Numerical methods using Matlab
Lindfield, George
2012-01-01
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use
An introduction to numerical methods and analysis
Epperson, James F
2013-01-01
Praise for the First Edition "". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.""-Zentralblatt MATH "". . . carefully structured with many detailed worked examples.""-The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to
Isaacson, Eugene
1994-01-01
This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.
Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples
Ramm, Alexander G
2012-01-01
Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and
Projector Method: theory and examples
International Nuclear Information System (INIS)
Dahl, E.D.
1985-01-01
The Projector Method technique for numerically analyzing lattice gauge theories was developed to take advantage of certain simplifying features of gauge theory models. Starting from a very general notion of what the Projector Method is, the techniques are applied to several model problems. After these examples have traced the development of the actual algorithm from the general principles of the Projector Method, a direct comparison between the Projector and the Euclidean Monte Carlo is made, followed by a discussion of the application to Periodic Quantum Electrodynamics in two and three spatial dimensions. Some methods for improving the efficiency of the Projector in various circumstances are outlined. 10 refs., 7 figs
Spectral Methods in Numerical Plasma Simulation
DEFF Research Database (Denmark)
Coutsias, E.A.; Hansen, F.R.; Huld, T.
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Numerical methods for characterization of synchrotron radiation based on the Wigner function method
Directory of Open Access Journals (Sweden)
Takashi Tanaka
2014-06-01
Full Text Available Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.
Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Verner Method
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T. Jayakumar
2015-01-01
Full Text Available In this paper we study the numerical methods for Fuzzy Differential equations by an application of the Runge-Kutta Verner method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.
Numerical method for the nonlinear Fokker-Planck equation
International Nuclear Information System (INIS)
Zhang, D.S.; Wei, G.W.; Kouri, D.J.; Hoffman, D.K.
1997-01-01
A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E 54, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schroedinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. copyright 1997 The American Physical Society
Numerical methods for metamaterial design
2013-01-01
This book describes a relatively new approach for the design of electromagnetic metamaterials. Numerical optimization routines are combined with electromagnetic simulations to tailor the broadband optical properties of a metamaterial to have predetermined responses at predetermined wavelengths. After a review of both the major efforts within the field of metamaterials and the field of mathematical optimization, chapters covering both gradient-based and derivative-free design methods are considered. Selected topics including surrogate-base optimization, adaptive mesh search, and genetic algorithms are shown to be effective, gradient-free optimization strategies. Additionally, new techniques for representing dielectric distributions in two dimensions, including level sets, are demonstrated as effective methods for gradient-based optimization. Each chapter begins with a rigorous review of the optimization strategy used, and is followed by numerous examples that combine the strategy with either electromag...
Numerical approaches towards life cycle interpretation five examples
Heijungs, R.; Kleijn, R.
2001-01-01
The ISO-standard for LCA distinguishes four phases, of which the last one, the interpretation, is the least elaborated. It can be regarded as containing procedural steps (like a completeness check) as well as numerical steps (like a sensitivity check). This paper provides five examples of techniques
A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method
Directory of Open Access Journals (Sweden)
Changqing Yang
2012-01-01
Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.
Numerical methods and analysis of multiscale problems
Madureira, Alexandre L
2017-01-01
This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai
2012-01-01
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar
2012-06-17
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
Explicit appropriate basis function method for numerical solution of stiff systems
International Nuclear Information System (INIS)
Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling
2015-01-01
Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations
An example of numerical simulation in causal set dynamics
International Nuclear Information System (INIS)
Krugly, Alexey L; Tserkovnikov, Ivan A
2013-01-01
The model of a discrete pregeometry on a microscopic scale is an x-graph. This is a directed acyclic graph. An outdegree and an indegree of each vertex are not more than 2. The sets of vertices and edges of x-graph are particular cases of causal sets. The sequential growth of a graph is an addition of new vertices one by one. A simple stochastic algorithm of sequential growth of x-graph are considered. It is based on a random walk at the x-graph. The particles in this model must be self-organized repetitive structures. We introduce the method of search of such repetitive structures. It is based on a discrete Fourier transformation. An example of numerical simulation is introduced.
Stochastic numerical methods an introduction for students and scientists
Toral, Raul
2014-01-01
Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability ConceptsMonte Carlo IntegrationGeneration of Uniform and Non-uniformRandom Numbers: Non-correlated ValuesDynamical MethodsApplications to Statistical MechanicsIn...
Numerical methods design, analysis, and computer implementation of algorithms
Greenbaum, Anne
2012-01-01
Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book a...
Numerical methods for image registration
Modersitzki, Jan
2003-01-01
Based on the author's lecture notes and research, this well-illustrated and comprehensive text is one of the first to provide an introduction to image registration with particular emphasis on numerical methods in medical imaging. Ideal for researchers in industry and academia, it is also a suitable study guide for graduate mathematicians, computer scientists, engineers, medical physicists, and radiologists.Image registration is utilised whenever information obtained from different viewpoints needs to be combined or compared and unwanted distortion needs to be eliminated. For example, CCTV imag
A student's guide to numerical methods
Hutchinson, Ian H
2015-01-01
This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introdu...
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Spectral methods in numerical plasma simulation
International Nuclear Information System (INIS)
Coutsias, E.A.; Hansen, F.R.; Huld, T.; Knorr, G.; Lynov, J.P.
1989-01-01
An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed. (orig.)
International Nuclear Information System (INIS)
Tomiyama, Akio; Matsuoka, Toshiyuki.
1995-01-01
A simple numerical method for solving a transient incompressible two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method for predicting transient flows in practical engineering devices. The simplicity of the present method is due to the fact that the field equations and constitutive equations were expressed in a tensor form in the general curvilinear coordinate system. When a conventional rectangular mesh is adopted in a calculation, the method reduces to a numerical method for a Cartesian coordinate system. As an example, the present method was applied to transient air-water bubbly flow in a vertical U-tube. It was confirmed that the effects of centrifugal and gravitational forces on the phase distribution in the U-tube were reasonably predicted. (author)
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
Directory of Open Access Journals (Sweden)
Min Hu
2016-01-01
Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations
International Nuclear Information System (INIS)
Feng Tinggui
2004-11-01
Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)
Methods of numerical relativity
International Nuclear Information System (INIS)
Piran, T.
1983-01-01
Numerical Relativity is an alternative to analytical methods for obtaining solutions for Einstein equations. Numerical methods are particularly useful for studying generation of gravitational radiation by potential strong sources. The author reviews the analytical background, the numerical analysis aspects and techniques and some of the difficulties involved in numerical relativity. (Auth.)
A two-dimensional adaptive numerical grids generation method and its realization
International Nuclear Information System (INIS)
Xu Tao; Shui Hongshou
1998-12-01
A two-dimensional adaptive numerical grids generation method and its particular realization is discussed. This method is effective and easy to realize if the control functions are given continuously, and the grids for some regions is showed in this case. For Computational Fluid Dynamics, because the control values of adaptive grids-numerical solution is given in dispersed form, it is needed to interpolate these values to get the continuous control functions. These interpolation techniques are discussed, and some efficient adaptive grids are given. A two-dimensional fluid dynamics example was also given
Direct design of LPV feedback controllers: technical details and numerical examples
Novara, Carlo
2014-01-01
The paper contains technical details of recent results developed by the author, regarding the design of LPV controllers directly from experimental data. Two numerical examples are also presented, about control of the Duffing oscillator and control of a two-degree-of-freedom manipulator.
Numerical method of identification of an unknown source term in a heat equation
Directory of Open Access Journals (Sweden)
Fatullayev Afet Golayo?lu
2002-01-01
Full Text Available A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.
A first course in ordinary differential equations analytical and numerical methods
Hermann, Martin
2014-01-01
This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...
Stability of numerical method for semi-linear stochastic pantograph differential equations
Directory of Open Access Journals (Sweden)
Yu Zhang
2016-01-01
Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.
[Effects decomposition in mediation analysis: a numerical example].
Zugna, Daniela; Richiardi, Lorenzo
2018-01-01
Mediation analysis aims to decompose the total effect of the exposure on the outcome into a direct effect (unmediated) and an indirect effect (mediated by a mediator). When the interest also lies on understanding whether the exposure effect differs in different sub-groups of study population or under different scenarios, the mediation analysis needs to be integrated with interaction analysis. In this setting it is necessary to decompose the total effect not only into two components, the direct and indirect effects, but other two components linked to interaction. The interaction between the exposure and the mediator in their effect on the outcome could indeed act through the effect of the exposure on the mediator or through the mediator when the mediator is not totally explained by the exposure. We describe options for decomposition, proposed in literature, of the total effect and we illustrate them through a hypothetical example of the effect of age at diagnosis of cancer on survival, mediated and unmediated by the therapeutical approach, and a numerical example.
Numerical method for solving linear Fredholm fuzzy integral equations of the second kind
Energy Technology Data Exchange (ETDEWEB)
Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)
2007-01-15
In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.
A difference quotient-numerical integration method for solving radiative transfer problems
International Nuclear Information System (INIS)
Ding Peizhu
1992-01-01
A difference quotient-numerical integration method is adopted to solve radiative transfer problems in an anisotropic scattering slab medium. By using the method, the radiative transfer problem is separated into a system of linear algebraic equations and the coefficient matrix of the system is a band matrix, so the method is very simple to evaluate on computer and to deduce formulae and easy to master for experimentalists. An example is evaluated and it is shown that the method is precise
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
Numerical proceessing of radioimmunoassay results using logit-log transformation method
International Nuclear Information System (INIS)
Textoris, R.
1983-01-01
The mathematical model and algorithm are described of the numerical processing of the results of a radioimmunoassay by the logit-log transformation method and by linear regression with weight factors. The limiting value of the curve for zero concentration is optimized with regard to the residual sum by the iterative method by multiple repeats of the linear regression. Typical examples are presented of the approximation of calibration curves. The method proved suitable for all hitherto used RIA sets and is well suited for small computers with internal memory of min. 8 Kbyte. (author)
International Nuclear Information System (INIS)
Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji; Yakuwa, Hiroshi; Hayabusa, Keisuke
2012-01-01
Highlights: ► A novel numerical method to analyze time dependent localized corrosion is developed. ► It takes electromigration, mass diffusion, chemical reactions, and moving boundaries. ► Our method perfectly satisfies the conservation of mass and electroneutrality. ► The behavior of typical crevice corrosion is successfully simulated. ► Both verification and validation of our method are carried out. - Abstract: A novel numerical method for time-dependent localized corrosion analysis is presented. Electromigration, mass diffusion, chemical reactions, and moving boundaries are considered in the numerical simulation of localized corrosion of engineering alloys in an underwater environment. Our method combines the finite volume method (FVM) and the voxel method. The FVM is adopted in the corrosion rate calculation so that the conservation of mass is satisfied. A newly developed decoupled algorithm with a projection method is introduced in the FVM to decouple the multiphysics problem into the electrostatic, mass transport, and chemical reaction analyses with electroneutrality maintained. The polarization curves for the corroding metal are used as boundary conditions for the metal surfaces to calculate the corrosion rates. The voxel method is adopted in updating the moving boundaries of cavities without remeshing and mesh-to-mesh solution mapping. Some modifications of the standard voxel method, which represents the boundaries as zigzag-shaped surfaces, are introduced to generate smooth surfaces. Our method successfully reproduces the numerical and experimental results of a capillary electrophoresis problem. Furthermore, the numerical results are qualitatively consistent with the experimental results for several examples of crevice corrosion.
Introduction to precise numerical methods
Aberth, Oliver
2007-01-01
Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.
Numerical methods in dynamic fracture mechanics
International Nuclear Information System (INIS)
Beskos, D.E.
1987-01-01
A review of numerical methods for the solution of dynamic problems of fracture mechanics is presented. Finite difference, finite element and boundary element methods as applied to linear elastic or viscoelastic and non-linear elastoplastic or elastoviscoplastic dynamic fracture mechanics problems are described and critically evaluated. Both cases of stationary cracks and rapidly propagating cracks of simple I, II, III or mixed modes are considered. Harmonically varying with time or general transient dynamic disturbances in the form of external loading or incident waves are taken into account. Determination of the dynamic stress intensity factor for stationary cracks or moving cracks with known velocity history as well as determination of the crack-tip propagation history for given dynamic fracture toughness versus crack velocity relation are described and illustrated by means of certain representative examples. Finally, a brief assessment of the present state of knowledge is made and research needs are identified
Katsaounis, T. D.
2005-02-01
The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using
Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation
International Nuclear Information System (INIS)
Raptis, A.D.; Cash, J.R.
1987-01-01
A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)
Numerical simulation of compressible two-phase flow using a diffuse interface method
International Nuclear Information System (INIS)
Ansari, M.R.; Daramizadeh, A.
2013-01-01
Highlights: ► Compressible two-phase gas–gas and gas–liquid flows simulation are conducted. ► Interface conditions contain shock wave and cavitations. ► A high-resolution diffuse interface method is investigated. ► The numerical results exhibit very good agreement with experimental results. -- Abstract: In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
Numerical methods in software and analysis
Rice, John R
1992-01-01
Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm
Numerical methods in simulation of resistance welding
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, Paulo A.F.; Zhang, Wenqi
2015-01-01
Finite element simulation of resistance welding requires coupling betweenmechanical, thermal and electrical models. This paper presents the numerical models and theircouplings that are utilized in the computer program SORPAS. A mechanical model based onthe irreducible flow formulation is utilized...... a resistance welding point of view, the most essential coupling between the above mentioned models is the heat generation by electrical current due to Joule heating. The interaction between multiple objects is anothercritical feature of the numerical simulation of resistance welding because it influences...... thecontact area and the distribution of contact pressure. The numerical simulation of resistancewelding is illustrated by a spot welding example that includes subsequent tensile shear testing...
Excel spreadsheet in teaching numerical methods
Djamila, Harimi
2017-09-01
One of the important objectives in teaching numerical methods for undergraduates’ students is to bring into the comprehension of numerical methods algorithms. Although, manual calculation is important in understanding the procedure, it is time consuming and prone to error. This is specifically the case when considering the iteration procedure used in many numerical methods. Currently, many commercial programs are useful in teaching numerical methods such as Matlab, Maple, and Mathematica. These are usually not user-friendly by the uninitiated. Excel spreadsheet offers an initial level of programming, which it can be used either in or off campus. The students will not be distracted with writing codes. It must be emphasized that general commercial software is required to be introduced later to more elaborated questions. This article aims to report on a teaching numerical methods strategy for undergraduates engineering programs. It is directed to students, lecturers and researchers in engineering field.
Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery
International Nuclear Information System (INIS)
Wu, Dazhuan; Chen, Tao; Wang, Leqin; Cheng, Wentao; Sun, Youbo
2013-01-01
In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.
Balancing of linkages and robot manipulators advanced methods with illustrative examples
Arakelian, Vigen
2015-01-01
In this book advanced balancing methods for planar and spatial linkages, hand operated and automatic robot manipulators are presented. It is organized into three main parts and eight chapters. The main parts are the introduction to balancing, the balancing of linkages and the balancing of robot manipulators. The review of state-of-the-art literature including more than 500 references discloses particularities of shaking force/moment balancing and gravity compensation methods. Then new methods for balancing of linkages are considered. Methods provided in the second part of the book deal with the partial and complete shaking force/moment balancing of various linkages. A new field for balancing methods applications is the design of mechanical systems for fast manipulation. Special attention is given to the shaking force/moment balancing of robot manipulators. Gravity balancing methods are also discussed. The suggested balancing methods are illustrated by numerous examples.
Numerical Methods for Pricing American Options with Time-Fractional PDE Models
Directory of Open Access Journals (Sweden)
Zhiqiang Zhou
2016-01-01
Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.
Energy Technology Data Exchange (ETDEWEB)
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Numerical methods for hydrodynamic stability problems
International Nuclear Information System (INIS)
Fujimura, Kaoru
1985-11-01
Numerical methods for solving the Orr-Sommerfeld equation, which is the fundamental equation of the hydrodynamic stability theory for various shear flows, are reviewed and typical numerical results are presented. The methods of asymptotic solution, finite difference methods, initial value methods and expansions in orthogonal functions are compared. (author)
A numerical method for complex structural dynamics in nuclear plant facilities
International Nuclear Information System (INIS)
Zeitner, W.
1979-01-01
The solution of dynamic problems is often connected with difficulties in setting up a system of equations of motion because of the constraint conditions of the system. Such constraint conditions may be of geometric nature as for example gaps or slidelines, they may be compatibility conditions or thermodynamic criteria for the energy balance of a system. The numerical method proposed in this paper for the treatment of a dynamic problem with constraint conditions requires only to set up the equations of motion without considering the constraints. This always leads to a relatively simple formulation. The constraint conditions themselves are included in the integration procedure by a numerical application of Gauss' principle. (orig.)
Numerical methods for the simulation of continuous sedimentation in ideal clarifier-thickener units
Energy Technology Data Exchange (ETDEWEB)
Buerger, R.; Karlsen, K.H.; Risebro, N.H.; Towers, J.D.
2001-10-01
We consider a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a nonlinear hyperbolic partial differential equation with a flux function that depends discontinuously on height. The purpose of this contribution is to present and demonstrate two numerical methods for simulating continuous sedimentation: a front tracking method and a finite finite difference method. The basic building blocks in the front tracking method are the solutions of a finite number of certain Riemann problems and a procedure for tracking local collisions of shocks. The solutions of the Riemann problems are recalled herein and the front tracking algorithm is described. As an alternative to the front tracking method, a simple scalar finite difference algorithm is proposed. This method is based on discretizing the spatially varying flux parameters on a mesh that is staggered with respect to that of the conserved variable, resulting in a straightforward generalization of the well-known Engquist-Osher upwind finite difference method. The result is an easily implemented upwind shock capturing method. Numerical examples demonstrate that the front tracking and finite difference methods can be used as efficient and accurate simulation tools for continuous sedimentation. The numerical results for the finite difference method indicate that discontinuities in the local solids concentration are resolved sharply and agree with those produced by the front tracking method. The latter is free of numerical dissipation, which leads to sharply resolved concentration discontinuities, but is more complicated to implement than the former. Available mathematical results for the proposed numerical methods are also briefly reviewed. (author)
Directory of Open Access Journals (Sweden)
SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
Mastorakis, Nikos E
2009-01-01
Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently.
Numerical simulation of subwoofer array congurations using the Finite Element Method
Directory of Open Access Journals (Sweden)
Xavier Banyuls-Juan
2017-08-01
Full Text Available Teaching in the Master of Acoustic Engineering includes contents that require the modeling of acoustic systems of two types: simple systems through analytical theory and complex models using simulation techniques. In the present work, we describe an example of complex acoustic sources modeling using the finite element method: subwoofer sound radiation in different configurations. Numerical simulations in the frequency domain can calculate the radiation pattern of systems that do not have a simple analytical solution.
Directory of Open Access Journals (Sweden)
Jilian Wu
2013-01-01
Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.
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Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
International Nuclear Information System (INIS)
Katsaounis, T D
2005-01-01
The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall
Numerical Analysis of Indoor Sound Quality Evaluation Using Finite Element Method
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Yu-Tuan Chou
2013-01-01
Full Text Available Indoors sound field distribution is important to Room Acoustics, but the field suffers numerous problems, for example, multipath propagation and scattering owing to sound absorption by furniture and other aspects of décor. Generally, an ideal interior space must have a sound field with clear quality. This provides both the speaker and the listener with a pleasant conversational environment. This investigation uses the Finite Element Method to assess the acoustic distribution based on the indoor space and chamber volume. In this situation, a fixed sound source at different frequencies is used to simulate the acoustic characteristics of the indoor space. This method considers the furniture and decoration sound absorbing material and thus different sound absorption coefficients and configurations. The preliminary numerical simulation provides a method that can forecast the distribution of sound in an indoor room in complex situations. Consequently, it is possible to arrange interior furnishings and appliances to optimize acoustic distribution and environmental friendliness. Additionally, the analytical results can also be used to calculate the Reverberation Time and speech intelligibility for specified indoor space.
Dahlquist, Germund
1974-01-01
""Substantial, detailed and rigorous . . . readers for whom the book is intended are admirably served."" - MathSciNet (Mathematical Reviews on the Web), American Mathematical Society.Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.
On vortex loops and filaments: three examples of numerical predictions of flows containing vortices.
Krause, Egon
2003-01-01
Vortex motion plays a dominant role in many flow problems. This article aims at demonstrating some of the characteristic features of vortices with the aid of numerical solutions of the governing equations of fluid mechanics, the Navier-Stokes equations. Their discretized forms will first be reviewed briefly. Thereafter three problems of fluid flow involving vortex loops and filaments are discussed. In the first, the time-dependent motion and the mutual interaction of two colliding vortex rings are discussed, predicted in good agreement with experimental observations. The second example shows how vortex rings are generated, move, and interact with each other during the suction stroke in the cylinder of an automotive engine. The numerical results, validated with experimental data, suggest that vortex rings can be used to influence the spreading of the fuel droplets prior to ignition and reduce the fuel consumption. In the third example, it is shown that vortices can also occur in aerodynamic flows over delta wings at angle of attack as well as pipe flows: of particular interest for technical applications of these flows is the situation in which the vortex cores are destroyed, usually referred to as vortex breakdown or bursting. Although reliable breakdown criteria could not be established as yet, the numerical predictions obtained so far are found to agree well with the few experimental data available in the recent literature.
Research development and teaching of numerical methods at the Atomic Centre of Bariloche, Argentina
International Nuclear Information System (INIS)
Pissanetzky, S.; Sarmiento, G.S.
1981-01-01
The areas of study of numerical methods, particularly the finite element method, are listed. These include numerical simulation of the thermo-mechanical behaviour of nuclear fuel elements and of the heat transfer in the industrial processing of sheaths for nuclear fuel cladding. Computer programs to support these studies are listed. Two examples of applications of these programs are given. The first is the modelling of high-vacuum annealing furnaces, particularly those used to manufacture zircaloy tubes for reactor sheaths. The second is the modelling of localized thermochemical problems in nuclear fuel elements and other nuclear reactor components. Details of where to obtain further information of work covered in this summary are given. (U.K.)
Directory of Open Access Journals (Sweden)
E. Majchrzak
2008-12-01
Full Text Available The dual reciprocity boundary element method is applied for numerical modelling of solidification process. This variant of the BEM is connected with the transformation of the domain integral to the boundary integrals. In the paper the details of the dual reciprocity boundary element method are presented and the usefulness of this approach to solidification process modelling is demonstrated. In the final part of the paper the examples of computations are shown.
Numerical Methods for Stochastic Computations A Spectral Method Approach
Xiu, Dongbin
2010-01-01
The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth
Numerical Methods for Partial Differential Equations
Guo, Ben-yu
1987-01-01
These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
Numerical investigation on exterior conformal mappings with application to airfoils
International Nuclear Information System (INIS)
Mohamad Rashidi Md Razali; Hu Laey Nee
2000-01-01
A numerical method is described in computing a conformal map from an exterior region onto the exterior of the unit disk. The numerical method is based on a boundary integral equation which is similar to the Kerzman-Stein integral equation for interior mapping. Some examples show that numerical results of high accuracy can be obtained provided that the boundaries are smooth. This numerical method has been applied to the mapping airfoils. However, due to the fact that the parametric representation of an air foil is not known, a cubic spline interpolation method has been used. Some numerical examples with satisfying results have been obtained for the symmetrical and cambered airfoils. (Author)
International Nuclear Information System (INIS)
Fronteau, J.; Combis, P.
1984-08-01
A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type
An outline review of numerical transport methods
International Nuclear Information System (INIS)
Budd, C.
1981-01-01
A brief review is presented of numerical methods for solving the neutron transport equation in the context of reactor physics. First the various forms of transport equation are given. Second, the various ways of classifying numerical transport methods are discussed. Finally each method (or class of methods) is outlined in turn. (U.K.)
