complexity. Processing data at a higher frequency increases energy consumption significantly. The development of advanced hardware systems is also expensive and time-consuming. Consequently, the approach of developing an efficient algorithm will be beneficial with or without hardware acceleration. The research described in this thesis proposes multiple solutions to accelerate the visual inertial odometry computation while maintaining a comparative estimation accuracy over long-term operation among state-ofthe- art algorithms. This research has resulted in three significant contributions. First, this research involved the design and validation of a novel nonlinear filtering sensor-fusion algorithm using trifocal tensor geometry and a cubature Kalman filter. The combination has handled the system nonlinearity effectively, while reducing the computational cost and system complexity significantly. Second, this research develops two solutions to address the error accumulation issue. For standalone self-localization projects, the first solution applies a local optimization procedure for the measurement update, which performs multiple corrections on a single measurement to optimize the latest filter state and covariance. For larger navigation projects, the second solution integrates VIO with additional pseudo-ranging measurements between the vehicle and multiple beacons in order to bound the accumulative errors. Third, this research develops a novel parallel-processing VIO algorithm to speed up the execution using a multi-core CPU. This allows the distribution of the filtering computation on each core to process and optimize each feature measurement update independently. The performance of the proposed visual inertial odometry framework is evaluated using publicly-available self-localization datasets, for comparison with some other open-source algorithms. The results illustrate that a proposed VIO framework is able to improve the VIO’s computational efficiency without the installation of specialized hardware computing platforms and advanced software libraries

Error in the invariant measure of numerical discretization schemes for canonical sampling of molecular dynamics

Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many applications use MD to compute ensemble averages of molecular systems at constant temperature. Langevin dynamics approximates the effects of weakly coupling an external energy reservoir to a system of interest, by adding the stochastic Ornstein- Uhlenbeck process to the system momenta, where the resulting trajectories are ergodic with respect to the canonical (Boltzmann-Gibbs) distribution. By solving the resulting stochastic differential equations (SDEs), we can compute trajectories that sample the accessible states of a system at a constant temperature by evolving the dynamics in time. The complexity of the classical potential energy function requires the use of efficient discretization schemes to evolve the dynamics.In this thesis we provide a systematic evaluation of splitting-based methods for the integration of Langevin dynamics. We focus on the weak properties of methods for confiurational sampling in MD, given as the accuracy of averages computed via numerical discretization. Our emphasis is on the application of discretization algorithms to high performance computing (HPC) simulations of a wide variety of phenomena, where configurational sampling is the goal. Our first contribution is to give a framework for the analysis of stochastic splitting methods in the spirit of backward error analysis, which provides, in certain cases, explicit formulae required to correct the errors in observed averages. A second contribution of this thesis is the investigation of the performance of schemes in the overdamped limit of Langevin dynamics (Brownian or Smoluchowski dynamics), showing the inconsistency of some numerical schemes in this limit. A new method is given that is second-order accurate (in law) but requires only one force evaluation per timestep. Finally we compare the performance of our derived schemes against those in common use in MD codes, by comparing the observed errors introduced by each algorithm when sampling a solvated alanine dipeptide molecule, based on our implementation of the schemes in state-of-the-art molecular simulation software. One scheme is found to give exceptional results for the computed averages of functions purely of position

Finite-Time Thermodynamics

The theory around the concept of finite time describes how processes of any nature can be optimized in situations when their rate is required to be non-negligible, i.e., they must come to completion in a finite time. What the theory makes explicit is “the cost of haste”. Intuitively, it is quite obvious that you drive your car differently if you want to reach your destination as quickly as possible as opposed to the case when you are running out of gas. Finite-time thermodynamics quantifies such opposing requirements and may provide the optimal control to achieve the best compromise. The theory was initially developed for heat engines (steam, Otto, Stirling, a.o.) and for refrigerators, but it has by now evolved into essentially all areas of dynamic systems from the most abstract ones to the most practical ones. The present collection shows some fascinating current examples

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion