30 research outputs found

    Towards Faster-than-real-time Power System Simulation Using a Semi-analytical Approach and High-performance Computing

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    This dissertation investigates two possible directions of achieving faster-than-real-time simulation of power systems. The first direction is to develop a semi-analytical solution which represents the nonlinear dynamic characteristics of power systems in a limited time period. The second direction is to develop a parallel simulation scheme which allows the local numerical solutions of power systems to be developed independently in consecutive time intervals and then iteratively corrected toward the accurate global solution through the entire simulation time period. For the first direction, the semi-analytical solution is acquired using Adomian decomposition method (ADM). The ADM assumes the analytical solution of any nonlinear system can be decomposed into the summation of infinite analytical expressions. Those expressions are derived recursively using the system differential equations. By only keeping a finite number of those analytical expressions, an approximation of the analytical solution is yielded, which is defined as a semi-analytical solution. The semi-analytical solutions can be developed offline and evaluated online to facilitate the speedup of simulations. A parallel implementation and variable time window approach for the online evaluation stage are proposed in addition to the time performance analysis. For the second direction, the Parareal-in-time algorithm is tested for power system simulation. Parareal is essentially a multiple shooting method. It decomposes the simulation time into coarse time intervals and then fine time intervals within each coarse interval. The numerical integration uses a computational cheap solver on the coarse time grid and an expensive solver on the fine time grids. The solution within each coarse interval is propagated independently using the fine solver. The mismatch of the solution between the coarse solution and fine solution is corrected iteratively. The theoretical speedup can be achieved is the ratio of the coarse interval number and iteration number. In this dissertation, the Parareal algorithm is tested on the North American eastern interconnection system with around 70,000 buses and 5,000 generators

    Adomian Decomposition Method for Solving Higher Order Boundary Value Problems

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    In this paper, we present efficient numerical algorithms for the approximate solution of linear and non-linear higher order boundary value problems. Algorithms are, based on Adomian decomposition. Also, the Laplace Transformation with Adomian decomposition technique is proposed to solve the problems when Adomian series diverges. Three examples are given to illustrate the performance of each technique. Keyword: Higher order Singular boundary value problems, Adomian decomposition techniques, Laplace transformations

    An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications

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    Since its introduction in the 1980\u27s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender\u27s delta-perturbation method

    Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

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    Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo

    Dynamic Response of a Beam Resting on a Nonlinear Foundation to a Moving Load: Coiflet-Based Solution

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    Study of reactor constitutive model and analysis of nuclear reactor kinetics by fractional calculus approach

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    The diffusion theory model of neutron transport plays a crucial role in reactor theory since it is simple enough to allow scientific insight, and it is sufficiently realistic to study many important design problems. The neutrons are here characterized by a single energy or speed, and the model allows preliminary design estimates. The mathematical methods used to analyze such a model are the same as those applied in more sophisticated methods such as multi-group diffusion theory, and transport theory. The neutron diffusion and point kinetic equations are most vital models of nuclear engineering which are included to countless studies and applications under neutron dynamics. By the help of neutron diffusion concept, we understand the complex behavior of average neutron motion. The simplest group diffusion problems involve only, one group of neutrons, which for simplicity, are assumed to be all thermal neutrons. A more accurate procedure, particularly for thermal reactors, is to split the neutrons into two groups; in which case thermal neutrons are included in one group called the thermal or slow group and all the other are included in fast group. The neutrons within each group are lumped together and their diffusion, scattering, absorption and other interactions are described in terms of suitably average diffusion coefficients and cross-sections, which are collectively known as group constants. We have applied Variational Iteration Method and Modified Decomposition Method to obtain the analytical approximate solution of the Neutron Diffusion Equation with fixed source. The analytical methods like Homotopy Analysis Method and Adomian Decomposition Method have been used to obtain the analytical approximate solutions of neutron diffusion equation for both finite cylinders and bare hemisphere. In addition to these, the boundary conditions like zero flux as well as extrapolated boundary conditions are investigated. The explicit solution for critical radius and flux distributions are also calculated. The solution obtained in explicit form which is suitable for computer programming and other purposes such as analysis of flux distribution in a square critical reactor. The Homotopy Analysis Method is a very powerful and efficient technique which yields analytical solutions. With the help of this method we can solve many functional equations such as ordinary, partial differential equations, integral equations and so many other equations. It does not require enough memory space in computer, free from rounding off errors and discretization of space variables. By using the excellence of these methods, we obtained the solutions which have been shown graphically

    Applied Mathematics and Fractional Calculus

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    In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia

    Advances in Vibration Analysis Research

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    Vibrations are extremely important in all areas of human activities, for all sciences, technologies and industrial applications. Sometimes these Vibrations are useful but other times they are undesirable. In any case, understanding and analysis of vibrations are crucial. This book reports on the state of the art research and development findings on this very broad matter through 22 original and innovative research studies exhibiting various investigation directions. The present book is a result of contributions of experts from international scientific community working in different aspects of vibration analysis. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area

    Series Representations and Approximation of some Quantile Functions appearing in Finance

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    It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of a cheap but accurate approximation of the quantile function. However for several probability distributions arising in practice a satisfactory method of approximating these functions is not available. The main focus of this thesis will be to develop Taylor and asymptotic series representations for quantile functions of the following probability distributions; Variance Gamma, Generalized Inverse Gaussian, Hyperbolic, -Stable and Snedecor’s F distributions. As a secondary matter we briefly investigate the problem of approximating the entire quantile function. Indeed with the availability of these new analytic expressions a whole host of possibilities become available. We outline several algorithms and in particular provide a C++ implementation for the variance gamma case. To our knowledge this is the fastest available algorithm of its sort
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