Development of numerical methods for reactive transport
International Nuclear Information System (INIS)
Bouillard, N.
2006-12-01
When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a
Theory and applications of numerical analysis
Phillips, G M
1996-01-01
This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Chaskalovic, Joël
2014-01-01
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic
International Nuclear Information System (INIS)
He, Y B; Tang, X H
2016-01-01
In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)
Numerical methods and modelling for engineering
Khoury, Richard
2016-01-01
This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...
Elimination of numerical diffusion in 1 - phase and 2 - phase flows
Energy Technology Data Exchange (ETDEWEB)
Rajamaeki, M. [VTT Energy (Finland)
1997-07-01
The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.
Elimination of numerical diffusion in 1 - phase and 2 - phase flows
International Nuclear Information System (INIS)
Rajamaeki, M.
1997-01-01
The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods
Kou, Jisheng
2015-07-16
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton\\'s method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
Kou, Jisheng; Sun, Shuyu
2015-01-01
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
Huang, Jie; Li, Piao; Yao, Weixing
2018-05-01
A loosely coupled fluid-structural thermal numerical method is introduced for the thermal protection system (TPS) gap thermal control analysis in this paper. The aerodynamic heating and structural thermal are analyzed by computational fluid dynamics (CFD) and numerical heat transfer (NHT) methods respectively. An interpolation algorithm based on the control surface is adopted for the data exchanges on the coupled surface. In order to verify the analysis precision of the loosely coupled method, a circular tube example was analyzed, and the wall temperature agrees well with the test result. TPS gap thermal control performance was studied by the loosely coupled method successfully. The gap heat flux is mainly distributed in the small region at the top of the gap which is the high temperature region. Besides, TPS gap temperature and the power of the active cooling system (CCS) calculated by the traditional uncoupled method are higher than that calculated by the coupled method obviously. The reason is that the uncoupled method doesn't consider the coupled effect between the aerodynamic heating and structural thermal, however the coupled method considers it, so TPS gap thermal control performance can be analyzed more accurately by the coupled method.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Energy Technology Data Exchange (ETDEWEB)
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
International Nuclear Information System (INIS)
Klein, R I; Stone, J M
2007-01-01
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments
Bateev, A. B.; Filippov, V. P.
2017-01-01
The principle possibility of using computer program Univem MS for Mössbauer spectra fitting as a demonstration material at studying such disciplines as atomic and nuclear physics and numerical methods by students is shown in the article. This program is associated with nuclear-physical parameters such as isomer (or chemical) shift of nuclear energy level, interaction of nuclear quadrupole moment with electric field and of magnetic moment with surrounded magnetic field. The basic processing algorithm in such programs is the Least Square Method. The deviation of values of experimental points on spectra from the value of theoretical dependence is defined on concrete examples. This value is characterized in numerical methods as mean square deviation. The shape of theoretical lines in the program is defined by Gaussian and Lorentzian distributions. The visualization of the studied material on atomic and nuclear physics can be improved by similar programs of the Mössbauer spectroscopy, X-ray Fluorescence Analyzer or X-ray diffraction analysis.
International Nuclear Information System (INIS)
Bodvarsson, G.S.; Lippmann, M.J.
1980-01-01
The computer program CCC (conduction-convection-consolidation), developed at Lawrence Berkeley Laboratory, solves numerically the heat and mass flow equations for a fully saturated medium, and computes one-dimensional consolidation of the simulated systems. The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated medium and formulating the governing equations. The sets of equations are solved either by an iterative solution technique (old version) or an efficient sparse solver (new version). The deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. In this paper, the numerical code is described, validation examples given and areas of application discussed. Several example problems involving flow through fractured media are also presented
Energy Technology Data Exchange (ETDEWEB)
Pogosyan, T A
1983-01-01
The article is dedicated to the solution of systems of differential equations which describe the transfer processes in an electric power system (EES) by implicit methods of numerical integration. The distinguishing feature of the implicit methods (Euler's reverse method and the trapeze method) is their absolute stability and, consequently, the relatively small accumulation of errors in each step of integration. Therefore, they are found to be very convenient for solving problems of electric power engineering, when the transfer processes are described by a rigid system of differential equations. The rigidity is associated with the range of values of the time constants considered. The advantage of the implicit methods over explicit are shown in a specific example (calculation of the dynamic stability of the simplest electric power system), along with the field of use of the implicit methods and the expedience of their use in power engineering problems.
Uranium prospection methods illustrated with examples
International Nuclear Information System (INIS)
Valsardieu, C.
1985-01-01
Uranium exploration methods are briefly reviewed: aerial (radiometric, spectrometric), surface (mapping, radiometric, geophysical, geochemical), sub-surface (well logging, boring) and mining methods in the different steps of a mine project: preliminary studies, general prospecting, detailed prospecting deposit area and deposit estimation. Choice of methods depends strongly on geographic and geologic environment. Three examples are given concerning: an intragranitic deposit Limousin (France), a deposit spatially related to a discordance Athabasca (Canada) and a sedimentary deposit Manyingee (Western Australia) [fr
Hybrid methods for airframe noise numerical prediction
Energy Technology Data Exchange (ETDEWEB)
Terracol, M.; Manoha, E.; Herrero, C.; Labourasse, E.; Redonnet, S. [ONERA, Department of CFD and Aeroacoustics, BP 72, Chatillon (France); Sagaut, P. [Laboratoire de Modelisation en Mecanique - UPMC/CNRS, Paris (France)
2005-07-01
This paper describes some significant steps made towards the numerical simulation of the noise radiated by the high-lift devices of a plane. Since the full numerical simulation of such configuration is still out of reach for present supercomputers, some hybrid strategies have been developed to reduce the overall cost of such simulations. The proposed strategy relies on the coupling of an unsteady nearfield CFD with an acoustic propagation solver based on the resolution of the Euler equations for midfield propagation in an inhomogeneous field, and the use of an integral solver for farfield acoustic predictions. In the first part of this paper, this CFD/CAA coupling strategy is presented. In particular, the numerical method used in the propagation solver is detailed, and two applications of this coupling method to the numerical prediction of the aerodynamic noise of an airfoil are presented. Then, a hybrid RANS/LES method is proposed in order to perform some unsteady simulations of complex noise sources. This method allows for significant reduction of the cost of such a simulation by considerably reducing the extent of the LES zone. This method is described and some results of the numerical simulation of the three-dimensional unsteady flow in the slat cove of a high-lift profile are presented. While these results remain very difficult to validate with experiments on similar configurations, they represent up to now the first 3D computations of this kind of flow. (orig.)
International Nuclear Information System (INIS)
Borcherds, P
2003-01-01
The two Numerical Recipes books are marvellous. The principal book, The Art of Scientific Computing, contains program listings for almost every conceivable requirement, and it also contains a well written discussion of the algorithms and the numerical methods involved. The Example Book provides a complete driving program, with helpful notes, for nearly all the routines in the principal book. The first edition of Numerical Recipes: The Art of Scientific Computing was published in 1986 in two versions, one with programs in Fortran, the other with programs in Pascal. There were subsequent versions with programs in BASIC and in C. The second, enlarged edition was published in 1992, again in two versions, one with programs in Fortran (NR(F)), the other with programs in C (NR(C)). In 1996 the authors produced Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing as a supplement, called Volume 2, with the original (Fortran) version referred to as Volume 1. Numerical Recipes in C++ (NR(C++)) is another version of the 1992 edition. The numerical recipes are also available on a CD ROM: if you want to use any of the recipes, I would strongly advise you to buy the CD ROM. The CD ROM contains the programs in all the languages. When the first edition was published I bought it, and have also bought copies of the other editions as they have appeared. Anyone involved in scientific computing ought to have a copy of at least one version of Numerical Recipes, and there also ought to be copies in every library. If you already have NR(F), should you buy the NR(C++) and, if not, which version should you buy? In the preface to Volume 2 of NR(F), the authors say 'C and C++ programmers have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons will be amply repaid in the future as C and C++ eventually develop standard parallel extensions'. In the preface and introduction to NR
Numerical analysis in electromagnetics the TLM method
Saguet, Pierre
2013-01-01
The aim of this book is to give a broad overview of the TLM (Transmission Line Matrix) method, which is one of the "time-domain numerical methods". These methods are reputed for their significant reliance on computer resources. However, they have the advantage of being highly general.The TLM method has acquired a reputation for being a powerful and effective tool by numerous teams and still benefits today from significant theoretical developments. In particular, in recent years, its ability to simulate various situations with excellent precision, including complex materials, has been
Numerical and adaptive grid methods for ideal magnetohydrodynamics
Loring, Burlen
2008-02-01
In this thesis numerical finite difference methods for ideal magnetohydrodynamics(MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be piece together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction of spurious forces due to the growth of the divergence of the magnetic flux density, the loss of pressure positivity, and the effects of non-conservative numerical methods are discussed, along with the practical approaches which can be used to remedy or minimize the negative consequences of each. The use of block structured adaptive mesh refinement is investigated in the context of a divergence free MHD code. A new method for conserving magnetic flux across AMR grid interfaces is developed and a detailed discussion of our implementation of this method using the CHOMBO AMR framework is given. A preliminary validation of the new method for conserving magnetic flux density across AMR grid interfaces illustrates that the method works. Finally a number of code validation cases are examined spurring a discussion of the strengths and weaknesses of the numerics employed.
Abell, Martha L
2005-01-01
Maple by Example, Third Edition, is a reference/text with CD for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear algebra, business mathematics, ordinary and partial differential equations, numerical methods, graphics and more. The CD-ROM provides updated Maple input and all text from the book.* Updated coverage of Maple features and functions * Backwards compatible for all versions* New applications from a variety of fields, including biology, physics and engineering* Expanded topics with many additional examples
International Nuclear Information System (INIS)
Miyagawa, Yuu; Ueta, Tsuyoshi
2008-01-01
The boundary element method (BEM) is so extended as to treat two-dimensional (2D) electron systems in the presence of pointlike islands of magnetic moment. In the present paper, the pointlike magnetic scatterer is modeled by a cylindrical barrier. The radius of the cylindrical barrier is assumed to be so small, keeping the volume definite, that the pointlike magnetic scatterer is approximated by a Dirac δ function. Then, we make an approximation on the BEM formulation, wherefore we derive a novel numerical method for electron transport in the presence of pointlike magnetic scatterers. In a numerical implementation of the method extended here, the numerical errors of probability conservation are less than 1% for any cases and the computational costs, that is, the required memory amount and CPU time, are much reduced. As examples, the proposed method is applied to transport problems through a quantum wire with four pointlike magnetic scatterers. It is clearly shown that magnetic scatterers, even pointlike magnetic moments, lead to spin flip-flop, localization and resonance
Bayesian Methods for the Physical Sciences. Learning from Examples in Astronomy and Physics.
Andreon, Stefano; Weaver, Brian
2015-05-01
Chapter 1: This chapter presents some basic steps for performing a good statistical analysis, all summarized in about one page. Chapter 2: This short chapter introduces the basics of probability theory inan intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods. Chapter 3: This chapter introduces the computational tools and methods that we use for sampling from the posterior distribution. Since all numerical computations, and Bayesian ones are no exception, may end in errors, we also provide a few tips to check that the numerical computation is sampling from the posterior distribution. Chapter 4: Many of the concepts of building, running, and summarizing the resultsof a Bayesian analysis are described with this step-by-step guide using a basic (Gaussian) model. The chapter also introduces examples using Poisson and Binomial likelihoods, and how to combine repeated independent measurements. Chapter 5: All statistical analyses make assumptions, and Bayesian analyses are no exception. This chapter emphasizes that results depend on data and priors (assumptions). We illustrate this concept with examples where the prior plays greatly different roles, from major to negligible. We also provide some advice on how to look for information useful for sculpting the prior. Chapter 6: In this chapter we consider examples for which we want to estimate more than a single parameter. These common problems include estimating location and spread. We also consider examples that require the modeling of two populations (one we are interested in and a nuisance population) or averaging incompatible measurements. We also introduce quite complex examples dealing with upper limits and with a larger-than-expected scatter. Chapter 7: Rarely is a sample randomly selected from the population we wish to study. Often, samples are affected by selection effects, e.g., easier
Favrie, N.; Gavrilyuk, S.
2017-07-01
A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.
A numerical method for resonance integral calculations
International Nuclear Information System (INIS)
Tanbay, Tayfun; Ozgener, Bilge
2013-01-01
A numerical method has been proposed for resonance integral calculations and a cubic fit based on least squares approximation to compute the optimum Bell factor is given. The numerical method is based on the discretization of the neutron slowing down equation. The scattering integral is approximated by taking into account the location of the upper limit in energy domain. The accuracy of the method has been tested by performing computations of resonance integrals for uranium dioxide isolated rods and comparing the results with empirical values. (orig.)
Design of heat exchangers by numerical methods
International Nuclear Information System (INIS)
Konuk, A.A.
1981-01-01
Differential equations describing the heat tranfer in shell - and tube heat exchangers are derived and solved numerically. The method of ΔT sub(lm) is compared with the proposed method in cases where the specific heat at constant pressure, Cp and the overall heat transfer coefficient, U, vary with temperature. The error of the method of ΔT sub (lm) for the computation of the exchanger lenght is less than + 10%. However, the numerical method, being more accurate and at the same time easy to use and economical, is recommended for the design of shell-and-tube heat exchangers. (Author) [pt
Numerical methods for coupled fracture problems
Viesca, Robert C.; Garagash, Dmitry I.
2018-04-01
We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.
Numerical methods for semiconductor heterostructures with band nonparabolicity
International Nuclear Information System (INIS)
Wang Weichung; Hwang Tsungmin; Lin Wenwei; Liu Jinnliang
2003-01-01
This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail
New method of processing heat treatment experiments with numerical simulation support
Kik, T.; Moravec, J.; Novakova, I.
2017-08-01
In this work, benefits of combining modern software for numerical simulations of welding processes with laboratory research was described. Proposed new method of processing heat treatment experiments leading to obtaining relevant input data for numerical simulations of heat treatment of large parts was presented. It is now possible, by using experiments on small tested samples, to simulate cooling conditions comparable with cooling of bigger parts. Results from this method of testing makes current boundary conditions during real cooling process more accurate, but also can be used for improvement of software databases and optimization of a computational models. The point is to precise the computation of temperature fields for large scale hardening parts based on new method of temperature dependence determination of the heat transfer coefficient into hardening media for the particular material, defined maximal thickness of processed part and cooling conditions. In the paper we will also present an example of the comparison standard and modified (according to newly suggested methodology) heat transfer coefficient data’s and theirs influence on the simulation results. It shows how even the small changes influence mainly on distribution of temperature, metallurgical phases, hardness and stresses distribution. By this experiment it is also possible to obtain not only input data and data enabling optimization of computational model but at the same time also verification data. The greatest advantage of described method is independence of used cooling media type.
Numerical method for the dispersion relation of a hot and inhomogeneous plasma with an electron beam
International Nuclear Information System (INIS)
Devia, A.; Orrego, C.E.; Buitrago, G.
1990-01-01
A numerical method that is based in kinetic theory (Vlasov-Poison equations) was developed in order to calculate the dispersion relation for the interaction between a hot cylindrical and electron beam in any temperature and density. The plasma-beam system is located in a strong magnetic field. Many examples showing the effect of the temperatures and densities on the dispersion relation are given. (Author)
Numerical implementation of the loop-tree duality method
Energy Technology Data Exchange (ETDEWEB)
Buchta, Sebastian; Rodrigo, German [Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, Parc Cientific, Instituto de Fisica Corpuscular, Valencia (Spain); Chachamis, Grigorios [Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Draggiotis, Petros [Institute of Nuclear and Particle Physics, NCSR ' ' Demokritos' ' , Agia Paraskevi (Greece)
2017-05-15
We present a first numerical implementation of the loop-tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs. (orig.)
Zeng, Guang-Ming; Jiang, Yi-Min; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing
2003-01-01
Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity-stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two-dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.
Lagrangian numerical methods for ocean biogeochemical simulations
Paparella, Francesco; Popolizio, Marina
2018-05-01
We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.
Directory of Open Access Journals (Sweden)
Poruba Z.
2009-06-01
Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.
Evaluation of steel corrosion by numerical analysis
Kawahigashi, Tatsuo
2017-01-01
Recently, various non-destructive and numerical methods have been used and many cases of steel corrosion are examined. For example, methods of evaluating corrosion through various numerical methods and evaluating macrocell corrosion and micro-cell corrosion using measurements have been proposed. However, there are few reports on estimating of corrosion loss with distinguishing the macro-cell and micro-cell corrosion and with resembling an actuality phenomenon. In this study, for distinguishin...
International Nuclear Information System (INIS)
Iwata, Koji; Tsukimori, Kazuyuki; Ueno, Mutsuo
2003-12-01
FINAS is a general purpose structural analysis computer program which was developed by Japan Nuclear Cycle Development Institute for the analysis of static, dynamic and thermal responses of elastic and inelastic structures by the finite element method. This manual contains typical analysis examples that illustrate applications of FINAS to a variety of structural engineering problems. The first part of this manual presents fundamental examples in which numerical solutions by FINAS are compared with some analytical reference solutions, and the second part of this manual presents more complex examples intended for practical application. All the input data images and principal results for each problem are included in this manual for beginners' convenience. All the analyses are performed by using the FINAS Version 13.0. (author)
Stability analysis of single-phase thermosyphon loops by finite difference numerical methods
International Nuclear Information System (INIS)
Ambrosini, W.
1998-01-01
In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs
Molecular dynamics with deterministic and stochastic numerical methods
Leimkuhler, Ben
2015-01-01
This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...
Numerical modeling of isothermal compositional grading by convex splitting methods
Li, Yiteng
2017-04-09
In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.
Tensor viscosity method for convection in numerical fluid dynamics
International Nuclear Information System (INIS)
Dukowicz, J.K.; Ramshaw, J.D.
1979-01-01
A new method, called the tensor viscosity method, is described for differencing the convective terms in multidimensional numerical fluid dynamics. The method is the proper generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping. It is a single-step method that is distinguished by simplicity and case of implementation, even in the case of an arbitrary non-rectangular mesh. It should therefore be useful in finite-element as well as finite-difference formulations
Directory of Open Access Journals (Sweden)
Predrag Pejovic
2013-12-01
Full Text Available Application of a single phase rectifier as an example in teaching circuit modeling, normalization, operating modes of nonlinear circuits, and circuit analysis methods is proposed.The rectifier supplied from a voltage source by an inductive impedance is analyzed in the discontinuous as well as in the continuous conduction mode. Completely analytical solution for the continuous conduction mode is derived. Appropriate numerical methods are proposed to obtain the circuit waveforms in both of the operating modes, and to compute the performance parameters. Source code of the program that performs such computation is provided.
Numerical simulation methods for phase-transitional flow
Pecenko, A.
2010-01-01
The object of the present dissertation is a numerical study of multiphase flow of one fluid component. In particular, the research described in this thesis focuses on the development of numerical methods that are based on a diffuse-interface model (DIM). With this approach, the modeling problem
Dehghan, Mehdi; Nikpour, Ahmad
2013-09-01
In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.
Assessing numerical methods used in nuclear aerosol transport models
International Nuclear Information System (INIS)
McDonald, B.H.
1987-01-01
Several computer codes are in use for predicting the behaviour of nuclear aerosols released into containment during postulated accidents in water-cooled reactors. Each of these codes uses numerical methods to discretize and integrate the equations that govern the aerosol transport process. Computers perform only algebraic operations and generate only numbers. It is in the numerical methods that sense can be made of these numbers and where they can be related to the actual solution of the equations. In this report, the numerical methods most commonly used in the aerosol transport codes are examined as special cases of a general solution procedure, the Method of Weighted Residuals. It would appear that the numerical methods used in the codes are all capable of producing reasonable answers to the mathematical problem when used with skill and care. 27 refs
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Numerical methods in multibody dynamics
Eich-Soellner, Edda
1998-01-01
Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
Numerical Methods for a Class of Differential Algebraic Equations
Directory of Open Access Journals (Sweden)
Lei Ren
2017-01-01
Full Text Available This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs. At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.
Lange, J.; O'Shaughnessy, R.; Boyle, M.; Calderón Bustillo, J.; Campanelli, M.; Chu, T.; Clark, J. A.; Demos, N.; Fong, H.; Healy, J.; Hemberger, D. A.; Hinder, I.; Jani, K.; Khamesra, B.; Kidder, L. E.; Kumar, P.; Laguna, P.; Lousto, C. O.; Lovelace, G.; Ossokine, S.; Pfeiffer, H.; Scheel, M. A.; Shoemaker, D. M.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.
2017-11-01
We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity (NR) simulations. In this study, we present a detailed investigation of the systematic and statistical parameter estimation errors of this method. This procedure bypasses approximations used in semianalytical models for compact binary coalescence. In this work, we use the full posterior parameter distribution for only generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log likelihood, ln L ) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both l ≤2 as well as l ≤3 harmonic modes. Using the l ≤3 higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin, GW150914-like, and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates that we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters.
Advanced numerical methods for three dimensional two-phase flow calculations
Energy Technology Data Exchange (ETDEWEB)
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Advanced numerical methods for three dimensional two-phase flow calculations
International Nuclear Information System (INIS)
Toumi, I.; Caruge, D.
1997-01-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations
Stable Numerical Approach for Fractional Delay Differential Equations
Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.
2017-12-01
In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.
Essential numerical computer methods
Johnson, Michael L
2010-01-01
The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide ...
International Nuclear Information System (INIS)
Jo, Jong Chull; Shin, Won Ky
1997-01-01
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available
Numerical methods and optimization a consumer guide
Walter, Éric
2014-01-01
Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to · discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; · understand the principles behind recognized algorithms used in state-of-the-art numerical software; · learn the advantag...
Operator theory and numerical methods
Fujita, H; Suzuki, T
2001-01-01
In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.
Numerical methods for scientists and engineers
Antia, H M
2012-01-01
This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.
The numerical simulation of convection delayed dominated diffusion equation
Directory of Open Access Journals (Sweden)
Mohan Kumar P. Murali
2016-01-01
Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.
Numerical methods for stochastic partial differential equations with white noise
Zhang, Zhongqiang
2017-01-01
This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...
Numerical method of singular problems on singular integrals
International Nuclear Information System (INIS)
Zhao Huaiguo; Mou Zongze
1992-02-01
As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily
Numerical functional integration method for studying the properties of the physical vacuum
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.
1998-01-01
The new approach to investigate the physical vacuum in quantum theories including its nonperturbative topological structure is discussed. This approach is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulas which we constructed for this kind of integral. No preliminary discretization of space and time is required, as well as no simplifying assumptions like semiclassical approximation, collective excitations, introduction of ''short-time'' propagators, etc. are necessary in this approach. The method allows to use the more preferable deterministic algorithms instead of the traditional stochastic technique. It has been proven that our approach has important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models and to the computation of the topological susceptibility and the θ-vacua energy are presented. (author)
Numerical solution of distributed order fractional differential equations
Katsikadelis, John T.
2014-02-01
In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.
Numerical methods for engine-airframe integration
International Nuclear Information System (INIS)
Murthy, S.N.B.; Paynter, G.C.
1986-01-01
Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment
NUMERICAL AND ANALYTIC METHODS OF ESTIMATION BRIDGES’ CONSTRUCTIONS
Directory of Open Access Journals (Sweden)
Y. Y. Luchko
2010-03-01
Full Text Available In this article the numerical and analytical methods of calculation of the stressed-and-strained state of bridge constructions are considered. The task on increasing of reliability and accuracy of the numerical method and its solution by means of calculations in two bases are formulated. The analytical solution of the differential equation of deformation of a ferro-concrete plate under the action of local loads is also obtained.
Numerical models for differential problems
Quarteroni, Alfio
2017-01-01
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...
Theoretical and numerical method in aeroacoustics
Directory of Open Access Journals (Sweden)
Nicuşor ALEXANDRESCU
2010-06-01
Full Text Available The paper deals with the mathematical and numerical modeling of the aerodynamic noisegenerated by the fluid flow interaction with the solid structure of a rotor blade.Our analysis use Lighthill’s acoustic analogy. Lighthill idea was to express the fundamental equationsof motion into a wave equation for acoustic fluctuation with a source term on the right-hand side. Theobtained wave equation is solved numerically by the spatial discretization. The method is applied inthe case of monopole source placed in different points of blade surfaces to find this effect of noisepropagation.
Numerical methods in finance and economics a MATLAB-based introduction
Brandimarte, Paolo
2006-01-01
A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions.Among this book''s most outstanding features is the...
Numerically and experimentally analysis of creep
International Nuclear Information System (INIS)
Fontanive, J.A.
1982-11-01
The problems of creep in concrete are analyzed experimentally and numerically, comparing with classical methods and suggesting a numerical procedure for the solution of these problems. Firstly, fundamentals of viscoelasticity and its application to concrete behaviour representation are presented. Then the theories of Dischinger and Arutyunyan are studied, and a computing numerical solutions are compared in several examples. Finally, experiences on creep and relaxation are described, and its result are analyzed. Some coments on possible future developments are included. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1998-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Partial differential equations with numerical methods
Larsson, Stig
2003-01-01
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.
Hybrid RANS-LES using high order numerical methods
Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael
2017-11-01
Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.
Park, SangWook; Kim, Minhyuk
2016-01-01
In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines.
International Nuclear Information System (INIS)
Hawong, Jai Sug; Lee, Dong Hun; Lee, Dong Ha; Tche, Konstantin
2004-01-01
In this research, the photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the photoelastic experimental hybrid method with Hook-Jeeves numerical method, we can separate stress components from isochromatics only and stress intensity factors and stress concentration factors can be determined. The photoelastic experimental hybrid method with Hook-Jeeves had better be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method
Numerical Analysis of Partial Differential Equations
Lui, S H
2011-01-01
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis
Numerical simulation of GEW equation using RBF collocation method
Directory of Open Access Journals (Sweden)
Hamid Panahipour
2012-08-01
Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.
Teaching numerical methods with IPython notebooks and inquiry-based learning
Ketcheson, David I.
2014-01-01
A course in numerical methods should teach both the mathematical theory of numerical analysis and the craft of implementing numerical algorithms. The IPython notebook provides a single medium in which mathematics, explanations, executable code, and visualizations can be combined, and with which the student can interact in order to learn both the theory and the craft of numerical methods. The use of notebooks also lends itself naturally to inquiry-based learning methods. I discuss the motivation and practice of teaching a course based on the use of IPython notebooks and inquiry-based learning, including some specific practical aspects. The discussion is based on my experience teaching a Masters-level course in numerical analysis at King Abdullah University of Science and Technology (KAUST), but is intended to be useful for those who teach at other levels or in industry.
Energy Technology Data Exchange (ETDEWEB)
Bouillard, N
2006-12-15
When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external
Energy Technology Data Exchange (ETDEWEB)
Bouillard, N
2006-12-15
When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a
Numerical methods in electron magnetic resonance
International Nuclear Information System (INIS)
Soernes, A.R.
1998-01-01
The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system
Numerical methods in electron magnetic resonance
Energy Technology Data Exchange (ETDEWEB)
Soernes, A.R
1998-07-01
The focal point of the thesis is the development and use of numerical methods in the analysis, simulation and interpretation of Electron Magnetic Resonance experiments on free radicals in solids to uncover the structure, the dynamics and the environment of the system.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Numerical simulation of the flow field in pump intakes by means of Lattice Boltzmann methods
International Nuclear Information System (INIS)
Schneider, A; Conrad, D; Böhle, M
2013-01-01
Lattice Boltzmann Methods are nowadays popular schemes for solving fluid flow problems of engineering interest. This popularity is due to the advantages of these schemes: For example, the meshing of the fluid domain can be performed fully automatically which results in great simplicity in handling complex geometries. In this paper a numerical scheme for the flow simulation in pump intakes based on a Lattice Boltzmann large eddy approach is presented. The ability of this scheme to capture the flow phenomena of the intake flow at different operating conditions is analysed. For the operational reliability and efficiency of pumps and pump systems, the incoming flow conditions are crucial. Since the efficiency and reliability requirements of pumps are rising and must be guaranteed, the flow conditions in pump intakes have to be evaluated during plant planning. Recent trends show that pump intakes are built more and more compact, which makes the flow in the intake even more complex. Numerical methods are a promising technique for conduction flow analysis in pump intakes, because they can be realised rapidly and cheaply
Rock, Adam J; Coventry, William L; Morgan, Methuen I; Loi, Natasha M
2016-01-01
Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal et al., 1997). Given the ubiquitous and distributed nature of eLearning systems (Nof et al., 2015), teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology.
Rock, Adam J.; Coventry, William L.; Morgan, Methuen I.; Loi, Natasha M.
2016-01-01
Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal et al., 1997). Given the ubiquitous and distributed nature of eLearning systems (Nof et al., 2015), teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology. PMID:27014147
Directory of Open Access Journals (Sweden)
Adam John Rock
2016-03-01
Full Text Available Generally, academic psychologists are mindful of the fact that, for many students, the study of research methods and statistics is anxiety provoking (Gal, Ginsburg, & Schau, 1997. Given the ubiquitous and distributed nature of eLearning systems (Nof, Ceroni, Jeong, & Moghaddam, 2015, teachers of research methods and statistics need to cultivate an understanding of how to effectively use eLearning tools to inspire psychology students to learn. Consequently, the aim of the present paper is to discuss critically how using eLearning systems might engage psychology students in research methods and statistics. First, we critically appraise definitions of eLearning. Second, we examine numerous important pedagogical principles associated with effectively teaching research methods and statistics using eLearning systems. Subsequently, we provide practical examples of our own eLearning-based class activities designed to engage psychology students to learn statistical concepts such as Factor Analysis and Discriminant Function Analysis. Finally, we discuss general trends in eLearning and possible futures that are pertinent to teachers of research methods and statistics in psychology.
Kou, Jisheng
2015-08-01
Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.
A method for the direct generation of comprehensive numerical solar building transfer functions
Energy Technology Data Exchange (ETDEWEB)
Chen, T.Y. [The Hong Kong Polytechnic University (China). Dept. of Building Services Engineering
2003-02-01
This paper describes a method for the direct generation of comprehensive numerical room transfer functions with any derived parameters as output, such as operative temperature or thermal load. Complex conductive, convective and radiant heat transfer processes, or any derived thermal parameters in buildings can be explicitly and precisely described by a generalized thermal network. This allows the s-transfer and z-transfer functions to be directly generated, using semi-symbolic analysis techniques, Cayley's expansion of determinant and Heaviside's expansion theorem. A simple algorithm is developed for finding the roots of the denominator in the inverse transform of the s-transfer functions, which ensures that no single root is missing. The techniques have been applied to generating the transfer functions of a passive solar room with floor heating. The example calculation demonstrates the high efficiency of the computational method. (author)
Mathematical and numerical methods for Vlasov-Maxwell equations: the contributions of data mining
International Nuclear Information System (INIS)
Assous, F.; Chaskalovic, J.
2014-01-01
There exist a lot of formulations that can model plasma physics or particle accelerators problems as the Vlasov- Maxwell equations. This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov-Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov-Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a P1 and a P2 finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov-Maxwell equations take a central part. (authors)
Numerical methods for the Lévy LIBOR model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
2010-01-01
but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure....... This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\\'evy LIBOR model of Eberlein and \\"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates...
Numerical Methods for the Lévy LIBOR Model
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Skovmand, David
are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables...... simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.......The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods...
Classical and modern numerical analysis theory, methods and practice
Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan
2009-01-01
Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...
The numerical solution of boundary value problems over an infinite domain
International Nuclear Information System (INIS)
Shepherd, M.; Skinner, R.
1976-01-01
A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail
Numerical methods for modeling photonic-crystal VCSELs
DEFF Research Database (Denmark)
Dems, Maciej; Chung, Il-Sug; Nyakas, Peter
2010-01-01
We show comparison of four different numerical methods for simulating Photonic-Crystal (PC) VCSELs. We present the theoretical basis behind each method and analyze the differences by studying a benchmark VCSEL structure, where the PC structure penetrates all VCSEL layers, the entire top-mirror DBR...... to the effective index method. The simulation results elucidate the strength and weaknesses of the analyzed methods; and outline the limits of applicability of the different models....
Numerical computer methods part E
Johnson, Michael L
2004-01-01
The contributions in this volume emphasize analysis of experimental data and analytical biochemistry, with examples taken from biochemistry. They serve to inform biomedical researchers of the modern data analysis methods that have developed concomitantly with computer hardware. Selected Contents: A practical approach to interpretation of SVD results; modeling of oscillations in endocrine networks with feedback; quantifying asynchronous breathing; sample entropy; wavelet modeling and processing of nasal airflow traces.
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto
2017-01-01
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano
2017-03-22
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
Penalty methods for the numerical solution of American multi-asset option problems
Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak
2008-12-01
We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.
High accuracy mantle convection simulation through modern numerical methods
Kronbichler, Martin
2012-08-21
Numerical simulation of the processes in the Earth\\'s mantle is a key piece in understanding its dynamics, composition, history and interaction with the lithosphere and the Earth\\'s core. However, doing so presents many practical difficulties related to the numerical methods that can accurately represent these processes at relevant scales. This paper presents an overview of the state of the art in algorithms for high-Rayleigh number flows such as those in the Earth\\'s mantle, and discusses their implementation in the Open Source code Aspect (Advanced Solver for Problems in Earth\\'s ConvecTion). Specifically, we show how an interconnected set of methods for adaptive mesh refinement (AMR), higher order spatial and temporal discretizations, advection stabilization and efficient linear solvers can provide high accuracy at a numerical cost unachievable with traditional methods, and how these methods can be designed in a way so that they scale to large numbers of processors on compute clusters. Aspect relies on the numerical software packages deal.II and Trilinos, enabling us to focus on high level code and keeping our implementation compact. We present results from validation tests using widely used benchmarks for our code, as well as scaling results from parallel runs. © 2012 The Authors Geophysical Journal International © 2012 RAS.
Directory of Open Access Journals (Sweden)
SangWook Park
Full Text Available In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP and the IEEE standard guidelines.
Kim, Minhyuk
2016-01-01
In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines. PMID:27898688
Numerical methods: Analytical benchmarking in transport theory
International Nuclear Information System (INIS)
Ganapol, B.D.
1988-01-01
Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered
A textbook of computer based numerical and statistical techniques
Jaiswal, AK
2009-01-01
About the Book: Application of Numerical Analysis has become an integral part of the life of all the modern engineers and scientists. The contents of this book covers both the introductory topics and the more advanced topics such as partial differential equations. This book is different from many other books in a number of ways. Salient Features: Mathematical derivation of each method is given to build the students understanding of numerical analysis. A variety of solved examples are given. Computer programs for almost all numerical methods discussed have been presented in `C` langu
A numerical method for a transient two-fluid model
International Nuclear Information System (INIS)
Le Coq, G.; Libmann, M.
1978-01-01
The transient boiling two-phase flow is studied. In nuclear reactors, the driving conditions for the transient boiling are a pump power decay or/and an increase in heating power. The physical model adopted for the two-phase flow is the two fluid model with the assumption that the vapor remains at saturation. The numerical method for solving the thermohydraulics problems is a shooting method, this method is highly implicit. A particular problem exists at the boiling and condensation front. A computer code using this numerical method allow the calculation of a transient boiling initiated by a steady state for a PWR or for a LMFBR
A numerical method for a model of two-phase flow in a coupled free flow and porous media system
Chen, Jie; Sun, Shuyu; Wang, Xiaoping
2014-01-01
In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.
A numerical method for a model of two-phase flow in a coupled free flow and porous media system
Chen, Jie
2014-07-01
In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.
Method for numerical simulation of two-term exponentially correlated colored noise
International Nuclear Information System (INIS)
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-01-01
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications
Numerical Simulation of Cyclic Thermodynamic Processes
DEFF Research Database (Denmark)
Andersen, Stig Kildegård
2006-01-01
This thesis is on numerical simulation of cyclic thermodynamic processes. A modelling approach and a method for finding periodic steady state solutions are described. Examples of applications are given in the form of four research papers. Stirling machines and pulse tube coolers are introduced...... and a brief overview of the current state of the art in methods for simulating such machines is presented. It was found that different simulation approaches, which model the machines with different levels of detail, currently coexist. Methods using many simplifications can be easy to use and can provide...... models flexible and easy to modify, and to make simulations fast. A high level of accuracy was achieved for integrations of a model created using the modelling approach; the accuracy depended on the settings for the numerical solvers in a very predictable way. Selection of fast numerical algorithms...
Numerical solution of neutral functional-differential equations with proportional delays
Directory of Open Access Journals (Sweden)
Mehmet Giyas Sakar
2017-07-01
Full Text Available In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.
Mathematica with a Numerical Methods Course
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
Numerical perturbative methods in the quantum theory of physical systems
International Nuclear Information System (INIS)
Adam, G.
1980-01-01
During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)
On the potential of computational methods and numerical simulation in ice mechanics
International Nuclear Information System (INIS)
Bergan, Paal G; Cammaert, Gus; Skeie, Geir; Tharigopula, Venkatapathi
2010-01-01
This paper deals with the challenge of developing better methods and tools for analysing interaction between sea ice and structures and, in particular, to be able to calculate ice loads on these structures. Ice loads have traditionally been estimated using empirical data and 'engineering judgment'. However, it is believed that computational mechanics and advanced computer simulations of ice-structure interaction can play an important role in developing safer and more efficient structures, especially for irregular structural configurations. The paper explains the complexity of ice as a material in computational mechanics terms. Some key words here are large displacements and deformations, multi-body contact mechanics, instabilities, multi-phase materials, inelasticity, time dependency and creep, thermal effects, fracture and crushing, and multi-scale effects. The paper points towards the use of advanced methods like ALE formulations, mesh-less methods, particle methods, XFEM, and multi-domain formulations in order to deal with these challenges. Some examples involving numerical simulation of interaction and loads between level sea ice and offshore structures are presented. It is concluded that computational mechanics may prove to become a very useful tool for analysing structures in ice; however, much research is still needed to achieve satisfactory reliability and versatility of these methods.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
Towards numerical simulations of supersonic liquid jets using ghost fluid method
International Nuclear Information System (INIS)
Majidi, Sahand; Afshari, Asghar
2015-01-01
Highlights: • A ghost fluid method based solver is developed for numerical simulation of compressible multiphase flows. • The performance of the numerical tool is validated via several benchmark problems. • Emergence of supersonic liquid jets in quiescent gaseous environment is simulated using ghost fluid method for the first time. • Bow-shock formation ahead of the liquid jet is clearly observed in the obtained numerical results. • Radiation of mach waves from the phase-interface witnessed experimentally is evidently captured in our numerical simulations. - Abstract: A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid
Bayesian methods for the physical sciences learning from examples in astronomy and physics
Andreon, Stefano
2015-01-01
Statistical literacy is critical for the modern researcher in Physics and Astronomy. This book empowers researchers in these disciplines by providing the tools they will need to analyze their own data. Chapters in this book provide a statistical base from which to approach new problems, including numerical advice and a profusion of examples. The examples are engaging analyses of real-world problems taken from modern astronomical research. The examples are intended to be starting points for readers as they learn to approach their own data and research questions. Acknowledging that scientific progress now hinges on the availability of data and the possibility to improve previous analyses, data and code are distributed throughout the book. The JAGS symbolic language used throughout the book makes it easy to perform Bayesian analysis and is particularly valuable as readers may use it in a myriad of scenarios through slight modifications.
Numerical methods in matrix computations
Björck, Åke
2015-01-01
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Hybrid numerical calculation method for bend waveguides
Garnier , Lucas; Saavedra , C.; Castro-Beltran , Rigoberto; Lucio , José Luis; Bêche , Bruno
2017-01-01
National audience; The knowledge of how the light will behave in a waveguide with a radius of curvature becomes more and more important because of the development of integrated photonics, which include ring micro-resonators, phasars, and other devices with a radius of curvature. This work presents a numerical calculation method to determine the eigenvalues and eigenvectors of curved waveguides. This method is a hybrid method which uses at first conform transformation of the complex plane gene...
Intelligent numerical methods applications to fractional calculus
Anastassiou, George A
2016-01-01
In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
Energy Technology Data Exchange (ETDEWEB)
Safta, Cosmin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Najm, Habib N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Phipps, Eric Todd [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-09-01
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
Implementing a flipped classroom approach in a university numerical methods mathematics course
Johnston, Barbara M.
2017-05-01
This paper describes and analyses the implementation of a 'flipped classroom' approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an examination of the attitudes of the 2014 cohort to the approach in general as well as analysing their use of the videos. Based on these responses, the instructor makes a number of changes (for example, the use of 'cloze' summary notes and the introduction of an extra, optional tutorial class) before repeating the 'flipped classroom' approach the following year. The attitudes to the approach and the video usage of the 2015 cohort are then compared with the 2014 cohort and further changes that could be implemented for the next cohort are suggested.
Zhang, H.-m.; Chen, X.-f.; Chang, S.
- It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.
The development of efficient numerical time-domain modeling methods for geophysical wave propagation
Zhu, Lieyuan
This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The
A Numerical Matrix-Based method in Harmonic Studies in Wind Power Plants
DEFF Research Database (Denmark)
Dowlatabadi, Mohammadkazem Bakhshizadeh; Hjerrild, Jesper; Kocewiak, Łukasz Hubert
2016-01-01
In the low frequency range, there are some couplings between the positive- and negative-sequence small-signal impedances of the power converter due to the nonlinear and low bandwidth control loops such as the synchronization loop. In this paper, a new numerical method which also considers...... these couplings will be presented. The numerical data are advantageous to the parametric differential equations, because analysing the high order and complex transfer functions is very difficult, and finally one uses the numerical evaluation methods. This paper proposes a numerical matrix-based method, which...
Numerical and experimental analysis of eddy currents induced in tokamak machines
International Nuclear Information System (INIS)
Takahashi, T.; Takahashi, G.; Kazawa, Y.; Suzuki, Y.
1977-01-01
This paper deals with eddy current phenomena in Tokamak machines. A numerical method is presented which will permit eddy currents to be calculated. Examples of numerical results and a discussion of the JT-60 are shown. Calculations are checked by measurements in basic models
Interdisciplinary Study of Numerical Methods and Power Plants Engineering
Directory of Open Access Journals (Sweden)
Ioana OPRIS
2014-08-01
Full Text Available The development of technology, electronics and computing opened the way for a cross-disciplinary research that brings benefits by combining the achievements of different fields. To prepare the students for their future interdisciplinary approach,aninterdisciplinary teaching is adopted. This ensures their progress in knowledge, understanding and ability to navigate through different fields. Aiming these results, the Universities introduce new interdisciplinary courses which explore complex problems by studying subjects from different domains. The paper presents a problem encountered in designingpower plants. The method of solvingthe problem isused to explain the numerical methods and to exercise programming.The goal of understanding a numerical algorithm that solves a linear system of equations is achieved by using the knowledge of heat transfer to design the regenerative circuit of a thermal power plant. In this way, the outcomes from the prior courses (mathematics and physics are used to explain a new subject (numerical methods and to advance future ones (power plants.
Numerical methods for Bayesian inference in the face of aging
International Nuclear Information System (INIS)
Clarotti, C.A.; Villain, B.; Procaccia, H.
1996-01-01
In recent years, much attention has been paid to Bayesian methods for Risk Assessment. Until now, these methods have been studied from a theoretical point of view. Researchers have been mainly interested in: studying the effectiveness of Bayesian methods in handling rare events; debating about the problem of priors and other philosophical issues. An aspect central to the Bayesian approach is numerical computation because any safety/reliability problem, in a Bayesian frame, ends with a problem of numerical integration. This aspect has been neglected until now because most Risk studies assumed the Exponential model as the basic probabilistic model. The existence of conjugate priors makes numerical integration unnecessary in this case. If aging is to be taken into account, no conjugate family is available and the use of numerical integration becomes compulsory. EDF (National Board of Electricity, of France) and ENEA (National Committee for Energy, New Technologies and Environment, of Italy) jointly carried out a research program aimed at developing quadrature methods suitable for Bayesian Interference with underlying Weibull or gamma distributions. The paper will illustrate the main results achieved during the above research program and will discuss, via some sample cases, the performances of the numerical algorithms which on the appearance of stress corrosion cracking in the tubes of Steam Generators of PWR French power plants. (authors)
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha; Ferreira, Rita; Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha
2016-10-04
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Methods tuned on the physical problem. A way to improve numerical codes
International Nuclear Information System (INIS)
Ixaru, L.Gr.
2010-01-01
We consider the problem on how the numerical methods tuned on the physical problem can contribute to the enhancement of the performance of the codes. We illustrate this on two simple cases: solution of time independent one-dimensional Schroedinger equation, and the computation of integrals with oscillatory integrands. In both cases the tuned versions bring a massive gain in accuracy at negligible extra cost. We presented two simple problems where successive levels of tuning enhance significantly the accuracy at negligible extra cost. These problems should be seen as representing only some illustrations on how the codes can be improved but we must also mention that in many cases tuned versions still have to be developed. Just for a suggestion, quadrature formulae which involve the integrand and a number of successive derivatives of this exist, but no formula is available when some of these derivatives are missing, for example when we dispose of y and y'' but not of y'. A direct application will be on the case when the integrand involves the solution of the Schrodinger equation by the method of Numerov. (author)
Borcard, Daniel; Legendre, Pierre
2018-01-01
This new edition of Numerical Ecology with R guides readers through an applied exploration of the major methods of multivariate data analysis, as seen through the eyes of three ecologists. It provides a bridge between a textbook of numerical ecology and the implementation of this discipline in the R language. The book begins by examining some exploratory approaches. It proceeds logically with the construction of the key building blocks of most methods, i.e. association measures and matrices, and then submits example data to three families of approaches: clustering, ordination and canonical ordination. The last two chapters make use of these methods to explore important and contemporary issues in ecology: the analysis of spatial structures and of community diversity. The aims of methods thus range from descriptive to explanatory and predictive and encompass a wide variety of approaches that should provide readers with an extensive toolbox that can address a wide palette of questions arising in contemporary mul...
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.; Saude, Joao
2017-01-01
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.
2017-04-29
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Developing Teaching Material Software Assisted for Numerical Methods
Handayani, A. D.; Herman, T.; Fatimah, S.
2017-09-01
The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.
Introduction to numerical methods for time dependent differential equations
Kreiss, Heinz-Otto
2014-01-01
Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t
Numerical solution of the polymer system
Energy Technology Data Exchange (ETDEWEB)
Haugse, V.; Karlsen, K.H.; Lie, K.-A.; Natvig, J.R.
1999-05-01
The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Remain solutions and exact tracking of waves. It is well known that the front tracking method may introduce a blow-up of the initial total variation for initial data along the curve where the two eigenvalues of the hyperbolic system are identical. It is demonstrated by numerical examples that the method converges to the correct solution after a finite time that decreases with the discretization parameter. For multidimensional problems, front tracking is combined with dimensional splitting and numerical experiments indicate that large splitting steps can be used without loss of accuracy. Typical CFL numbers are in the range of 10 to 20 and comparisons with the Riemann free, high-resolution method confirm the high efficiency of front tracking. The polymer system, coupled with an elliptic pressure equation, models two-phase, tree-component polymer flooding in an oil reservoir. Two examples are presented where this model is solved by a sequential time stepping procedure. Because of the approximate Riemann solver, the method is non-conservative and CFL members must be chosen only moderately larger than unity to avoid substantial material balance errors generated in near-well regions after water breakthrough. Moreover, it is demonstrated that dimensional splitting may introduce severe grid orientation effects for unstable displacements that are accentuated for decreasing discretization parameters. 9 figs., 2 tabs., 26 refs.
Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method
Directory of Open Access Journals (Sweden)
Jun He
2018-05-01
Full Text Available One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM is developed in this study to simulate the thermo-elastic fracturing of rocklike granular materials. The Voronoi tessellation is incorporated into the pre-processor of NMM to represent the grain structure. A contact-based heat transfer model is developed to reflect heat interaction among grains. Based on the model, the transient thermal conduction algorithm for granular materials is established. To simulate the cohesion effects among grains and the fracturing process between grains, a damage-based contact fracture model is developed to improve the contact algorithm of NMM. In the developed numerical method, the heat interaction among grains as well as the heat transfer inside each solid grain are both simulated. Additionally, as damage evolution and fracturing at grain interfaces are also considered, the developed numerical method is applicable to simulate the geothermal-related thermal fracturing process.
Rigid inclusions-Comparison between analytical and numerical methods
International Nuclear Information System (INIS)
Gomez Perez, R.; Melentijevic, S.
2014-01-01
This paper compares different analytical methods for analysis of rigid inclusions with finite element modeling. First of all, the load transfer in the distribution layer is analyzed for its different thicknesses and different inclusion grids to define the range between results obtained by analytical and numerical methods. The interaction between the soft soil and the inclusion in the estimation of settlements is studied as well. Considering different stiffness of the soft soil, settlements obtained analytical and numerically are compared. The influence of the soft soil modulus of elasticity on the neutral point depth was also performed by finite elements. This depth has a great importance for the definition of the total length of rigid inclusion. (Author)
Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling
Dobronets, B. S.; Popova, O. A.
2018-05-01
Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.
Efficient numerical methods for fluid- and electrodynamics on massively parallel systems
Energy Technology Data Exchange (ETDEWEB)
Zudrop, Jens
2016-07-01
In the last decade, computer technology has evolved rapidly. Modern high performance computing systems offer a tremendous amount of computing power in the range of a few peta floating point operations per second. In contrast, numerical software development is much slower and most existing simulation codes cannot exploit the full computing power of these systems. Partially, this is due to the numerical methods themselves and partially it is related to bottlenecks within the parallelization concept and its data structures. The goal of the thesis is the development of numerical algorithms and corresponding data structures to remedy both kinds of parallelization bottlenecks. The approach is based on a co-design of the numerical schemes (including numerical analysis) and their realizations in algorithms and software. Various kinds of applications, from multicomponent flows (Lattice Boltzmann Method) to electrodynamics (Discontinuous Galerkin Method) to embedded geometries (Octree), are considered and efficiency of the developed approaches is demonstrated for large scale simulations.
Wang, Yi
2016-07-21
Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.
Implementation and assessment of high-resolution numerical methods in TRACE
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Wang, Dean, E-mail: wangda@ornl.gov [Oak Ridge National Laboratory, 1 Bethel Valley RD 6167, Oak Ridge, TN 37831 (United States); Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G. [U.S. Nuclear Regulatory Commission, Washington, DC 20555 (United States)
2013-10-15
Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency.
Implementation and assessment of high-resolution numerical methods in TRACE
International Nuclear Information System (INIS)
Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph; Thurston, Carl G.
2013-01-01
Highlights: • Study and implement high-resolution numerical methods for two-phase flow. • They can achieve better numerical accuracy than the 1st-order upwind scheme. • They are of great numerical robustness and efficiency. • Great application for BWR stability analysis and boron injection. -- Abstract: The 1st-order upwind differencing numerical scheme is widely employed to discretize the convective terms of the two-phase flow transport equations in reactor systems analysis codes such as TRACE and RELAP. While very robust and efficient, 1st-order upwinding leads to excessive numerical diffusion. Standard 2nd-order numerical methods (e.g., Lax–Wendroff and Beam–Warming) can effectively reduce numerical diffusion but often produce spurious oscillations for steep gradients. To overcome the difficulties with the standard higher-order schemes, high-resolution schemes such as nonlinear flux limiters have been developed and successfully applied in numerical simulation of fluid-flow problems in recent years. The present work contains a detailed study on the implementation and assessment of six nonlinear flux limiters in TRACE. These flux limiters selected are MUSCL, Van Leer (VL), OSPRE, Van Albada (VA), ENO, and Van Albada 2 (VA2). The assessment is focused on numerical stability, convergence, and accuracy of the flux limiters and their applicability for boiling water reactor (BWR) stability analysis. It is found that VA and MUSCL work best among of the six flux limiters. Both of them not only have better numerical accuracy than the 1st-order upwind scheme but also preserve great robustness and efficiency
International Nuclear Information System (INIS)
Saurel, Richard; Franquet, Erwin; Daniel, Eric; Le Metayer, Olivier
2007-01-01
A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures
Numerical methods in nuclear engineering. Part 1
International Nuclear Information System (INIS)
Phillips, G.J.
1983-08-01
These proceedings, published in two parts contain the full text of 56 papers and summaries of six papers presented at the conference. They cover the use of numerical methods in thermal hydraulics, reactor physics, neutron diffusion, subchannel analysis, risk assessment, transport theory, and fuel behaviour
Advanced numerical methods for three dimensional two-phase flow calculations in PWR
International Nuclear Information System (INIS)
Toumi, I.; Gallo, D.; Royer, E.
1997-01-01
This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)
Numerical solution of the Navier-Stokes equations by discontinuous Galerkin method
Krasnov, M. M.; Kuchugov, P. A.; E Ladonkina, M.; E Lutsky, A.; Tishkin, V. F.
2017-02-01
Detailed unstructured grids and numerical methods of high accuracy are frequently used in the numerical simulation of gasdynamic flows in areas with complex geometry. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach offers a number of advantages inherent to both finite-element and finite-difference approximations. Moreover, the present paper shows that DGM schemes can be viewed as Godunov method extension to piecewise-polynomial functions. As is known, DGM involves significant computational complexity, and this brings up the question of ensuring the most effective use of all the computational capacity available. In order to speed up the calculations, operator programming method has been applied while creating the computational module. This approach makes possible compact encoding of mathematical formulas and facilitates the porting of programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. With the software package, based on DGM, numerical simulations of supersonic flow past solid bodies has been carried out. The numerical results are in good agreement with the experimental ones.
Numerical methods to solve the two-dimensional heat conduction equation
International Nuclear Information System (INIS)
Santos, R.S. dos.
1981-09-01
A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt
Numerical Simulation of Polynomial-Speed Convergence Phenomenon
Li, Yao; Xu, Hui
2017-11-01
We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to seek numerical justification for the ergodicity of two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.
Geothermal-Related Thermo-Elastic Fracture Analysis by Numerical Manifold Method
Jun He; Quansheng Liu; Zhijun Wu; Yalong Jiang
2018-01-01
One significant factor influencing geothermal energy exploitation is the variation of the mechanical properties of rock in high temperature environments. Since rock is typically a heterogeneous granular material, thermal fracturing frequently occurs in the rock when the ambient temperature changes, which can greatly influence the geothermal energy exploitation. A numerical method based on the numerical manifold method (NMM) is developed in this study to simulate the thermo-elastic fracturing ...
A hybrid numerical method for orbit correction
International Nuclear Information System (INIS)
White, G.; Himel, T.; Shoaee, H.
1997-09-01
The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
FORECASTING PILE SETTLEMENT ON CLAYSTONE USING NUMERICAL AND ANALYTICAL METHODS
Directory of Open Access Journals (Sweden)
Ponomarev Andrey Budimirovich
2016-06-01
Full Text Available In the article the problem of designing pile foundations on claystones is reviewed. The purpose of this paper is comparative analysis of the analytical and numerical methods for forecasting the settlement of piles on claystones. The following tasks were solved during the study: 1 The existing researches of pile settlement are analyzed; 2 The characteristics of experimental studies and the parameters for numerical modeling are presented, methods of field research of single piles’ operation are described; 3 Calculation of single pile settlement is performed using numerical methods in the software package Plaxis 2D and analytical method according to the requirements SP 24.13330.2011; 4 Experimental data is compared with the results of analytical and numerical calculations; 5 Basing on these results recommendations for forecasting pile settlement on claystone are presented. Much attention is paid to the calculation of pile settlement considering the impacted areas in ground space beside pile and the comparison with the results of field experiments. Basing on the obtained results, for the prediction of settlement of single pile on claystone the authors recommend using the analytical method considered in SP 24.13330.2011 with account for the impacted areas in ground space beside driven pile. In the case of forecasting the settlement of single pile on claystone by numerical methods in Plaxis 2D the authors recommend using the Hardening Soil model considering the impacted areas in ground space beside the driven pile. The analyses of the results and calculations are presented for examination and verification; therefore it is necessary to continue the research work of deep foundation at another experimental sites to improve the reliability of the calculation of pile foundation settlement. The work is of great interest for geotechnical engineers engaged in research, design and construction of pile foundations.
Numerical simulation in plasma physics
International Nuclear Information System (INIS)
Samarskii, A.A.
1980-01-01
Plasma physics is not only a field for development of physical theories and mathematical models but also an object of application of the computational experiment comprising analytical and numerical methods adapted for computers. The author considers only MHD plasma physics problems. Examples treated are dissipative structures in plasma; MHD model of solar dynamo; supernova explosion simulation; and plasma compression by a liner. (Auth.)
Application of numerical analysis methods to thermoluminescence dosimetry
International Nuclear Information System (INIS)
Gomez Ros, J. M.; Delgado, A.
1989-01-01
This report presents the application of numerical methods to thermoluminescence dosimetry (TLD), showing the advantages obtained over conventional evaluation systems. Different configurations of the analysis method are presented to operate in specific dosimetric applications of TLD, such as environmental monitoring and mailed dosimetry systems for quality assurance in radiotherapy facilities. (Author) 10 refs
Numerical method for three dimensional steady-state two-phase flow calculations
International Nuclear Information System (INIS)
Raymond, P.; Toumi, I.
1992-01-01
This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaofeng, E-mail: xfyang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Zhao, Jia, E-mail: zhao62@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (United States); Wang, Qi, E-mail: qwang@math.sc.edu [Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States); Beijing Computational Science Research Center, Beijing (China); School of Materials Science and Engineering, Nankai University, Tianjin (China)
2017-03-15
The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.
Numerical methods of mathematical optimization with Algol and Fortran programs
Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner
1971-01-01
Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition
A numerical method for solving singular De`s
Energy Technology Data Exchange (ETDEWEB)
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Ortleb, Sigrun; Seidel, Christian
2017-07-01
In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.
Numerical method for two phase flow with a unstable interface
International Nuclear Information System (INIS)
Glimm, J.; Marchesin, D.; McBryan, O.
1981-01-01
The random choice method is used to compute the oil-water interface for two dimensional porous media equations. The equations used are a pair of coupled equations; the (elliptic) pressure equation and the (hyperbolic) saturation equation. The equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion. The method resolves saturation discontinuities sharply. The main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case. Two methods of inducing fingers are considered: deterministically, through choice of Cauchy data and heterogeneity, through maximizing the randomness of the random choice method
An implicit second order numerical method for two-fluid models
International Nuclear Information System (INIS)
Toumi, I.
1995-01-01
We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)
Directory of Open Access Journals (Sweden)
Qi Wang
2012-01-01
Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.
Directory of Open Access Journals (Sweden)
D. G. Patalakh
2018-02-01
Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.
Numerical methods for differential equations and applications
International Nuclear Information System (INIS)
Ixaru, L.G.
1984-01-01
This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
A numerical test of the collective coordinate method
International Nuclear Information System (INIS)
Dobrowolski, T.; Tatrocki, P.
2008-01-01
The purpose of this Letter is to compare the dynamics of the kink interacting with the imperfection which follows from the collective coordinate method with the numerical results obtained on the ground of the field theoretical model. We showed that for weekly interacting kinks the collective coordinate method works similarly well for low and extremely large speeds
Structural dynamics teaching example: A linear test analysis case using open software
DEFF Research Database (Denmark)
Sturesson, P. O.; Brandt, A.; Ristinmaa, M.
2013-01-01
Teaching the topic of structural dynamics in any engineering field is a true challenge due to the wide span of the underlying subjects like mathematics, mechanics (both rigid body and continuum mechanics), numerical analysis, random data analysis and physical understanding.With the increased avai...... available as open source code. © The Society for Experimental Mechanics, Inc. 2013....... experimental modal analysis data. By using open software, based on MATLAB®1 as a basis for the example, the applied numerical methods are made transparent to the student. The example is built on a combination of the free CALFEM®2 and ABRAVIBE toolboxes, and thus all code used in this paper is publically...
Increased-accuracy numerical modeling of electron-optical systems with space-charge
International Nuclear Information System (INIS)
Sveshnikov, V.
2011-01-01
This paper presents a method for improving the accuracy of space-charge computation for electron-optical systems. The method proposes to divide the computational region into two parts: a near-cathode region in which analytical solutions are used and a basic one in which numerical methods compute the field distribution and trace electron ray paths. A numerical method is used for calculating the potential along the interface, which involves solving a non-linear equation. Preliminary results illustrating the improvement of accuracy and the convergence of the method for a simple test example are presented.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
Energy Technology Data Exchange (ETDEWEB)
R. A. Berry; M. O. Delchini; J. Ragusa
2014-06-01
The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.
Multi-example feature-constrained back-projection method for image super-resolution
Institute of Scientific and Technical Information of China (English)
Junlei Zhang; Dianguang Gai; Xin Zhang; Xuemei Li
2017-01-01
Example-based super-resolution algorithms,which predict unknown high-resolution image information using a relationship model learnt from known high- and low-resolution image pairs, have attracted considerable interest in the field of image processing. In this paper, we propose a multi-example feature-constrained back-projection method for image super-resolution. Firstly, we take advantage of a feature-constrained polynomial interpolation method to enlarge the low-resolution image. Next, we consider low-frequency images of different resolutions to provide an example pair. Then, we use adaptive k NN search to find similar patches in the low-resolution image for every image patch in the high-resolution low-frequency image, leading to a regression model between similar patches to be learnt. The learnt model is applied to the low-resolution high-frequency image to produce high-resolution high-frequency information. An iterative back-projection algorithm is used as the final step to determine the final high-resolution image.Experimental results demonstrate that our method improves the visual quality of the high-resolution image.
International Nuclear Information System (INIS)
Garratt, T.J.
1989-05-01
Safety assessments of radioactive waste disposal require efficient computer models for the important processes. The present paper is based on an efficient computational technique which can be used to solve a wide variety of safety assessment models. It involves the numerical inversion of analytical solutions to the Laplace-transformed differential equations using a method proposed by Talbot. This method has been implemented on a personal computer in a user-friendly manner. The steps required to implement a particular transform and run the program are outlined. Four examples are described which illustrate the flexibility, accuracy and efficiency of the program. The improvements in computational efficiency described in this paper have application to the probabilistic safety assessment codes ESCORT and MASCOT which are currently under development. Also, it is hoped that the present work will form the basis of software for personal computers which could be used to demonstrate safety assessment procedures to a wide audience. (author)
Advanced Numerical and Theoretical Methods for Photonic Crystals and Metamaterials
Felbacq, Didier
2016-11-01
This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
A asymptotic numerical method for the steady-state convection diffusion equation
International Nuclear Information System (INIS)
Wu Qiguang
1988-01-01
In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size
Numerical methods and computers used in elastohydrodynamic lubrication
Hamrock, B. J.; Tripp, J. H.
1982-01-01
Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.
Numerical Characterization of Piezoceramics Using Resonance Curves
Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar
2016-01-01
Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875
Numerical Characterization of Piezoceramics Using Resonance Curves
Directory of Open Access Journals (Sweden)
Nicolás Pérez
2016-01-01
Full Text Available Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM, to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.
Direct numerical methods of mathematical modeling in mechanical structural design
International Nuclear Information System (INIS)
Sahili, Jihad; Verchery, Georges; Ghaddar, Ahmad; Zoaeter, Mohamed
2002-01-01
Full text.Structural design and numerical methods are generally interactive; requiring optimization procedures as the structure is analyzed. This analysis leads to define some mathematical terms, as the stiffness matrix, which are resulting from the modeling and then used in numerical techniques during the dimensioning procedure. These techniques and many others involve the calculation of the generalized inverse of the stiffness matrix, called also the 'compliance matrix'. The aim of this paper is to introduce first, some different existing mathematical procedures, used to calculate the compliance matrix from the stiffness matrix, then apply direct numerical methods to solve the obtained system with the lowest computational time, and to compare the obtained results. The results show a big difference of the computational time between the different procedures
Selection of robust methods. Numerical examples and results
Czech Academy of Sciences Publication Activity Database
Víšek, Jan Ámos
2005-01-01
Roč. 21, č. 11 (2005), s. 1-58 ISSN 1212-074X R&D Projects: GA ČR(CZ) GA402/03/0084 Institutional research plan: CEZ:AV0Z10750506 Keywords : robust regression * model selection * uniform consistency of M-estimators Subject RIV: BA - General Mathematics
Numerical Methods for the Design and Analysis of Photonic Crystal Fibres
DEFF Research Database (Denmark)
Roberts, John
2008-01-01
The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted.......The numerical methods available for calculating the electromagnetic mode properties of photonic crystal fibres are reviewed. The preferred schemes for analyzing TIR guiding and band gap guiding fibres are contrasted....
On numerical solution of Burgers' equation by homotopy analysis method
International Nuclear Information System (INIS)
Inc, Mustafa
2008-01-01
In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions
Theoretical and applied aerodynamics and related numerical methods
Chattot, J J
2015-01-01
This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and h...
A numerical method to compute interior transmission eigenvalues
International Nuclear Information System (INIS)
Kleefeld, Andreas
2013-01-01
In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
Energy Technology Data Exchange (ETDEWEB)
FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
On the Hughes model and numerical aspects
Gomes, Diogo A.
2017-01-05
We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.
Directory of Open Access Journals (Sweden)
Nicholas W. Mitiukov
2015-12-01
Full Text Available In paper there is proposed a new method of historical research, based on analysis of derivatives coefficients of database (for example, the form factor in the database of ballistic data. This method has a much greater protection from subjectivism and direct falsification, compared with the analysis obtained directly from the source of the numerical series, as any intentional or unintentional distortion of the raw data provides a significant contrast ratio derived from the average sample values. Application of this method to the analysis of ballistic data base of naval artillery allowed to find the facts, forcing a new look at some of the events in the history data on the German naval artillery before World War I, probably overpriced for disinformation opponents of the Entente; during the First World War, Spain, apparently held secret talks with the firm Bofors ended purchase of Swedish shells; the first Russian naval rifled guns were created obvious based on the project Blackly, not Krupp as traditionally considered.
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Communication Patterns in Preschool Education Institutions ? Practical Examples
Radic-Hozo, Endica
2014-01-01
Introduction: Proper communication in pre-school institutions for education is undeniable importance to the development of the child, as evidenced by numerous studies. After the child's birth follows the most complex phase in its early phases - preschool education. Only high-quality, synergistic relationship triad: parent-child-educator and the modern postulates of preschool child education, warrants successful preschool child education. Methods and materials: Description, with examples from ...
Second GAMM-conference on numerical methods in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.; Geller, W.
1977-01-01
Proceedings of the Second GAMM-Conference on Numerical Methods in Fluid Mechanics held at the DFVLR, Koeln, October 11 to 13, 1977. The conference was attended by approximately 100 participants from 13 European countries representing quite different fields ranging from Aerodynamics to Nuclear Energy. At the meeting 34 papers were presented, many of them concerned with basic problems in the field. It was well demonstrated that Numerical Methods in Fluid Mechanics do not only serve as means for the computation of flow fields but also as tools in the analysis of fluid mechanical phenomena, a role of large future importance if one considers the complexity especially of three-dimensional flows. (orig./RW) [de
Some Numerical Aspects on Crowd Motion - The Hughes Model
Gomes, Diogo A.
2016-01-06
Here, we study a crowd model proposed by R. Hughes in [5] and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solution. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.
Uniqueness and numerical methods in inverse obstacle scattering
International Nuclear Information System (INIS)
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
Numerical solution of electrostatic problems of the accelerator project VICKSI
International Nuclear Information System (INIS)
Janetzki, U.
1975-03-01
In this work, the numerical solution to a few of the electrostatic problems is dealt with which have occured within the framework of the heavy ion accelerator project VICKSI. By means of these selected examples, the versatile applicability of the numerical method is to be demonstrated, and simultaneously assistance is given for the solution of similar problems. The numerical process for solving ion-optics problems consists generally of two steps. In the first step, the potential distribution for a given boundary value problem is iteratively calculated for the Laplace equation, and then the image characteristics of the electostatic lense are investigated using the Raytrace method. (orig./LH) [de
Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems
International Nuclear Information System (INIS)
Meyer-Spasche, R.
1975-12-01
It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de
An analytical-numerical comprehensive method for optimizing the fringing magnetic field
International Nuclear Information System (INIS)
Xiao Meiqin; Mao Naifeng
1991-01-01
The criterion of optimizing the fringing magnetic field is discussed, and an analytical-numerical comprehensive method for realizing the optimization is introduced. The method mentioned above consists of two parts, the analytical part calculates the field of the shims, which corrects the fringing magnetic field by using uniform magnetizing method; the numerical part fulfils the whole calculation of the field distribution by solving the equation of magnetic vector potential A within the region covered by arbitrary triangular meshes with the aid of finite difference method and successive over relaxation method. On the basis of the method, the optimization of the fringing magnetic field for a large-scale electromagnetic isotope separator is finished
Energy Technology Data Exchange (ETDEWEB)
Sanada, Y; Ashida, Y; Sassa, K [Kyoto University, Kyoto (Japan)
1996-10-01
3-D numerical modeling by FDTD method was studied for ground penetrating radar. Radar radiates electromagnetic wave, and determines the existence and distance of objects by reflection wave. Ground penetrating radar uses the above functions for underground surveys, however, its resolution and velocity analysis accuracy are problems. In particular, propagation characteristics of electromagnetic wave in media such as heterogeneous and anisotropic soil and rock are essential. The behavior of electromagnetic wave in the ground could be precisely reproduced by 3-D numerical modeling using FDTD method. FDTD method makes precise analysis in time domain and electric and magnetic fields possible by sequentially calculating the difference equation of Maxwell`s equation. Because of the high calculation efficiency of FDTD method, more precise complicated analysis can be expected by using the latest advanced computers. The numerical model and calculation example are illustrated for surface type electromagnetic pulse ground penetrating radar assuming the survey of steel pipes of 1m deep. 4 refs., 3 figs., 1 tab.
A virtual component method in numerical computation of cascades for isotope separation
International Nuclear Information System (INIS)
Zeng Shi; Cheng Lu
2014-01-01
The analysis, optimization, design and operation of cascades for isotope separation involve computations of cascades. In analytical analysis of cascades, using virtual components is a very useful analysis method. For complicated cases of cascades, numerical analysis has to be employed. However, bound up to the conventional idea that the concentration of a virtual component should be vanishingly small, virtual component is not yet applied to numerical computations. Here a method of introducing the method of using virtual components to numerical computations is elucidated, and its application to a few types of cascades is explained and tested by means of numerical experiments. The results show that the concentration of a virtual component is not restrained at all by the 'vanishingly small' idea. For the same requirements on cascades, the cascades obtained do not depend on the concentrations of virtual components. (authors)
Numerical methods for axisymmetric and 3D nonlinear beams
Pinton, Gianmarco F.; Trahey, Gregg E.
2005-04-01
Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.
Methods for enhancing numerical integration
International Nuclear Information System (INIS)
Doncker, Elise de
2003-01-01
We give a survey of common strategies for numerical integration (adaptive, Monte-Carlo, Quasi-Monte Carlo), and attempt to delineate their realm of applicability. The inherent accuracy and error bounds for basic integration methods are given via such measures as the degree of precision of cubature rules, the index of a family of lattice rules, and the discrepancy of uniformly distributed point sets. Strategies incorporating these basic methods often use paradigms to reduce the error by, e.g., increasing the number of points in the domain or decreasing the mesh size, locally or uniformly. For these processes the order of convergence of the strategy is determined by the asymptotic behavior of the error, and may be too slow in practice for the type of problem at hand. For certain problem classes we may be able to improve the effectiveness of the method or strategy by such techniques as transformations, absorbing a difficult part of the integrand into a weight function, suitable partitioning of the domain, transformations and extrapolation or convergence acceleration. Situations warranting the use of these techniques (possibly in an 'automated' way) are described and illustrated by sample applications
Valve cam design using numerical step-by-step method
Vasilyev, Aleksandr; Bakhracheva, Yuliya; Kabore, Ousman; Zelenskiy, Yuriy
2014-01-01
This article studies the numerical step-by-step method of cam profile design. The results of the study are used for designing the internal combustion engine valve gear. This method allows to profile the peak efficiency of cams in view of many restrictions, connected with valve gear serviceability and reliability.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
Solutions manual to accompany An introduction to numerical methods and analysis
Epperson, James F
2014-01-01
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp
Numerical solution of ordinary differential equations
Fox, L
1987-01-01
Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...
International Nuclear Information System (INIS)
Okazaki, Motoaki
1997-11-01
In the previous report, the usefulness of a new numerical method to achieve a rigorous numerical calculation using a simple explicit method with the volume-junction model was presented with the verification calculation for the depressurization of a saturated two-phase mixture. In this report, on the basis of solution method above, a numerical method for general condition of two-phase flow in non-equilibrium states is presented. In general condition of two-phase flow, the combinations of saturated and non-saturated conditions of each phase are considered in the each flow of volume and junction. Numerical evaluation programs are separately prepared for each combination of flow condition. Several numerical calculations of various kinds of non-equilibrium two-phase flow are made to examine the validity of the numerical method. Calculated results showed that the thermodynamic states obtained in different solution schemes were consistent with each other. In the first scheme, the states are determined by using the steam table as a function of pressure and specific enthalpy which are obtained as the solutions of simultaneous equations. In the second scheme, density and specific enthalpy of each phase are directly calculated by using conservation equations of mass and enthalpy of each phase, respectively. Further, no accumulation of error in mass and energy was found. As for the specific enthalpy, two cases of using energy equations for the volume are examined. The first case uses total energy conservation equation and the second case uses the type of the first law of thermodynamics. The results of both cases agreed well. (author)
Energy Technology Data Exchange (ETDEWEB)
Abbas, Mahmoud I., E-mail: mabbas@physicist.net [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Badawi, M.S. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Ruskov, I.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); El-Khatib, A.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Grozdanov, D.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); Thabet, A.A. [Department of Medical Equipment Technology, Faculty of Allied Medical Sciences, Pharos University in Alexandria (Egypt); Kopatch, Yu.N. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Gouda, M.M. [Physics Department, Faculty of Science, Alexandria University, 21511 Alexandria (Egypt); Skoy, V.R. [Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2015-01-21
Gamma-ray detector systems are important instruments in a broad range of science and new setup are continually developing. The most recent step in the evolution of detectors for nuclear spectroscopy is the construction of large arrays of detectors of different forms (for example, conical, pentagonal, hexagonal, etc.) and sizes, where the performance and the efficiency can be increased. In this work, a new direct numerical method (NAM), in an integral form and based on the efficiency transfer (ET) method, is used to calculate the full-energy peak efficiency of a single hexagonal NaI(Tl) detector. The algorithms and the calculations of the effective solid angle ratios for a point (isotropic irradiating) gamma-source situated coaxially at different distances from the detector front-end surface, taking into account the attenuation of the gamma-rays in the detector's material, end-cap and the other materials in-between the gamma-source and the detector, are considered as the core of this (ET) method. The calculated full-energy peak efficiency values by the (NAM) are found to be in a good agreement with the measured experimental data.
A detailed survey of numerical methods for unconstrained minimization. Pt. 1
International Nuclear Information System (INIS)
Mika, K.; Chaves, T.
1980-01-01
A detailed description of numerical methods for unconstrained minimization is presented. This first part surveys in particular conjugate direction and gradient methods, whereas variable metric methods will be the subject of the second part. Among the results of special interest we quote the following. The conjugate direction methods of Powell, Zangwill and Sutti can be best interpreted if the Smith approach is adopted. The conditions for quadratic termination of Powell's first procedure are analyzed. Numerical results based on nonlinear least squares problems are presented for the following conjugate direction codes: VA04AD from Harwell Subroutine Library and ZXPOW from IMSL, both implementations of Powell's second procedure, DFMND from IBM-SILMATH (Zangwill's method) and Brent's algorithm PRAXIS. VA04AD turns out to be superior in all cases, PRAXIS improves for high-dimensional problems. All codes clearly exhibit superlinear convergence. Akaike's result for the method of steepest descent is derived directly from a set of nonlinear recurrence relations. Numerical results obtained with the highly ill conditioned Hilbert function confirm the theoretical predictions. Several properties of the conjugate gradient method are presented and a new derivation of the equivalence of steepest descent partan and the CG method is given. A comparison of numerical results from the CG codes VA08AD (Fletcher-Reeves), DFMCG (the SSP version of the Fletcher-Reevens algorithm) and VA14AD (Powell's implementation of the Polak-Ribiere formula) reveals that VA14AD is clearly superior in all cases, but that the convergence rate of these codes is only weakly superlinear such that high accuracy solutions require extremely large numbers of function calls. (orig.)
Numerical Methods for Free Boundary Problems
1991-01-01
About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...
A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry
International Nuclear Information System (INIS)
Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan
1988-01-01
The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory
Numerical calculation of two-phase flows
International Nuclear Information System (INIS)
Travis, J.R.; Harlow, F.H.; Amsden, A.A.
1975-06-01
The theoretical study of time-varying two-phase flow problems in several space dimensions introduces such a complicated set of coupled nonlinear partial differential equations that numerical solution procedures for high-speed computers are required in almost all but the simplest examples. Efficient attainment of realistic solutions for practical problems requires a finite- difference formulation that is simultaneously implicit in the treatment of mass convection, equations of state, and the momentum coupling between phases. Such a method is described, the equations on which it is based are discussed, and its properties are illustrated by means of examples. In particular, the capability for calculating physical instabilities and other time-varying dynamics, at the same time avoiding numerical instability is emphasized. The computer code is applicable to problems in reactor safety analysis, the dynamics of fluidized dust beds, raindrops or aerosol transport, and a variety of similar circumstances, including the effects of phase transitions and the release of latent heat or chemical energy. (U.S.)
MATH: A Scientific Tool for Numerical Methods Calculation and Visualization
Directory of Open Access Journals (Sweden)
Henrich Glaser-Opitz
2016-02-01
Full Text Available MATH is an easy to use application for various numerical methods calculations with graphical user interface and integrated plotting tool written in Qt with extensive use of Qwt library for plotting options and use of Gsl and MuParser libraries as a numerical and parser helping libraries. It can be found at http://sourceforge.net/projects/nummath. MATH is a convenient tool for use in education process because of its capability of showing every important step in solution process to better understand how it is done. MATH also enables fast comparison of similar method speed and precision.
International Nuclear Information System (INIS)
Garcia-Torano, E.
1990-01-01
A set of numerical methods to analize alpha spectra measured with semiconductor detectors are presented. The methods can be divided in two groups, the first being based in the X 2 minimization ands the second in the use of the Fourier Transform. The methods based in the minimization of X 2 can, in turn, be divided according to the model used to fit the spectra. Some of them use a monoenergetic line for the intercomparison with the other peaks in the same spectrum. The others take into account the analytical function developed to represent an alpha line. Both allow the determination of positions and areas of the components, as well as the uncertainties of the results. The Fast Fourier Transform is applied to the second group of methods, which include the smoothing of experimental data, and the deconvolution of spectra. Examples are given of the application of these methods to real spectra. The alpha spectra of 237 Np and 236 Np are studied by using some of the methods described in this work. (Author)
Directory of Open Access Journals (Sweden)
Sandvik Leiv
2011-04-01
Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.
Numerical method for partial equilibrium flow
International Nuclear Information System (INIS)
Ramshaw, J.D.; Cloutman, L.D.; Los Alamos, New Mexico 87545)
1981-01-01
A numerical method is presented for chemically reactive fluid flow in which equilibrium and nonequilibrium reactions occur simultaneously. The equilibrium constraints on the species concentrations are established by a quadratic iterative procedure. If the equilibrium reactions are uncoupled and of second or lower order, the procedure converges in a single step. In general, convergence is most rapid when the reactions are weakly coupled. This can frequently be achieved by a judicious choice of the independent reactions. In typical transient calculations, satisfactory accuracy has been achieved with about five iterations per time step
On the numerical stability analysis of pipelined Krylov subspace methods
Czech Academy of Sciences Publication Activity Database
Carson, E.T.; Rozložník, Miroslav; Strakoš, Z.; Tichý, P.; Tůma, M.
submitted 2017 (2018) R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : Krylov subspace methods * the conjugate gradient method * numerical stability * inexact computations * delay of convergence * maximal attainable accuracy * pipelined Krylov subspace methods * exascale computations
Workshop on Numerical Methods for Ordinary Differential Equations
Gear, Charles; Russo, Elvira
1989-01-01
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Application of symplectic integrator to numerical fluid analysis
International Nuclear Information System (INIS)
Tanaka, Nobuatsu
2000-01-01
This paper focuses on application of the symplectic integrator to numerical fluid analysis. For the purpose, we introduce Hamiltonian particle dynamics to simulate fluid behavior. The method is based on both the Hamiltonian formulation of a system and the particle methods, and is therefore called Hamiltonian Particle Dynamics (HPD). In this paper, an example of HPD applications, namely the behavior of incompressible inviscid fluid, is solved. In order to improve accuracy of HPD with respect to space, CIVA, which is a highly accurate interpolation method, is combined, but the combined method is subject to problems in that the invariants of the system are not conserved in a long-time computation. For solving the problems, symplectic time integrators are introduced and the effectiveness is confirmed by numerical analyses. (author)
Analytic-numerical method of determining the freezing front location
Directory of Open Access Journals (Sweden)
R. Grzymkowski
2011-07-01
Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic boundary problems with the moving boundary. Solution of such defined problem requires, most often, to use sophisticated numerical techniques and far advanced mathematical tools. Excellent illustration of the complexity of considered problems, as well as of the variety of approaches used for finding their solutions, gives the papers [1-4]. In the current paper, the authors present the, especially attractive from the engineer point of view, analytic-numerical method for finding the approximate solution of selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of the sought function describing the temperature field into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of the function defining the location of freezing front with the broken line, parameters of which are numerically determined.
A method for solving the KDV equation and some numerical experiments
International Nuclear Information System (INIS)
Chang Jinjiang.
1993-01-01
In this paper, by means of difference method for discretization of space partial derivatives of KDV equation, an initial value problem in ordinary differential equations of large dimensions is produced. By using this ordinary differential equations the existence and the uniqueness of the solution of the KDV equation and the conservation of scheme are proved. This ordinary differential equation can be solved by using implicit Runge-Kutta methods, so a new method for finding the numerical solution of the KDV equation is presented. Numerical experiments not only describe in detail the procedure of two solitons collision, soliton reflex and soliton produce, but also show that this method is very effective. (author). 7 refs, 3 figs
An analytically based numerical method for computing view factors in real urban environments
Lee, Doo-Il; Woo, Ju-Wan; Lee, Sang-Hyun
2018-01-01
A view factor is an important morphological parameter used in parameterizing in-canyon radiative energy exchange process as well as in characterizing local climate over urban environments. For realistic representation of the in-canyon radiative processes, a complete set of view factors at the horizontal and vertical surfaces of urban facets is required. Various analytical and numerical methods have been suggested to determine the view factors for urban environments, but most of the methods provide only sky-view factor at the ground level of a specific location or assume simplified morphology of complex urban environments. In this study, a numerical method that can determine the sky-view factors ( ψ ga and ψ wa ) and wall-view factors ( ψ gw and ψ ww ) at the horizontal and vertical surfaces is presented for application to real urban morphology, which are derived from an analytical formulation of the view factor between two blackbody surfaces of arbitrary geometry. The established numerical method is validated against the analytical sky-view factor estimation for ideal street canyon geometries, showing a consolidate confidence in accuracy with errors of less than 0.2 %. Using a three-dimensional building database, the numerical method is also demonstrated to be applicable in determining the sky-view factors at the horizontal (roofs and roads) and vertical (walls) surfaces in real urban environments. The results suggest that the analytically based numerical method can be used for the radiative process parameterization of urban numerical models as well as for the characterization of local urban climate.
Wakabayashi, Hideaki; Asai, Masamitsu; Matsumoto, Keiji; Yamakita, Jiro
2016-11-01
Nakayama's shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.
A calculation method for RF couplers design based on numerical simulation by microwave studio
International Nuclear Information System (INIS)
Wang Rong; Pei Yuanji; Jin Kai
2006-01-01
A numerical simulation method for coupler design is proposed. It is based on the matching procedure for the 2π/3 structure given by Dr. R.L. Kyhl. Microwave Studio EigenMode Solver is used for such numerical simulation. the simulation for a coupler has been finished with this method and the simulation data are compared with experimental measurements. The results show that this numerical simulation method is feasible for coupler design. (authors)
Numerical simulation methods for wave propagation through optical waveguides
International Nuclear Information System (INIS)
Sharma, A.
1993-01-01
The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs
Directory of Open Access Journals (Sweden)
Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
A Broyden numerical Kutta condition for an unsteady panel method
International Nuclear Information System (INIS)
Liu, P.; Bose, N.; Colbourne, B.
2003-01-01
In panel methods, numerical Kutta conditions are applied in order to ensure that pressure differences between the surfaces at the trailing edges of lifting surface elements are close to zero. Previous numerical Kutta conditions for 3-D panel methods have focused on use of the Newton-Raphson iterative procedure. For extreme unsteady motions, such as for oscillating hydrofoils or for a propeller behind a blockage, the Newton-Raphson procedure can have severe convergence difficulties. The Broyden iteration, a modified Newton-Raphson iteration procedure, is applied here to obtain improved convergence behavior. Using the Broyden iteration increases the reliability, robustness and in many cases computing efficiency for unsteady, multi-body interactive flows. This method was tested in a time domain code for an ice class propeller in both open water flow and during interaction with a nearby ice blockage. Predictions showed that the method was effective in these extreme flows. (author)
Assi, I. A.; Sous, A. J.
2018-05-01
The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.
Numerical Verification Methods for Spherical $t$-Designs
Chen, Xiaojun
2009-01-01
The construction of spherical $t$-designs with $(t+1)^2$ points on the unit sphere $S^2$ in $\\mathbb{R}^3$ can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degree $t$ polynomial in $(t+1)^4$ arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations...
International Nuclear Information System (INIS)
Kamitani, A.; Takayama, T.; Itoh, T.; Ikuno, S.
2011-01-01
A fast method is proposed for calculating the shielding current density in an HTS. The J-E constitutive relation is modified so as not to change the solution. A numerical code is developed on the basis of the proposed method. The permanent magnet method is successfully simulated by means of the code. A fast method has been proposed for calculating the shielding current density in a high-temperature superconducting thin film. An initial-boundary-value problem of the shielding current density cannot be always solved by means of the Runge-Kutta method even when an adaptive step-size control algorithm is incorporated to the method. In order to suppress an overflow in the algorithm, the J-E constitutive relation is modified so that its solution may satisfy the original constitutive relation. A numerical code for analyzing the shielding current density has been developed on the basis of this method and, as an application of the code, the permanent magnet method for measuring the critical current density has been investigated numerically.
Introduction to Numerical Computation - analysis and Matlab illustrations
DEFF Research Database (Denmark)
Elden, Lars; Wittmeyer-Koch, Linde; Nielsen, Hans Bruun
In a modern programming environment like eg MATLAB it is possible by simple commands to perform advanced calculations on a personal computer. In order to use such a powerful tool efiiciently it is necessary to have an overview of available numerical methods and algorithms and to know about...... are illustrated by examples in MATLAB....
On a method of numerical calculation of nonlinear radial pulsations of stars
International Nuclear Information System (INIS)
Kosovichev, A.G.
1984-01-01
Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars
Numerical simulation of bubble deformation in magnetic fluids by finite volume method
International Nuclear Information System (INIS)
Yamasaki, Haruhiko; Yamaguchi, Hiroshi
2017-01-01
Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field. - Highlights: • A magnetic field analysis is developed to simulate the bubble dynamics in magnetic fluid with two-phase interface. • The elongation of bubble increased with increasing magnetic flux intensities due to strong magnetic normal force. • Proposed technique explains the bubble dynamics, taking into account of the continuity of the magnetic flux density.
Numerical treatment of experimental data in calibration procedures
International Nuclear Information System (INIS)
Moreno, C.
1993-06-01
A discussion of a numerical procedure to find the proportionality factor between two measured quantities is given in the framework of the least-squares method. Variable, as well as constant, amounts of experimental uncertainties are considered for each variable along their measured range. The variance of the proportionality factor is explicitly given as a closed analytical expression valid for the general case. Limits of the results obtained here have been studied allowing comparisons with those obtained using classical least-squares expressions. Analytical and numerical examples are also discussed. (author). 11 refs, 1 fig., 1 tab
International Nuclear Information System (INIS)
Ohira, H.; Ara, K.
2002-11-01
Advanced electromagnetic components are investigated in Feasibility Studies on Commercialized FR Cycle System to apply to the main cooling systems of Liquid Metal Fast Reactor. Although a lot of experiments and numerical analysis were carried out on both high Reynolds numbers and high magnetic Reynolds numbers, the complex phenomena could not be evaluated in detail. As the first step of the development of the numerical methods for the liquid metal magnetohydrodynamics, we investigated numerical methods that could be applied to the electromagnetic components with both complex structures and high magnetic turbulent field. As a result, we selected GSMAC (Generalized-Simplified MArker and Cell) method for calculating the liquid metal fluid dynamics because it could be easily applied to the complex flow field. We also selected the vector-FEM for calculating the magnetic field of the large components because the method had no interaction procedure. In the high magnetic turbulent field, the dynamic-SGS models would be also a promising model for the good estimation, because it could calculate the field directly without any experimental constant. In order to verify the GSMAC and the vector-FEM, we developed the 2D numerical models and calculated the magnetohydrodynamics in the large electromagnetic pump. It was estimated from these results that the methods were basically reasonable, because the calculated pressure differences had the similar tendencies to the experimental ones. (author)
Kabuth, Alina; Dahmke, Andreas; Hagrey, Said Attia al; Berta, Márton; Dörr, Cordula; Koproch, Nicolas; Köber, Ralf; Köhn, Daniel; Nolde, Michael; Tilmann Pfeiffer, Wolf; Popp, Steffi; Schwanebeck, Malte; Bauer, Sebastian
2016-04-01
Within the framework of the transition to renewable energy sources ("Energiewende"), the German government defined the target of producing 60 % of the final energy consumption from renewable energy sources by the year 2050. However, renewable energies are subject to natural fluctuations. Energy storage can help to buffer the resulting time shifts between production and demand. Subsurface geological structures provide large potential capacities for energy stored in the form of heat or gas on daily to seasonal time scales. In order to explore this potential sustainably, the possible induced effects of energy storage operations have to be quantified for both specified normal operation and events of failure. The ANGUS+ project therefore integrates experimental laboratory studies with numerical approaches to assess subsurface energy storage scenarios and monitoring methods. Subsurface storage options for gas, i.e. hydrogen, synthetic methane and compressed air in salt caverns or porous structures, as well as subsurface heat storage are investigated with respect to site prerequisites, storage dimensions, induced effects, monitoring methods and integration into spatial planning schemes. The conceptual interdisciplinary approach of the ANGUS+ project towards the integration of subsurface energy storage into a sustainable subsurface planning scheme is presented here, and this approach is then demonstrated using the examples of two selected energy storage options: Firstly, the option of seasonal heat storage in a shallow aquifer is presented. Coupled thermal and hydraulic processes induced by periodic heat injection and extraction were simulated in the open-source numerical modelling package OpenGeoSys. Situations of specified normal operation as well as cases of failure in operational storage with leaking heat transfer fluid are considered. Bench-scale experiments provided parameterisations of temperature dependent changes in shallow groundwater hydrogeochemistry. As a
New numerical method for iterative or perturbative solution of quantum field theory
International Nuclear Information System (INIS)
Hahn, S.C.; Guralnik, G.S.
1999-01-01
A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)
Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes
International Nuclear Information System (INIS)
Scheibe, T D; Tartakovsky, A M; Tartakovsky, D M; Redden, G D; Meakin, P
2007-01-01
Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale. Important examples include 1. molecular simulations (e.g., molecular dynamics); 2. simulation of microbial processes at the cell level (e.g., cellular automata or particle individual-based models); 3. pore-scale simulations (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics); and 4. macroscopic continuum-scale simulations (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each
Directory of Open Access Journals (Sweden)
F. Ghomanjani
2016-10-01
Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.
Furihata, Daisuke
2010-01-01
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer
A numeric-analytic method for approximating the chaotic Chen system
International Nuclear Information System (INIS)
Mossa Al-sawalha, M.; Noorani, M.S.M.
2009-01-01
The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.
International Nuclear Information System (INIS)
Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong
2017-01-01
Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and
Numerical solutions of multi-order fractional differential equations by Boubaker polynomials
Directory of Open Access Journals (Sweden)
Bolandtalat A.
2016-01-01
Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.
A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method
Bondesan , Andrea; Boudin , Laurent; Grec , Bérénice
2018-01-01
In this article, we consider a multi-species kinetic model which leads to the Maxwell-Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well-posedness of the discrete problem. We also present numerical examples where we observe the as...
Appraisal of numerical methods in predicting the aerodynamics of forward-swept wings
CSIR Research Space (South Africa)
Lombardi, G
1998-07-01
Full Text Available The capabilities of different numerical methods in evaluating the aerodynamic characteristics of a forward-swept wing in subsonic and transonic now are analyzed. The numerical results, obtained by means of potential, Euler, and Navier-Stokes solvers...
Mathematical properties of numerical inversion for jet calibrations
Energy Technology Data Exchange (ETDEWEB)
Cukierman, Aviv [Physics Department, Stanford University, Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025 (United States); Nachman, Benjamin, E-mail: bnachman@cern.ch [Physics Department, Stanford University, Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025 (United States); Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94704 (United States)
2017-06-21
Numerical inversion is a general detector calibration technique that is independent of the underlying spectrum. This procedure is formalized and important statistical properties are presented, using high energy jets at the Large Hadron Collider as an example setting. In particular, numerical inversion is inherently biased and common approximations to the calibrated jet energy tend to over-estimate the resolution. Analytic approximations to the closure and calibrated resolutions are demonstrated to effectively predict the full forms under realistic conditions. Finally, extensions of numerical inversion are presented which can reduce the inherent biases. These methods will be increasingly important to consider with degraded resolution at low jet energies due to a much higher instantaneous luminosity in the near future.
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
International Nuclear Information System (INIS)
Inc, Mustafa; Ugurlu, Yavuz
2007-01-01
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions
Numerical comparison of improved methods of testing in contingency tables with small frequencies
Energy Technology Data Exchange (ETDEWEB)
Sugiura, Nariaki; Otake, Masanori
1968-11-14
The significance levels of various tests for a general c x k contingency table are usually given by large sample theory. But they are not accurate for the one having small frequencies. In this paper, a numerical evaluation was made to determine how good the approximation of significance level is for various improved tests that have been developed by Nass, Yoshimura, Gart, etc. for c x k contingency table with small frequencies in some of cells. For this purpose we compared the significance levels of the various approximate methods (i) with those of one-sided tail defined in terms of exact probabilities for given marginals in 2 x 2 table; (ii) with those of exact probabilities accumulated in the order of magnitude of Chi/sup 2/ statistic or likelihood ratio (=LR) statistic in 2 x 3 table mentioned by Yates. In 2 x 2 table it is well known that Yates' correction gives satisfactory result for small cell frequencies and the other methods that we have not referred here, can be considered if we devote our attention only to 2 x 2 or 2 x k table. But we are mainly interested in comparing the methods that are applicable to a general c x k table. It appears that such a comparison for the various improved methods in the same example has not been made explicitly, even though these tests are frequently used in biological and medical research. 9 references, 6 figures, 6 tables.
Abramov, G. V.; Gavrilov, A. N.
2018-03-01
The article deals with the numerical solution of the mathematical model of the particles motion and interaction in multicomponent plasma by the example of electric arc synthesis of carbon nanostructures. The high order of the particles and the number of their interactions requires a significant input of machine resources and time for calculations. Application of the large particles method makes it possible to reduce the amount of computation and the requirements for hardware resources without affecting the accuracy of numerical calculations. The use of technology of GPGPU parallel computing using the Nvidia CUDA technology allows organizing all General purpose computation on the basis of the graphical processor graphics card. The comparative analysis of different approaches to parallelization of computations to speed up calculations with the choice of the algorithm in which to calculate the accuracy of the solution shared memory is used. Numerical study of the influence of particles density in the macro particle on the motion parameters and the total number of particle collisions in the plasma for different modes of synthesis has been carried out. The rational range of the coherence coefficient of particle in the macro particle is computed.
Numerical modelling of mine workings.
CSIR Research Space (South Africa)
Lightfoot, N
1999-03-01
Full Text Available to cover most of what is required for a practising rock mechanics engineer to be able to use any of these five programs to solve practical mining problems. The chapters on specific programs discuss their individual strengths and weaknesses and highlight... and applications of numerical modelling in the context of the South African gold and platinum mining industries. This includes an example that utilises a number of different numerical 3 modelling programs to solve a single problem. This particular example...
Rao, G Shanker
2006-01-01
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...
Efficient numerical method for district heating system hydraulics
International Nuclear Information System (INIS)
Stevanovic, Vladimir D.; Prica, Sanja; Maslovaric, Blazenka; Zivkovic, Branislav; Nikodijevic, Srdjan
2007-01-01
An efficient method for numerical simulation and analyses of the steady state hydraulics of complex pipeline networks is presented. It is based on the loop model of the network and the method of square roots for solving the system of linear equations. The procedure is presented in the comprehensive mathematical form that could be straightforwardly programmed into a computer code. An application of the method to energy efficiency analyses of a real complex district heating system is demonstrated. The obtained results show a potential for electricity savings in pumps operation. It is shown that the method is considerably more effective than the standard Hardy Cross method still widely used in engineering practice. Because of the ease of implementation and high efficiency, the method presented in this paper is recommended for hydraulic steady state calculations of complex networks
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...
A different approach to estimate nonlinear regression model using numerical methods
Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.
2017-11-01
This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].
New numerical method for solving the solute transport equation
International Nuclear Information System (INIS)
Ross, B.; Koplik, C.M.
1978-01-01
The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste
Numerical solution of boundary-integral equations for molecular electrostatics.
Bardhan, Jaydeep P
2009-03-07
Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.
Bao, Kai
2012-10-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping
2012-01-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
An efficient soil water balance model based on hybrid numerical and statistical methods
Mao, Wei; Yang, Jinzhong; Zhu, Yan; Ye, Ming; Liu, Zhao; Wu, Jingwei
2018-04-01
Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new
Numerical Optimization Design of Dynamic Quantizer via Matrix Uncertainty Approach
Directory of Open Access Journals (Sweden)
Kenji Sawada
2013-01-01
Full Text Available In networked control systems, continuous-valued signals are compressed to discrete-valued signals via quantizers and then transmitted/received through communication channels. Such quantization often degrades the control performance; a quantizer must be designed that minimizes the output difference between before and after the quantizer is inserted. In terms of the broadbandization and the robustness of the networked control systems, we consider the continuous-time quantizer design problem. In particular, this paper describes a numerical optimization method for a continuous-time dynamic quantizer considering the switching speed. Using a matrix uncertainty approach of sampled-data control, we clarify that both the temporal and spatial resolution constraints can be considered in analysis and synthesis, simultaneously. Finally, for the slow switching, we compare the proposed and the existing methods through numerical examples. From the examples, a new insight is presented for the two-step design of the existing continuous-time optimal quantizer.
Relaxation methods for gauge field equilibrium equations
International Nuclear Information System (INIS)
Adler, S.L.; Piran, T.
1984-01-01
This article gives a pedagogical introduction to relaxation methods for the numerical solution of elliptic partial differential equations, with particular emphasis on treating nonlinear problems with delta-function source terms and axial symmetry, which arise in the context of effective Lagrangian approximations to the dynamics of quantized gauge fields. The authors present a detailed theoretical analysis of three models which are used as numerical examples: the classical Abelian Higgs model (illustrating charge screening), the semiclassical leading logarithm model (illustrating flux confinement within a free boundary or ''bag''), and the axially symmetric Bogomol'nyi-Prasad-Sommerfield monopoles (illustrating the occurrence of p topological quantum numbers in non-Abelian gauge fields). They then proceed to a self-contained introduction to the theory of relaxation methods and allied iterative numerical methods and to the practical aspects of their implementation, with attention to general issues which arise in the three examples. The authors conclude with a brief discussion of details of the numerical solution of the models, presenting sample numerical results
Yang, Yan-Pu; Chen, Deng-Kai; Gu, Rong; Gu, Yu-Feng; Yu, Sui-Huai
2016-01-01
Consumers' Kansei needs reflect their perception about a product and always consist of a large number of adjectives. Reducing the dimension complexity of these needs to extract primary words not only enables the target product to be explicitly positioned, but also provides a convenient design basis for designers engaging in design work. Accordingly, this study employs a numerical design structure matrix (NDSM) by parameterizing a conventional DSM and integrating genetic algorithms to find optimum Kansei clusters. A four-point scale method is applied to assign link weights of every two Kansei adjectives as values of cells when constructing an NDSM. Genetic algorithms are used to cluster the Kansei NDSM and find optimum clusters. Furthermore, the process of the proposed method is presented. The details of the proposed approach are illustrated using an example of electronic scooter for Kansei needs clustering. The case study reveals that the proposed method is promising for clustering Kansei needs adjectives in product emotional design.
Re-Computation of Numerical Results Contained in NACA Report No. 496
Perry, Boyd, III
2015-01-01
An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and re-computing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time- and effort-saving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The re-computations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fair-to-very-good agreement with the re-computed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and re-computed results differed significantly, were in excellent agreement with the re-computed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the re-computation of results; Appendix C presents three alternate solution methods, with examples, for the two-degree-of-freedom solution method of NACA 496; Appendix D contains the three-degree-of-freedom solution method (outlined in NACA 496 but never implemented), with examples.
Development of CAD implementing the algorithm of boundary elements’ numerical analytical method
Directory of Open Access Journals (Sweden)
Yulia V. Korniyenko
2015-03-01
Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.
Automatic validation of numerical solutions
DEFF Research Database (Denmark)
Stauning, Ole
1997-01-01
This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... are described: The forward, the backward, and the Taylor expansion methods. The three methods have been implemented in the C++ program packages FADBAD/TADIFF. Some examples showing how to use the three metho ds are presented. A feature of FADBAD/TADIFF not present in other automatic differentiation packages...
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
International Nuclear Information System (INIS)
Laucoin, E.
2008-10-01
Numerical resolution of partial differential equations can be made reliable and efficient through the use of adaptive numerical methods.We present here the work we have done for the design, the implementation and the validation of such a method within an industrial software platform with applications in thermohydraulics. From the geometric point of view, this method can deal both with mesh refinement and mesh coarsening, while ensuring the quality of the mesh cells. Numerically, we use the mortar elements formalism in order to extend the Finite Volumes-Elements method implemented in the Trio-U platform and to deal with the non-conforming meshes arising from the adaptation procedure. Finally, we present an implementation of this method using concepts from domain decomposition methods for ensuring its efficiency while running in a parallel execution context. (author)
Numerical method for wave forces acting on partially perforated caisson
Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou
2015-04-01
The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.
Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method
Directory of Open Access Journals (Sweden)
Hossein Aminikhah
2016-01-01
Full Text Available A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.
Steady-state transport equation resolution by particle methods, and numerical results
International Nuclear Information System (INIS)
Mercier, B.
1985-10-01
A method to solve steady-state transport equation has been given. Principles of the method are given. The method is studied in two different cases; estimations given by the theory are compared to numerical results. Results got in 1-D (spherical geometry) and in 2-D (axisymmetric geometry) are given [fr
Somerville, W. R. C.; Auguié, B.; Le Ru, E. C.
2013-07-01
We propose, describe, and demonstrate a new numerically stable implementation of the extended boundary-condition method (EBCM) to compute the T-matrix for electromagnetic scattering by spheroidal particles. Our approach relies on the fact that for many of the EBCM integrals in the special case of spheroids, a leading part of the integrand integrates exactly to zero, which causes catastrophic loss of precision in numerical computations. This feature was in fact first pointed out by Waterman in the context of acoustic scattering and electromagnetic scattering by infinite cylinders. We have recently studied it in detail in the case of electromagnetic scattering by particles. Based on this study, the principle of our new implementation is therefore to compute all the integrands without the problematic part to avoid the primary cause of loss of precision. Particular attention is also given to choosing the algorithms that minimise loss of precision in every step of the method, without compromising on speed. We show that the resulting implementation can efficiently compute in double precision arithmetic the T-matrix and therefore optical properties of spheroidal particles to a high precision, often down to a remarkable accuracy (10-10 relative error), over a wide range of parameters that are typically considered problematic. We discuss examples such as high-aspect ratio metallic nanorods and large size parameter (≈35) dielectric particles, which had been previously modelled only using quadruple-precision arithmetic codes.
Numerical method for solving the three-dimensional time-dependent neutron diffusion equation
International Nuclear Information System (INIS)
Khaled, S.M.; Szatmary, Z.
2005-01-01
A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)
DEFF Research Database (Denmark)
Liu, Yuanrong; Chen, Weimin; Zhong, Jing
2017-01-01
The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Development of a set of benchmark problems to verify numerical methods for solving burnup equations
International Nuclear Information System (INIS)
Lago, Daniel; Rahnema, Farzad
2017-01-01
Highlights: • Description transmutation chain benchmark problems. • Problems for validating numerical methods for solving burnup equations. • Analytical solutions for the burnup equations. • Numerical solutions for the burnup equations. - Abstract: A comprehensive set of transmutation chain benchmark problems for numerically validating methods for solving burnup equations was created. These benchmark problems were designed to challenge both traditional and modern numerical methods used to solve the complex set of ordinary differential equations used for tracking the change in nuclide concentrations over time due to nuclear phenomena. Given the development of most burnup solvers is done for the purpose of coupling with an established transport solution method, these problems provide a useful resource in testing and validating the burnup equation solver before coupling for use in a lattice or core depletion code. All the relevant parameters for each benchmark problem are described. Results are also provided in the form of reference solutions generated by the Mathematica tool, as well as additional numerical results from MATLAB.
International Nuclear Information System (INIS)
Pazos, Enrique; Dorband, Ernst Nils; Nagar, Alessandro; Palenzuela, Carlos; Schnetter, Erik; Tiglio, Manuel
2007-01-01
in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution
Energy Technology Data Exchange (ETDEWEB)
Pazos, Enrique [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Dorband, Ernst Nils [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Nagar, Alessandro [Dipartimento di Fisica, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino (Italy); Palenzuela, Carlos [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Schnetter, Erik [Center for Computation and Technology, 216 Johnston Hall, Louisiana State University, Baton Rouge, LA 70803 (United States); Tiglio, Manuel [Department of Physics and Astronomy, 202 Nicholson Hall, Louisiana State University, Baton Rouge, LA 70803 (United States)
2007-06-21
in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution.
A CNN-Based Method of Vehicle Detection from Aerial Images Using Hard Example Mining
Directory of Open Access Journals (Sweden)
Yohei Koga
2018-01-01
Full Text Available Recently, deep learning techniques have had a practical role in vehicle detection. While much effort has been spent on applying deep learning to vehicle detection, the effective use of training data has not been thoroughly studied, although it has great potential for improving training results, especially in cases where the training data are sparse. In this paper, we proposed using hard example mining (HEM in the training process of a convolutional neural network (CNN for vehicle detection in aerial images. We applied HEM to stochastic gradient descent (SGD to choose the most informative training data by calculating the loss values in each batch and employing the examples with the largest losses. We picked 100 out of both 500 and 1000 examples for training in one iteration, and we tested different ratios of positive to negative examples in the training data to evaluate how the balance of positive and negative examples would affect the performance. In any case, our method always outperformed the plain SGD. The experimental results for images from New York showed improved performance over a CNN trained in plain SGD where the F1 score of our method was 0.02 higher.
Introductory numerical analysis
Pettofrezzo, Anthony J
2006-01-01
Written for undergraduates who require a familiarity with the principles behind numerical analysis, this classical treatment encompasses finite differences, least squares theory, and harmonic analysis. Over 70 examples and 280 exercises. 1967 edition.
Numerical Simulation of Partially-Coherent Broadband Optical Imaging Using the FDTD Method
Çapoğlu, İlker R.; White, Craig A.; Rogers, Jeremy D.; Subramanian, Hariharan; Taflove, Allen; Backman, Vadim
2012-01-01
Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially-coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results. PMID:21540939
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
Happola, Juho
2017-09-19
Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
Happola, Juho
2017-01-01
Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.
Jacques, Ian
1987-01-01
This book is primarily intended for undergraduates in mathematics, the physical sciences and engineering. It introduces students to most of the techniques forming the core component of courses in numerical analysis. The text is divided into eight chapters which are largely self-contained. However, with a subject as intricately woven as mathematics, there is inevitably some interdependence between them. The level of difficulty varies and, although emphasis is firmly placed on the methods themselves rather than their analysis, we have not hesitated to include theoretical material when we consider it to be sufficiently interesting. However, it should be possible to omit those parts that do seem daunting while still being able to follow the worked examples and to tackle the exercises accompanying each section. Familiarity with the basic results of analysis and linear algebra is assumed since these are normally taught in first courses on mathematical methods. For reference purposes a list of theorems used in the t...
The numerical simulation of accelerator components
International Nuclear Information System (INIS)
Herrmannsfeldt, W.B.; Hanerfeld, H.
1987-05-01
The techniques of the numerical simulation of plasmas can be readily applied to problems in accelerator physics. Because the problems usually involve a single component ''plasma,'' and times that are at most, a few plasma oscillation periods, it is frequently possible to make very good simulations with relatively modest computation resources. We will discuss the methods and illustrate them with several examples. One of the more powerful techniques of understanding the motion of charged particles is to view computer-generated motion pictures. We will show several little movie strips to illustrate the discussions. The examples will be drawn from the application areas of Heavy Ion Fusion, electron-positron linear colliders and injectors for free-electron lasers. 13 refs., 10 figs., 2 tabs
Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites
Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.
2018-04-01
Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.
Energy Technology Data Exchange (ETDEWEB)
Nielsen, Bjoern Fredrik
1997-12-31
The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.
Energy Technology Data Exchange (ETDEWEB)
Nielsen, Bjoern Fredrik
1998-12-31
The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
2015-01-01
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut
2015-01-07
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
Strongly correlated systems numerical methods
Mancini, Ferdinando
2013-01-01
This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possi...
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
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F. Hosseini Shekarabi
2016-03-01
Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.
Application of Numerical Integration and Data Fusion in Unit Vector Method
Zhang, J.
2012-01-01
The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of
Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method
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Ghanmi Helmi
2018-05-01
Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
Prediction of Chloride Diffusion in Concrete Structure Using Meshless Methods
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Ling Yao
2016-01-01
Full Text Available Degradation of RC structures due to chloride penetration followed by reinforcement corrosion is a serious problem in civil engineering. The numerical simulation methods at present mainly involve finite element methods (FEM, which are based on mesh generation. In this study, element-free Galerkin (EFG and meshless weighted least squares (MWLS methods are used to solve the problem of simulation of chloride diffusion in concrete. The range of a scaling parameter is presented using numerical examples based on meshless methods. One- and two-dimensional numerical examples validated the effectiveness and accuracy of the two meshless methods by comparing results obtained by MWLS with results computed by EFG and FEM and results calculated by an analytical method. A good agreement is obtained among MWLS and EFG numerical simulations and the experimental data obtained from an existing marine concrete structure. These results indicate that MWLS and EFG are reliable meshless methods that can be used for the prediction of chloride ingress in concrete structures.
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S. Psakhie
2013-04-01
Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.
Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods
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Frank Weichert
2013-01-01
Full Text Available The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs and lattice Boltzmann methods (LBMs. The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
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H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
Novel Parallel Numerical Methods for Radiation and Neutron Transport
International Nuclear Information System (INIS)
Brown, P N
2001-01-01
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both
Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects
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Mahmoud A. Eissa
2017-01-01
Full Text Available Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES. The RES investment is characterized by uncertainty, which is long-term, costly and depends on feed-in tariff and support schemes. In this paper, we address the real option valuation (ROV of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price and, further, the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assessing the value of the deferred option are discussed. The new three-stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM methods. The numerical methods are integrated with the concept of Black–Scholes option pricing theory and applied in option valuation for solar energy investment with uncertainty. The numerical results of the L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our dataset refers to the Arab Republic of Egypt.
Numerical computation of FCT equilibria by inverse equilibrium method
International Nuclear Information System (INIS)
Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki
1986-11-01
FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Energy Technology Data Exchange (ETDEWEB)
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
International Nuclear Information System (INIS)
Kako, T.; Watanabe, T.
1999-04-01
This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)
Energy Technology Data Exchange (ETDEWEB)
Kako, T.; Watanabe, T. [eds.
1999-04-01
This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)
Numerical method for solving the inverse problem of quantum scattering theory
International Nuclear Information System (INIS)
Ajrapetyan, R.G.; Puzynin, I.V.; Zhidkov, E.P.
1996-01-01
A new numerical method for solving the problem of the reconstruction of interaction potential by a phase shift given on a set of closed intervals in (l,k)-plane, satisfying certain geometrical 'Staircase Condition', is suggested. The method is based on the Variable Phase Approach and on the modification of the Continuous Analogy of the Newton Method. 22 refs., 1 fig
International Nuclear Information System (INIS)
Lau, T.
2006-01-01
In this work modifications of the classical Particle-In-Cell method for the solution of the Maxwell-Vlasov equations are investigated with respect to their application in particle accelerator physics. The aim of the work is to find modifications of the method which minimize and under certain conditions even eliminate the numerical dispersion effect along the beam axis in the numerical solution of Maxwell's equations. This is achieved by the development of dedicated time-integration methods for the Finite Integration Technique and two Finite Volume Methods. The methods are theoretically investigated regarding the conservation of a discrete energy and the existence of a discrete continuity equation. Finally, some of the methods are applied to the simulation of a high frequency rf-gun. (orig.)
Numerical simulation of low Mach number reacting flows
International Nuclear Information System (INIS)
Bell, J B; Aspden, A J; Day, M S; Lijewski, M J
2007-01-01
Using examples from active research areas in combustion and astrophysics, we demonstrate a computationally efficient numerical approach for simulating multiscale low Mach number reacting flows. The method enables simulations that incorporate an unprecedented range of temporal and spatial scales, while at the same time, allows an extremely high degree of reaction fidelity. Sample applications demonstrate the efficiency of the approach with respect to a traditional time-explicit integration method, and the utility of the methodology for studying the interaction of turbulence with terrestrial and astrophysical flame structures
Numerical divergence effects of equivalence theory in the nodal expansion method
International Nuclear Information System (INIS)
Zika, M.R.; Downar, T.J.
1993-01-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible
Directory of Open Access Journals (Sweden)
Xia Xiaozhou
2013-01-01
Full Text Available In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.
The numerical solution of linear multi-term fractional differential equations: systems of equations
Edwards, John T.; Ford, Neville J.; Simpson, A. Charles
2002-11-01
In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.
Numerical methods on flow instabilities in steam generator
International Nuclear Information System (INIS)
Yoshikawa, Ryuji; Hamada, Hirotsugu; Ohshima, Hiroyuki; Yanagisawa, Hideki
2008-06-01
The phenomenon of two-phase flow instability is important for the design and operation of many industrial systems and equipment, such as steam generators. The designer's job is to predict the threshold of flow instability in order to design around it or compensate for it. So it is essential to understand the physical phenomena governing such instability and to develop computational tools to model the dynamics of boiling systems. In Japan Atomic Energy Agency, investigations on heat transfer characteristics of steam generator are being performed for the development of Sodium-cooled Fast Breeder Reactor. As one part of the research work, the evaluations of two-phase flow instability in the steam generator are being carried out experimentally and numerically. In this report, the numerical methods were studied for two-phase flow instability analysis in steam generator. For numerical simulation purpose, the special algorithm to calculate inlet flow rate iteratively with inlet pressure and outlet pressure as boundary conditions for the density-wave instability analysis was established. There was no need to solve property derivatives and large matrices, so the spurious numerical instabilities caused by discontinuous property derivatives at boiling boundaries were avoided. Large time-step was possible. The flow instability in single heat transfer tube was successfully simulated with homogeneous equilibrium model by using the present algorithm. Then the drift-flux model including the effects of subcooled boiling and two phase slip was adopted to improve the accuracy. The computer code was developed after selecting the correlations of drift velocity and distribution parameter. The capability of drift flux model together with the present algorithm for simulating density-wave instability in single tube was confirmed. (author)
Climate Prediction for Brazil's Nordeste: Performance of Empirical and Numerical Modeling Methods.
Moura, Antonio Divino; Hastenrath, Stefan
2004-07-01
Comparisons of performance of climate forecast methods require consistency in the predictand and a long common reference period. For Brazil's Nordeste, empirical methods developed at the University of Wisconsin use preseason (October January) rainfall and January indices of the fields of meridional wind component and sea surface temperature (SST) in the tropical Atlantic and the equatorial Pacific as input to stepwise multiple regression and neural networking. These are used to predict the March June rainfall at a network of 27 stations. An experiment at the International Research Institute for Climate Prediction, Columbia University, with a numerical model (ECHAM4.5) used global SST information through February to predict the March June rainfall at three grid points in the Nordeste. The predictands for the empirical and numerical model forecasts are correlated at +0.96, and the period common to the independent portion of record of the empirical prediction and the numerical modeling is 1968 99. Over this period, predicted versus observed rainfall are evaluated in terms of correlation, root-mean-square error, absolute error, and bias. Performance is high for both approaches. Numerical modeling produces a correlation of +0.68, moderate errors, and strong negative bias. For the empirical methods, errors and bias are small, and correlations of +0.73 and +0.82 are reached between predicted and observed rainfall.
Approaches to qualitative research in mathematics education examples of methodology and methods
Bikner-Ahsbahs, Angelika; Presmeg, Norma
2014-01-01
This volume documents a range of qualitative research approaches emerged within mathematics education over the last three decades, whilst at the same time revealing their underlying methodologies. Continuing the discussion as begun in the two 2003 ZDM issues dedicated to qualitative empirical methods, this book presents astate of the art overview on qualitative research in mathematics education and beyond. The structure of the book allows the reader to use it as an actual guide for the selection of an appropriate methodology, on a basis of both theoretical depth and practical implications. The methods and examples illustrate how different methodologies come to life when applied to a specific question in a specific context. Many of the methodologies described are also applicable outside mathematics education, but the examples provided are chosen so as to situate the approach in a mathematical context.
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Numerical analysis of jet breakup behavior using particle method
International Nuclear Information System (INIS)
Shibata, Kazuya; Koshizuka, Seiichi; Oka, Yoshiaki
2002-01-01
A continuous jet changes to droplets where jet breakup occurs. In this study, two-dimensional numerical analysis of jet breakup is performed using the MPS method (Moving Particle Semi-implicit Method) which is a particle method for incompressible flows. The continuous fluid surrounding the jet is neglected. Dependencies of the jet breakup length on the Weber number and the Froude number agree with the experiment. The size distribution of droplets is in agreement with the Nukiyama-Tanasawa distribution which has been widely used as an experimental correlation. Effects of the Weber number and the Froude number on the size distribution are also obtained. (author)
Numerical evaluation of methods for computing tomographic projections
International Nuclear Information System (INIS)
Zhuang, W.; Gopal, S.S.; Hebert, T.J.
1994-01-01
Methods for computing forward/back projections of 2-D images can be viewed as numerical integration techniques. The accuracy of any ray-driven projection method can be improved by increasing the number of ray-paths that are traced per projection bin. The accuracy of pixel-driven projection methods can be increased by dividing each pixel into a number of smaller sub-pixels and projecting each sub-pixel. The authors compared four competing methods of computing forward/back projections: bilinear interpolation, ray-tracing, pixel-driven projection based upon sub-pixels, and pixel-driven projection based upon circular, rather than square, pixels. This latter method is equivalent to a fast, bi-nonlinear interpolation. These methods and the choice of the number of ray-paths per projection bin or the number of sub-pixels per pixel present a trade-off between computational speed and accuracy. To solve the problem of assessing backprojection accuracy, the analytical inverse Fourier transform of the ramp filtered forward projection of the Shepp and Logan head phantom is derived
Automatic numerical integration methods for Feynman integrals through 3-loop
International Nuclear Information System (INIS)
De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K
2015-01-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)
Numerical renormalization group method for entanglement negativity at finite temperature
Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.
2018-04-01
We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.
New numerical methods for quantum field theories on the continuum
Energy Technology Data Exchange (ETDEWEB)
Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C
2000-03-01
The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.
Numerical spin tracking in a synchrotron computer code Spink: Examples (RHIC)
International Nuclear Information System (INIS)
Luccio, A.
1995-01-01
In the course of acceleration of polarized protons in a synchrotron, many depolarizing resonances are encountered. They are classified in two categories: Intrinsic resonances that depend on the lattice structure of the ring and arise from the coupling of betatron oscillations with horizontal magnetic fields, and imperfection resonances caused by orbit distortions due to field errors. In general, the spectrum of resonances vs spin tune Gγ(G = 1.7928, the proton gyromagnetic anomaly, and y the proton relativistic energy ratio) for a given lattice tune ν, or vs ν for a given Gγ, contains a multitude of lines with various amplitudes or resonance strengths. The depolarization due to the resonance lines can be studied by numerically tracking protons with spin in a model accelerator. Tracking will allow one to check the strength of resonances, to study the effects of devices like Siberian Snakes, to find safe lattice tune regions where to operate, and finally to study in detail the operation of special devices such as Spin Flippers. A few computer codes exist that calculate resonance strengths E k and perform tracking, for proton and electron machines. Most relevant to our work for the AGS and RHIC machines are the programs Depol and Snake. Depol, calculates the E k 's by Fourier analysis. The input to Depol is the output of a machine model code, such as Synch or Mad, containing all details of the lattice. Snake, does the tracking, starting from a synthetic machine, that contains a certain number of periods, of FODO cells, of Siberian snakes, etc. We believed the complexities of machines like the AGS or RHIC could not be adequately represented by Snake. Then, we decided to write a new code, Spink, that combines some of the features of Depol and Snake. I.E., Spink reads a Mad output like Depol and tracks as Snake does. The structure of the code and examples for RHIC are described in the following
Collecting and analyzing qualitative data: Hermeneutic principles, methods and case examples
Michael E. Patterson; Daniel R. Williams
2002-01-01
Over the past three decades, the use of qualitative research methods has become commonplace in social science as a whole and increasingly represented in tourism and recrearion research. In tourism, for example, Markwell and Basche (1998) recently noted the emergence of a pluralistic perspective on science and the growth of research employing qualitative frameworks....
Numerical experiment on finite element method for matching data
International Nuclear Information System (INIS)
Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.
1993-03-01
Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)
Introduction to numerical electrostatics using MATLAB
Dworsky, Lawrence N
2014-01-01
The first of its kind uniquely devoted to the field of computational electrostatics, this book dives headfirst into the actual problems that engineers are expected to solve using method of moment (MoM), finite difference, and finite element techniques. Readers are guided step by step through specific problems and challenges, covering all aspects of electrostatics with an emphasis on numerical procedures. Focusing on practical examples, mathematical equations, and common issues with algorithms, this is an ideal text for students in engineering, physics, and electrostatics-and working engineers
Numerical simulation of pseudoelastic shape memory alloys using the large time increment method
Gu, Xiaojun; Zhang, Weihong; Zaki, Wael; Moumni, Ziad
2017-04-01
The paper presents a numerical implementation of the large time increment (LATIN) method for the simulation of shape memory alloys (SMAs) in the pseudoelastic range. The method was initially proposed as an alternative to the conventional incremental approach for the integration of nonlinear constitutive models. It is adapted here for the simulation of pseudoelastic SMA behavior using the Zaki-Moumni model and is shown to be especially useful in situations where the phase transformation process presents little or lack of hardening. In these situations, a slight stress variation in a load increment can result in large variations of strain and local state variables, which may lead to difficulties in numerical convergence. In contrast to the conventional incremental method, the LATIN method solve the global equilibrium and local consistency conditions sequentially for the entire loading path. The achieved solution must satisfy the conditions of static and kinematic admissibility and consistency simultaneously after several iterations. 3D numerical implementation is accomplished using an implicit algorithm and is then used for finite element simulation using the software Abaqus. Computational tests demonstrate the ability of this approach to simulate SMAs presenting flat phase transformation plateaus and subjected to complex loading cases, such as the quasi-static behavior of a stent structure. Some numerical results are contrasted to those obtained using step-by-step incremental integration.
Using Mixed Methods to Analyze Video Data: A Mathematics Teacher Professional Development Example
DeCuir-Gunby, Jessica T.; Marshall, Patricia L.; McCulloch, Allison W.
2012-01-01
This article uses data from 65 teachers participating in a K-2 mathematics professional development research project as an example of how to analyze video recordings of teachers' classroom lessons using mixed methods. Through their discussion, the authors demonstrate how using a mixed methods approach to classroom video analysis allows researchers…
Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems
International Nuclear Information System (INIS)
Mei Shuli; Du Chengjin; Zhang Senwen
2008-01-01
Homotopy perturbation method (HPM) proposed by Ji-Huan He is very effective and convenient for single-degree-of-freedom systems. In this paper a coupling technique of He's method and precise integration method (PIM) is suggested to solve multi-degree-of-freedom nonlinear dynamic systems. The new technique keeps the merits of the two methods. Some examples are given to illustrate its effectiveness and convenience. Furthermore the obtained solution is of high accuracy
Directory of Open Access Journals (Sweden)
Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
International Nuclear Information System (INIS)
Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.
1995-07-01
In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)
Directory of Open Access Journals (Sweden)
Leah M. Courtland
2012-07-01
Full Text Available The Tephra2 numerical model for tephra fallout from explosive volcanic eruptions is specifically designed to enable students to probe ideas in model literacy, including code validation and verification, the role of simplifying assumptions, and the concepts of uncertainty and forecasting. This numerical model is implemented on the VHub.org website, a venture in cyberinfrastructure that brings together volcanological models and educational materials. The VHub.org resource provides students with the ability to explore and execute sophisticated numerical models like Tephra2. We present a strategy for using this model to introduce university students to key concepts in the use and evaluation of Tephra2 for probabilistic forecasting of volcanic hazards. Through this critical examination students are encouraged to develop a deeper understanding of the applicability and limitations of hazard models. Although the model and applications are intended for use in both introductory and advanced geoscience courses, they could easily be adapted to work in other disciplines, such as astronomy, physics, computational methods, data analysis, or computer science.
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
Ghosh, Pradipto
is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.
International Nuclear Information System (INIS)
Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.
2010-01-01
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
Generalization of the linear algebraic method to three dimensions
International Nuclear Information System (INIS)
Lynch, D.L.; Schneider, B.I.
1991-01-01
We present a numerical method for the solution of the Lippmann-Schwinger equation for electron-molecule collisions. By performing a three-dimensional numerical quadrature, this approach avoids both a basis-set representation of the wave function and a partial-wave expansion of the scattering potential. The resulting linear equations, analogous in form to the one-dimensional linear algebraic method, are solved with the direct iteration-variation method. Several numerical examples are presented. The prospect for using this numerical quadrature scheme for electron-polyatomic molecules is discussed
Nodal methods in numerical reactor calculations
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del
2004-01-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Nodal methods in numerical reactor calculations
Energy Technology Data Exchange (ETDEWEB)
Hennart, J P [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico); Valle, E del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)
2004-07-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Improved numerical methods for quantum field theory (Outstanding junior investigator award)
International Nuclear Information System (INIS)
Sokal, A.D.
1992-01-01
We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo, Swendsen-Wang and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory
Improved numerical methods for quantum field theory (Outstanding junior investigator award)
International Nuclear Information System (INIS)
Sokal, A.D.
1993-01-01
We are developing new and more efficient numerical methods for problems in quantum field theory. Our principal goal is to achieve radical reductions in critical slowing-down. We are concentrating at present on three new families of algorithms: multi-grid Monte Carlo (MGMC), Swendsen-Wang (SW) and generalized Wolff-type embedding algorithms. In addition, we are making a high-precision numerical study of the hyperscaling conjecture for the self-avoiding walk, which is closely related to the triviality problem for var-phi 4 quantum field theory
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-01-01
A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S N ) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S N equations. Numerical results are given to illustrate the method's accuracy
To the development of numerical methods in problems of radiation transport
International Nuclear Information System (INIS)
Germogenova, T.A.
1990-01-01
Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation
Numerical simulation methods for electron and ion optics
International Nuclear Information System (INIS)
Munro, Eric
2011-01-01
This paper summarizes currently used techniques for simulation and computer-aided design in electron and ion beam optics. Topics covered include: field computation, methods for computing optical properties (including Paraxial Rays and Aberration Integrals, Differential Algebra and Direct Ray Tracing), simulation of Coulomb interactions, space charge effects in electron and ion sources, tolerancing, wave optical simulations and optimization. Simulation examples are presented for multipole aberration correctors, Wien filter monochromators, imaging energy filters, magnetic prisms, general curved axis systems and electron mirrors.
Numerical sedimentation particle-size analysis using the Discrete Element Method
Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.
2015-12-01
Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.
Dating method by fission tracks: some Brazilian examples
International Nuclear Information System (INIS)
Fonseca, Ariadne do Carmo
1996-01-01
The Fission Track method (TF) complements the dating of a interval of tectonic events occurred in low temperatures not detected by another radiometric methods. In the South part of Craton of Sao Francisco the dating of apatites of archaean rocks produced ages TF between 900 and 500 Ma, reflecting the progressive acting of the Brazilian margin mobile belts in the archaean craton areas. Apatite of some igneous and metamorphic rocks of the Braziliana age, in the Faixa Ribeira segment, between the Rio de Janeiro and Salvador cities, produced TF ages between 140 and 80 Ma. The basaltic and alkaline volcanism related to the Atlantic Ocean opening dated from this interval. The TF dating in apatites of the continental margin rocks allowed to date the event. In the Cabo Frio region (Southeastern part of Rio de Janeiro State), titanite and apatite of the Transamazonic orthognaisses produced TF dates between 190 and 80 to 40 Ma. The age around 190 Ma date previously the rift formation precursor of the South Atlantic Ocean opening, while the ages between 80 and 40 Ma were related to the alkaline rocks intrusion. The examples mentioned demonstrate the event diversity which may be dated by the Fission Tracks method, mainly in the craton area and margin belts study
Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
International Nuclear Information System (INIS)
Wei, T; Qin, H H; Shi, R
2008-01-01
In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method
Towards standard testbeds for numerical relativity
International Nuclear Information System (INIS)
Alcubierre, Miguel; Allen, Gabrielle; Bona, Carles; Fiske, David; Goodale, Tom; Guzman, F Siddhartha; Hawke, Ian; Hawley, Scott H; Husa, Sascha; Koppitz, Michael; Lechner, Christiane; Pollney, Denis; Rideout, David; Salgado, Marcelo; Schnetter, Erik; Seidel, Edward; Shinkai, Hisa-aki; Shoemaker, Deirdre; Szilagyi, Bela; Takahashi, Ryoji; Winicour, Jeff
2004-01-01
In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step towards building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources and can be used with many different approaches used in the relativity community
Towards standard testbeds for numerical relativity
Energy Technology Data Exchange (ETDEWEB)
Alcubierre, Miguel [Inst. de Ciencias Nucleares, Univ. Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico Distrito Federal 04510 (Mexico); Allen, Gabrielle; Goodale, Tom; Guzman, F Siddhartha; Hawke, Ian; Husa, Sascha; Koppitz, Michael; Lechner, Christiane; Pollney, Denis; Rideout, David [Max-Planck-Inst. fuer Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm (Germany); Bona, Carles [Departament de Fisica, Universitat de les Illes Balears, Ctra de Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Fiske, David [Dept. of Physics, Univ. of Maryland, College Park, MD 20742-4111 (United States); Hawley, Scott H [Center for Relativity, Univ. of Texas at Austin, Austin, Texas 78712 (United States); Salgado, Marcelo [Inst. de Ciencias Nucleares, Univ. Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico Distrito Federal 04510 (Mexico); Schnetter, Erik [Inst. fuer Astronomie und Astrophysik, Universitaet Tuebingen, 72076 Tuebingen (Germany); Seidel, Edward [Max-Planck-Inst. fuer Gravitationsphysik, Albert-Einstein-Inst., 14476 Golm (Germany); Shinkai, Hisa-aki [Computational Science Div., Inst. of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama 351-0198 (Japan); Shoemaker, Deirdre [Center for Radiophysics and Space Research, Cornell Univ., Ithaca, NY 14853 (United States); Szilagyi, Bela [Dept. of Physics and Astronomy, Univ. of Pittsburgh, Pittsburgh, PA 15260 (United States); Takahashi, Ryoji [Theoretical Astrophysics Center, Juliane Maries Vej 30, 2100 Copenhagen, (Denmark); Winicour, Jeff [Max-Planck-Inst. fuer Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm (Germany)
2004-01-21
In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step towards building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources and can be used with many different approaches used in the relativity community.
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
Ling, Hong; Luo, Ercang; Dai, Wei
2006-12-22
Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy.
Martínez, Sergio; Sánchez, David; Valls, Aida
2013-04-01
Structured patient data like Electronic Health Records (EHRs) are a valuable source for clinical research. However, the sensitive nature of such information requires some anonymisation procedure to be applied before releasing the data to third parties. Several studies have shown that the removal of identifying attributes, like the Social Security Number, is not enough to obtain an anonymous data file, since unique combinations of other attributes as for example, rare diagnoses and personalised treatments, may lead to patient's identity disclosure. To tackle this problem, Statistical Disclosure Control (SDC) methods have been proposed to mask sensitive attributes while preserving, up to a certain degree, the utility of anonymised data. Most of these methods focus on continuous-scale numerical data. Considering that part of the clinical data found in EHRs is expressed with non-numerical attributes as for example, diagnoses, symptoms, procedures, etc., their application to EHRs produces far from optimal results. In this paper, we propose a general framework to enable the accurate application of SDC methods to non-numerical clinical data, with a focus on the preservation of semantics. To do so, we exploit structured medical knowledge bases like SNOMED CT to propose semantically-grounded operators to compare, aggregate and sort non-numerical terms. Our framework has been applied to several well-known SDC methods and evaluated using a real clinical dataset with non-numerical attributes. Results show that the exploitation of medical semantics produces anonymised datasets that better preserve the utility of EHRs. Copyright © 2012 Elsevier Inc. All rights reserved.
A fast numerical method for the valuation of American lookback put options
Song, Haiming; Zhang, Qi; Zhang, Ran
2015-10-01
A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.
Numerical study on visualization method for material distribution using photothermal effect
International Nuclear Information System (INIS)
Kim, Moo Joong; Yoo, Jai Suk; Kim, Dong Kwon; Kim, Hyun Jung
2015-01-01
Visualization and imaging techniques have become increasingly essential in a wide range of industrial fields. A few imaging methods such as X-ray imaging, computed tomography and magnetic resonance imaging have been developed for medical applications to materials that are basically transparent or X-ray penetrable; however, reliable techniques for optically opaque materials such as semiconductors or metallic circuits have not been suggested yet. The photothermal method has been developed mainly for the measurement of thermal properties using characteristics that exhibit photothermal effects depending on the thermal properties of the materials. This study attempts to numerically investigate the feasibility of using photothermal effects to visualize or measure the material distribution of opaque substances. For this purpose, we conducted numerical analyses of various intaglio patterns with approximate sizes of 1.2-6 mm in stainless steel 0.5 mm below copper. In addition, images of the intaglio patterns in stainless steel were reconstructed by two-dimensional numerical scanning. A quantitative comparison of the reconstructed results and the original geometries showed an average difference of 0.172 mm and demonstrated the possibility of application to experimental imaging.
Pedagogies in Action: A Community Resource Linking Teaching Methods to Examples of their Use
Manduca, C. A.; Fox, S. P.; Iverson, E. A.; Kirk, K.; Ormand, C. J.
2009-12-01
The Pedagogies in Action portal (http://serc.carleton.edu/sp) provides access to information on more than 40 teaching methods with examples of their use in geoscience and beyond. Each method is described with pages addressing what the method is, why or when it is useful, and how it can be implemented. New methods added this year include Teaching with Google Earth, Jigsaw, Teaching the Process of Science, Guided Discovery Problems, Teaching Urban Students, and Using ConceptTests. Examples then show specifically how the method has been used to teach concepts in a variety of disciplines. The example collection now includes 775 teaching activities of which more than 550 are drawn from the geosciences. Geoscience faculty are invited to add their own examples to this collection or to test examples in the collection and provide a review. Evaluation results show that the combination of modules and activities inspires teachers at all levels to use a new pedagogy and increases their confidence that they can use it successfully. In addition, submitting activities to the collection, including writing summary information for other instructors, helps them think more carefully about the design of their activity. The activity collections are used both for ready to use activities and to find ideas for new activities. The portal provides overarching access to materials developed by a wide variety of collaborating partners each of which uses the service to create a customized pedagogic portal addressing a more specific audience. Of interest to AGU members are pedagogic portals on Starting Point: Teaching Introductory Geoscience (http://serc.carleton.edu/introgeo); On the Cutting Edge (http://serc.carleton.edu/NAGTWorkshops); Enduring Resources for Earth System Education (http://earthref.org/ERESE) Microbial Life Educational Resources (http://serc.carleton.edu/microbe_life); the National Numeracy Network (http://serc.carleton.edu/nnn/index.html); CAUSE: The Consortium for
D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice
2018-05-01
In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.
Numerical methods for multi-scale modeling of non-Newtonian flows
Symeonidis, Vasileios
This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches. The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Ravlin (RR) and the viscoelastic FENE-P model. (1) A spectral viscosity method defined by two parameters ε, M is used to stabilize the FENE-P conformation tensor c. Convergence studies are presented for different combinations of these parameters. Two boundary conditions for the tensor c are also investigated. (2) Agreement is achieved with other works for Stokes flow of a two-dimensional cylinder in a channel. Comparison of the axial normal stress and drag coefficient on the cylinder is presented. Further, similar results from unsteady two- and three-dimensional turbulent flows past a flat plate in a channel are shown. (3) The RR problem is formulated for nearly incompressible flows, with the introduction of a mathematically equivalent tensor formulation. A spectral viscosity method and polynomial over-integration are studied. Convergence studies, including a three-dimensional channel flow with a parallel slot, investigate numerical problems arising from elemental boundaries and sharp corners. (4) The round hole pressure problem is presented for Newtonian and RR fluids in geometries with different hole sizes. Comparison with experimental data is made for the Newtonian case. The flaw in the experimental assumptions of undisturbed pressure opposite the hole is revealed, while good agreement with the data is shown. The Higashitani-Pritchard kinematical theory for RR, fluids is recovered for round holes and an approximate formula for the RR Stokes hole pressure is presented. The mesoscopic
International Nuclear Information System (INIS)
Kako, T.; Watanabe, T.
2000-06-01
This is the proceeding of 'study on numerical methods related to plasma confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. There are also various lectures on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. Separate abstracts were presented for 13 of the papers in this report. The remaining 6 were considered outside the subject scope of INIS. (J.P.N.)
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)
2007-09-17
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.
International Nuclear Information System (INIS)
Uchibori, Akihiro; Ohshima, Hiroyuki
2008-01-01
A numerical analysis method for melting/solidification phenomena has been developed to evaluate a feasibility of several candidate techniques in the nuclear fuel cycle. Our method is based on the eXtended Finite Element Method (X-FEM) which has been used for moving boundary problems. Key technique of the X-FEM is to incorporate signed distance function into finite element interpolation to represent a discontinuous gradient of the temperature at a moving solid-liquid interface. Construction of the finite element equation, the technique of quadrature and the method to solve the equation are reported here. The numerical solutions of the one-dimensional Stefan problem, solidification in a two-dimensional square corner and melting of pure gallium are compared to the exact solutions or to the experimental data. Through these analyses, validity of the newly developed numerical analysis method has been demonstrated. (author)
Vectorization on the star computer of several numerical methods for a fluid flow problem
Lambiotte, J. J., Jr.; Howser, L. M.
1974-01-01
A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.
A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger
DEFF Research Database (Denmark)
Berning, Torsten
2011-01-01
This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft Excel...
Interactive Numerical and Symbolic Analysis: A New Paradigm for Teaching Electronics
Directory of Open Access Journals (Sweden)
Jean-Claude Thomassian
2008-09-01
Full Text Available Analog Insydes, Mathematica’s symbolic circuit analysis toolbox, uses modern algorithms of expression simplification depending on comparisons with a numerical reference solution of the circuit under investigation. Some insight is offered on how the complexity of an expression barrier is overcome followed by two classical examples, a BJT emitter follower and a MOSFET common-gate amplifier stage to illustrate the proposed method at work. A concluding section discusses that time spent teaching introductory electronics by computer-aided circuit analysis, interactive numerical and symbolic, is a worthwhile investment.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Numerical method for estimating the size of chaotic regions of phase space
International Nuclear Information System (INIS)
Henyey, F.S.; Pomphrey, N.
1987-10-01
A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs
DEFF Research Database (Denmark)
Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug
2014-01-01
Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed.......Four different numerical methods for calculating the quality factor and resonance wavelength of a nano or micro photonic cavity are compared. Good agreement was found for a wide range of quality factors. Advantages and limitations of the different methods are discussed....
The instanton method and its numerical implementation in fluid mechanics
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
The instanton method and its numerical implementation in fluid mechanics
International Nuclear Information System (INIS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-01-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin–Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler–Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier–Stokes equations. (topical review)
Java technology for implementing efficient numerical analysis in intranet
International Nuclear Information System (INIS)
Song, Hee Yong; Ko, Sung Ho
2001-01-01
This paper introduces some useful Java technologies for utilizing the internet in numerical analysis, and suggests one architecture performing efficient numerical analysis in the intranet by using them. The present work has verified it's possibility by implementing some parts of this architecture with two easy examples. One is based on Servlet-Applet communication, JDBC and swing. The other is adding multi-threads, file transfer and Java remote method invocation to the former. Through this work it has been intended to make the base for the later advanced and practical research that will include efficiency estimates of this architecture and deal with advanced load balancing
Khabaza, I M
1960-01-01
Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput
Azis, Moh. Ivan; Kasbawati; Haddade, Amiruddin; Astuti Thamrin, Sri
2018-03-01
A boundary element method (BEM) is obtained for solving a boundary value problem of homogeneous anisotropic media governed by diffusion-convection equation. The application of the BEM is shown for two particular pollutant transport problems of Tello river and Unhas lake in Makassar Indonesia. For the two particular problems a variety of the coefficients of diffusion and the velocity components are taken. The results show that the solutions vary as the parameters change. And this suggests that one has to be careful in measuring or determining the values of the parameters.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
Khoromskaia, Venera; Khoromskij, Boris N
2015-12-21
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.
A Numerical Algorithm and a Graphical Method to Size a Heat Exchanger
DEFF Research Database (Denmark)
Berning, Torsten
2011-01-01
This paper describes the development of a numerical algorithm and a graphical method that can be employed in order to determine the overall heat transfer coefficient inside heat exchangers. The method is based on an energy balance and utilizes the spreadsheet application software Microsoft ExcelTM...
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr
Numerical comparison of robustness of some reduction methods in rough grids
Hou, Jiangyong
2014-04-09
In this article, we present three nonsymmetric mixed hybrid RT 1 2 methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken RT 1 2 method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed. © 2014 Wiley Periodicals, Inc.
Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method
International Nuclear Information System (INIS)
Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr
2008-01-01
Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code
Numerical analysis of creep brittle rupture by the finite element method
International Nuclear Information System (INIS)
Goncalves, O.J.A.; Owen, D.R.J.
1983-01-01
In this work an implicit algorithm is proposed for the numerical analysis of creep brittle rupture problems by the finite element method. This kind of structural failure, typical in components operating at high temperatures for long periods of time, is modelled using either a three dimensional generalization of the Kachanov-Rabotnov equations due to Leckie and Hayhurst or the Monkman-Grant fracture criterion together with the Linear Life Fraction Rule. The finite element equations are derived by the displacement method and isoparametric elements are used for the spatial discretization. Geometric nonlinear effects (large displacements) are accounted for by an updated Lagrangian formulation. Attention is also focussed on the solution of the highly stiff differential equations that govern damage growth. Finally the numerical results of a three-dimensional analysis of a pressurized thin cylinder containing oxidised pits in its external wall are discussed. (orig.)
Numerical analysis of short-pulse laser interactions with thin metal film
Directory of Open Access Journals (Sweden)
E. Majchrzak
2010-10-01
Full Text Available Thin metal film subjected to a short-pulse laser heating is considered. The hyperbolic two-temperature model describing the temporal andspatial evolution of the lattice and electrons temperatures is discussed. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.
International Nuclear Information System (INIS)
Wang, Wenyan; Han, Bo; Yamamoto, Masahiro
2013-01-01
We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)
Jain, Sonal
2018-01-01
In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.
Adaptive and dynamic meshing methods for numerical simulations
Acikgoz, Nazmiye
-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging multi-physics and multi-field problems that are unsteady in nature are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, which typically occurs when implicit time marching procedures are used, degenerate elements are easily formed in the grid such that frequent remeshing is required. To deal with this problem, in the second part of this work, we propose a new r-adaptation methodology. The new technique is valid for both simplicial (e.g., triangular, tet) and non-simplicial (e.g., quadrilateral, hex) deforming grids that undergo large imposed displacements at their boundaries. A two- or three-dimensional grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. This is accomplished by confining each vertex to its ball through springs that are attached to the vertex and its projection on the ball entities. The resulting linear problem is solved using a preconditioned conjugate gradient method. The new method is compared with the classical spring analogy technique in two- and three-dimensional examples, highlighting the performance improvements achieved by the new method. Meshes are an important part of numerical simulations. Depending on the geometry and flow conditions, the most suitable mesh for each particular problem is different. Meshes are usually generated by either using a suitable software package or solving a PDE. In both cases, engineering intuition plays a significant role in deciding where clusterings should take place. In addition, for unsteady problems, the gradients vary for each time step, which requires frequent remeshing during simulations
Numerical solution of the Navier--Stokes equations at high Reynolds numbers
International Nuclear Information System (INIS)
Shestakov, A.I.
1974-01-01
A numerical method is presented which is designed to solve the Navier-Stokes equations for two-dimensional, incompressible flow. The method is intended for use on problems with high Reynolds numbers for which calculations via finite difference methods have been unattainable or unreliable. The proposed scheme is a hybrid utilizing a time-splitting finite difference method in areas away from the boundaries. In areas neighboring the boundaries, the equations of motion are solved by the newly proposed vortex method by Chorin. The major accomplishment of the new scheme is that it contains a simple way for merging the two methods at the interface of the two subdomains. The proposed algorithm is designed for use on the time-dependent equations but can be used on steady state problems as well. The method is tested on the popular, time-independent, square cavity problem, an example of a separated flow with closed streamlines. Numerical results are presented for a Reynolds number of 10 3 . (auth)
Kovalovs, A.; Rucevskis, S.; Akishin, P.; Kolupajevs, J.
2017-10-01
The paper presents numerical results of loss of prestress in the reinforced prestressed precast hollow core slabs by modal analysis. Loss of prestress is investigated by the 3D finite element method, using ANSYS software. In the numerical examples, variables initial stresses were introduced into seven-wire stress-relieved strands of the concrete slabs. The effects of span and material properties of concrete on the modal frequencies of the concrete structure under initial stress were studied. Modal parameters computed from the finite element models were compared. Applicability and effectiveness of the proposed method was investigated.
Dadashzadeh, N.; Duzgun, H. S. B.; Yesiloglu-Gultekin, N.
2017-08-01
While advanced numerical techniques in slope stability analysis are successfully used in deterministic studies, they have so far found limited use in probabilistic analyses due to their high computation cost. The first-order reliability method (FORM) is one of the most efficient probabilistic techniques to perform probabilistic stability analysis by considering the associated uncertainties in the analysis parameters. However, it is not possible to directly use FORM in numerical slope stability evaluations as it requires definition of a limit state performance function. In this study, an integrated methodology for probabilistic numerical modeling of rock slope stability is proposed. The methodology is based on response surface method, where FORM is used to develop an explicit performance function from the results of numerical simulations. The implementation of the proposed methodology is performed by considering a large potential rock wedge in Sumela Monastery, Turkey. The accuracy of the developed performance function to truly represent the limit state surface is evaluated by monitoring the slope behavior. The calculated probability of failure is compared with Monte Carlo simulation (MCS) method. The proposed methodology is found to be 72% more efficient than MCS, while the accuracy is decreased with an error of 24%.
Problem of the Moving Boundary in Continuous Casting Solved by The Analytic-Numerical Method
Directory of Open Access Journals (Sweden)
Grzymkowski R.
2013-03-01
Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase - liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Problem of the Moving Boundary in Continuous Casting Solved by the Analytic-Numerical Method
Directory of Open Access Journals (Sweden)
R. Grzymkowski
2013-01-01
Full Text Available Mathematical modeling of thermal processes combined with the reversible phase transitions of type: solid phase – liquid phase leads to formulation of the parabolic or elliptic moving boundary problem. Solution of such defined problem requires, most often, to use some sophisticated numerical techniques and far advanced mathematical tools. The paper presents an analytic-numerical method, especially attractive from the engineer’s point of view, applied for finding the approximate solutions of the selected class of problems which can be reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial expansion of a sought function, describing the field of temperature, into the power series, some coefficients of which are determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which are determined numerically. The method represents a combination of the analytical and numerical techniques and seems to be an effective and relatively easy in using tool for solving problems of considered kind.
Analysis and presentation of experimental results with examples, problems and programs
Christodoulides, Costas
2017-01-01
This book is intended as a guide to the analysis and presentation of experimental results. It develops various techniques for the numerical processing of experimental data, using basic statistical methods and the theory of errors. After presenting basic theoretical concepts, the book describes the methods by which the results can be presented, both numerically and graphically. The book is divided into three parts, of roughly equal length, addressing the theory, the analysis of data, and the presentation of results. Examples are given and problems are solved using the Excel, Origin, Python and R software packages. In addition, programs in all four languages are made available to readers, allowing them to use them in analyzing and presenting the results of their own experiments. Subjects are treated at a level appropriate for undergraduate students in the natural sciences, but this book should also appeal to anyone whose work involves dealing with experimental results.
Testing the accuracy and stability of spectral methods in numerical relativity
International Nuclear Information System (INIS)
Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.
2007-01-01
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test
An alternative method for determination of oscillator strengths: The example of Sc II
International Nuclear Information System (INIS)
Ruczkowski, J.; Elantkowska, M.; Dembczyński, J.
2014-01-01
We describe our method for determining oscillator strengths and hyperfine structure splittings that is an alternative to the commonly used, purely theoretical calculations, or to the semi-empirical approach combined with theoretically calculated transition integrals. We have developed our own computer programs that allow us to determine all attributes of the structure of complex atoms starting from the measured frequencies emitted by the atoms. As an example, we present the results of the calculation of the structure, electric dipole transitions, and hyperfine splittings of Sc II. The angular coefficients of the transition matrix in pure SL coupling were found from straightforward Racah algebra. The transition matrix was transformed into the actual intermediate coupling by the fine structure eigenvectors obtained from the semi-empirical approach. The transition integrals were treated as free parameters in the least squares fit to experimental gf values. For most transitions, the experimental and the calculated gf-values are consistent with the accuracy claimed in the NIST compilation. - Highlights: • The method of simultaneous determination of all the attributes of atomic structure. • The semi-empirical method of parameterization of oscillator strengths. • Illustration of the method application for the example of Sc II data
Directory of Open Access Journals (Sweden)
Metin Varan
2017-08-01
Full Text Available Field theory is one of the two sub-field theories in electrical and electronics engineering that for creates difficulties for undergraduate students. In undergraduate period, field theory has been taught under the theory of electromagnetic fields by which describes using partial differential equations and integral methods. Analytical methods for solution of field problems on the basis of a mathematical model may result the understanding difficulties for undergraduate students due to their mathematical and physical infrastructure. The analytical methods which can be applied in simple model lose their applicability to more complex models. In this case, the numerical methods are used to solve more complex equations. In this study, by preparing some field theory‘s web-based graphical user interface numerical methods of applications it has been aimed to increase learning levels of field theory problems for undergraduate and graduate students while taking in mind their computer programming capabilities.
Numerical Simulation of Transitional, Hypersonic Flows using a Hybrid Particle-Continuum Method
Verhoff, Ashley Marie
Analysis of hypersonic flows requires consideration of multiscale phenomena due to the range of flight regimes encountered, from rarefied conditions in the upper atmosphere to fully continuum flow at low altitudes. At transitional Knudsen numbers there are likely to be localized regions of strong thermodynamic nonequilibrium effects that invalidate the continuum assumptions of the Navier-Stokes equations. Accurate simulation of these regions, which include shock waves, boundary and shear layers, and low-density wakes, requires a kinetic theory-based approach where no prior assumptions are made regarding the molecular distribution function. Because of the nature of these types of flows, there is much to be gained in terms of both numerical efficiency and physical accuracy by developing hybrid particle-continuum simulation approaches. The focus of the present research effort is the continued development of the Modular Particle-Continuum (MPC) method, where the Navier-Stokes equations are solved numerically using computational fluid dynamics (CFD) techniques in regions of the flow field where continuum assumptions are valid, and the direct simulation Monte Carlo (DSMC) method is used where strong thermodynamic nonequilibrium effects are present. Numerical solutions of transitional, hypersonic flows are thus obtained with increased physical accuracy relative to CFD alone, and improved numerical efficiency is achieved in comparison to DSMC alone because this more computationally expensive method is restricted to those regions of the flow field where it is necessary to maintain physical accuracy. In this dissertation, a comprehensive assessment of the physical accuracy of the MPC method is performed, leading to the implementation of a non-vacuum supersonic outflow boundary condition in particle domains, and more consistent initialization of DSMC simulator particles along hybrid interfaces. The relative errors between MPC and full DSMC results are greatly reduced as a
Elliptic differential equations theory and numerical treatment
Hackbusch, Wolfgang
2017-01-01
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Innovative Public Procurement Methods: Examples Of Selected Country And Lessons For Turkey
Directory of Open Access Journals (Sweden)
Elif Ayşe ŞAHİN İPEK
2016-12-01
Full Text Available Innovative public procurement considered as demand-side policies aimed at economic competitiveness, growth and development through the development of private sector innovation supply. In this study it is examined the methods of innovative procurement policy and country examples. It is exerted obstacles and solutions from the results of this examination.
Multiple predictor smoothing methods for sensitivity analysis: Example results
International Nuclear Information System (INIS)
Storlie, Curtis B.; Helton, Jon C.
2008-01-01
The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described in the first part of this presentation: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. In this, the second and concluding part of the presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present
The Role of Numerical Methods in the Sensitivity Analysis of a ...
African Journals Online (AJOL)
The mathematical modelling of physiochemical interaction in the framework of industrial and environmental physics which relies on an initial value problem is defined by a first order ordinary differential equation. Two numerical methods of studying sensitivity analysis of physiochemical interaction data are developed.
Mathematical methods for physical and analytical chemistry
Goodson, David Z
2011-01-01
Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical
Numerical and experimental validation of a particle Galerkin method for metal grinding simulation
Wu, C. T.; Bui, Tinh Quoc; Wu, Youcai; Luo, Tzui-Liang; Wang, Morris; Liao, Chien-Chih; Chen, Pei-Yin; Lai, Yu-Sheng
2018-03-01
In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach.
Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method
International Nuclear Information System (INIS)
Zhang Xu; Tan Duowang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)
Hu, Ping; Liu, Li-zhong; Zhu, Yi-guo
2013-01-01
Over the last 15 years, the application of innovative steel concepts in the automotive industry has increased steadily. Numerical simulation technology of hot forming of high-strength steel allows engineers to modify the formability of hot forming steel metals and to optimize die design schemes. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming focuses on hot and cold forming theories, numerical methods, relative simulation and experiment techniques for high-strength steel forming and die design in the automobile industry. Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming introduces the general theories of cold forming, then expands upon advanced hot forming theories and simulation methods, including: • the forming process, • constitutive equations, • hot boundary constraint treatment, and • hot forming equipment and experiments. Various calculation methods of cold and hot forming, based on the authors’ experience in commercial CAE software f...
International Nuclear Information System (INIS)
Eoh, Jae-Hyuk; Jeong, Ji-Young; Kim, Seong-O; Hahn, Dohee; Park, Nam-Cook
2005-01-01
A quasi-steady system analysis of the sodium-water reaction (SWR) phenomena in a liquid-metal reactor (LMR) was performed using the Sodium-water reaction Event Later Phase System Transient Analyzer (SELPSTA) computer simulation code. The code has been formulated by implementing various physical assumptions to simplify the complex SWR phenomena, and it adopts the long-term mass and energy transfer (LMET) model developed in the present study. The LMET model is based on the hypothesis that the system transient can be described by the pressure and temperature transient of the cover gas space, and it can be applied only to the reaction period characterized by bulk motion. To evaluate the feasibility of the physical model and its assumptions, a scale-down mock-up test was carried out, and it was demonstrated that the numerical simulation using the LMET model adequately replicates the overall phenomena of the experiment with reasonable understanding. Based on the findings, as a numerical example, the long-term system transient responses during the SWR event of the Korea Advanced LIquid MEtal Reactor (KALIMER) were investigated, and it was found that the long-term dynamic responses are strongly dependent on the design parameters and operational strategies. As a result, the numerical simulation method developed in the present study is practicable; furthermore, the SELPSTA code is useful to resolve the risk for the SWR event
International Nuclear Information System (INIS)
Kaya, Dogan; El-Sayed, Salah M.
2003-01-01
In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions
Weierstrass method for quaternionic polynomial root-finding
Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana
2018-01-01
Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.
New numerical method to study phase transitions and its applications
International Nuclear Information System (INIS)
Lee, Jooyoung; Kosterlitz, J.M.
1991-11-01
We present a powerful method of identifying the nature of transitions by numerical simulation of finite systems. By studying the finite size scaling properties of free energy barrier between competing states, we can identify unambiguously a weak first order transition even when accessible system sizes are L/ξ < 0.05 as in the five state Potts model in two dimensions. When studying a continuous phase transition we obtain quite accurate estimates of critical exponents by treating it as a field driven first order transition. The method has been successfully applied to various systems
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Energy Technology Data Exchange (ETDEWEB)
Lucas, D.S.
2004-10-03
This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.
Energy Technology Data Exchange (ETDEWEB)
Reinert, U. [DEKRA-ETS Europaeische Gesellschaft fuer Technische Sicherheit mbH, Saarbruecken (Germany); Klaer, P. [Saar-Hartmetall und Werkzeuge GmbH, Voelklingen (Germany)
1999-02-01
The nonoxidic ceramics (for example SiC), used as a supporting structure in kilns, are subject to instantaneous damage, which as a rule is accompanied by high costs. Of interest in this context is the question whether a satisfactory statement can be made about the increase of damage frequency as a function of the firing temperature, the firing time, the geometry of the component, the material properties and the loading. Knowledge of these correlations provides the user with the possibility of minimizing the costs of damage by means of suitable selection of material and timely replacement of the components. The procedure presented in the following is based on the combination of numerical studies with statistically evaluated experiments. (orig.)
Combined Effects of Numerical Method Type and Time Step on Water Stressed Actual Crop ET
Directory of Open Access Journals (Sweden)
B. Ghahraman
2016-02-01
Full Text Available Introduction: Actual crop evapotranspiration (Eta is important in hydrologic modeling and irrigation water management issues. Actual ET depends on an estimation of a water stress index and average soil water at crop root zone, and so depends on a chosen numerical method and adapted time step. During periods with no rainfall and/or irrigation, actual ET can be computed analytically or by using different numerical methods. Overal, there are many factors that influence actual evapotranspiration. These factors are crop potential evapotranspiration, available root zone water content, time step, crop sensitivity, and soil. In this paper different numerical methods are compared for different soil textures and different crops sensitivities. Materials and Methods: During a specific time step with no rainfall or irrigation, change in soil water content would be equal to evapotranspiration, ET. In this approach, however, deep percolation is generally ignored due to deep water table and negligible unsaturated hydraulic conductivity below rooting depth. This differential equation may be solved analytically or numerically considering different algorithms. We adapted four different numerical methods, as explicit, implicit, and modified Euler, midpoint method, and 3-rd order Heun method to approximate the differential equation. Three general soil types of sand, silt, and clay, and three different crop types of sensitive, moderate, and resistant under Nishaboor plain were used. Standard soil fraction depletion (corresponding to ETc=5 mm.d-1, pstd, below which crop faces water stress is adopted for crop sensitivity. Three values for pstd were considered in this study to cover the common crops in the area, including winter wheat and barley, cotton, alfalfa, sugar beet, saffron, among the others. Based on this parameter, three classes for crop sensitivity was considered, sensitive crops with pstd=0.2, moderate crops with pstd=0.5, and resistive crops with pstd=0
Energy Technology Data Exchange (ETDEWEB)
Han, Bing; Jing, Hongyuan; Liu, Jianping; Wu, Zhangzhong [PetroChina Pipeline RandD Center, Langfang, Hebei (China); Hao, Jianbin [School of Petroleum Engineering, Southwest Petroleum University, Chengdu, Sichuan (China)
2010-07-01
Landslides have a serious impact on the integrity of oil and gas pipelines in the tough terrain of Western China. This paper introduces a solving method of axial stress, which uses numerical simulation and regression analysis for the pipelines subjected to landslides. Numerical simulation is performed to analyze the change regularity of pipe stresses for the five vulnerability assessment indexes, which are: the distance between pipeline and landslide tail; the thickness of landslide; the inclination angle of landslide; the pipeline length passing through landslide; and the buried depth of pipeline. A pipeline passing through a certain landslide in southwest China was selected as an example to verify the feasibility and effectiveness of this method. This method has practical applicability, but it would need large numbers of examples to better verify its reliability and should be modified accordingly. Also, it only considers the case where the direction of the pipeline is perpendicular to the primary slip direction of the landslide.
Numerical treatment of linearized equations describing inhomogeneous collisionless plasmas
International Nuclear Information System (INIS)
Lewis, H.R.
1979-01-01
The equations governing the small-signal response of spatially inhomogeneous collisionless plasmas have practical significance in physics, for example in controlled thermonuclear fusion research. Although the solutions are very complicated and the equations are different to solve numerically, effective methods for them are being developed which are applicable when the equilibrium involves only one nonignorable coordinate. The general theoretical framework probably will provide a basis for progress when there are two or three nonignorable coordinates
On nitrogen condensation in hypersonic nozzle flows: Numerical method and parametric study
Lin, Longyuan; Cheng, Wan; Luo, Xisheng; Qin, Fenghua
2013-01-01
A numerical method for calculating two-dimensional planar and axisymmetric hypersonic nozzle flows with nitrogen condensation is developed. The classical nucleation theory with an empirical correction function and the modified Gyarmathy model
On the numerical treatment of selected oscillatory evolutionary problems
Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice
2017-07-01
We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.
On nitrogen condensation in hypersonic nozzle flows: Numerical method and parametric study
Lin, Longyuan
2013-12-17
A numerical method for calculating two-dimensional planar and axisymmetric hypersonic nozzle flows with nitrogen condensation is developed. The classical nucleation theory with an empirical correction function and the modified Gyarmathy model are used to describe the nucleation rate and the droplet growth, respectively. The conservation of the liquid phase is described by a finite number of moments of the size distribution function. The moment equations are then combined with the Euler equations and are solved by the finite-volume method. The numerical method is first validated by comparing its prediction with experimental results from the literature. The effects of nitrogen condensation on hypersonic nozzle flows are then numerically examined. The parameters at the nozzle exit under the conditions of condensation and no-condensation are evaluated. For the condensation case, the static pressure, the static temperature, and the amount of condensed fluid at the nozzle exit decrease with the increase of the total temperature. Compared with the no-condensation case, both the static pressure and temperature at the nozzle exit increase, and the Mach number decreases due to the nitrogen condensation. It is also indicated that preheating the nitrogen gas is necessary to avoid the nitrogen condensation even for a hypersonic nozzle with a Mach number of 5 operating at room temperatures. © 2013 Springer-Verlag Berlin Heidelberg.
Directory of Open Access Journals (Sweden)
M. A. Farkov
2014-01-01
Full Text Available An analysis of numerical optimization methods for solving a problem of molecular docking has been performed. Some additional requirements for optimization methods according to GPU architecture features were specified. A promising method for implementation on GPU was selected. Its implementation was described and performance and accuracy tests were performed.
A numerical calculation method of environmental impacts for the deep sea mining industry - a review.
Ma, Wenbin; van Rhee, Cees; Schott, Dingena
2018-03-01
Since the gradual decrease of mineral resources on-land, deep sea mining (DSM) is becoming an urgent and important emerging activity in the world. However, until now there has been no commercial scale DSM project in progress. Together with the reasons of technological feasibility and economic profitability, the environmental impact is one of the major parameters hindering its industrialization. Most of the DSM environmental impact research focuses on only one particular aspect ignoring that all the DSM environmental impacts are related to each other. The objective of this work is to propose a framework for the numerical calculation methods of the integrated DSM environmental impacts through a literature review. This paper covers three parts: (i) definition and importance description of different DSM environmental impacts; (ii) description of the existing numerical calculation methods for different environmental impacts; (iii) selection of a numerical calculation method based on the selected criteria. The research conducted in this paper provides a clear numerical calculation framework for DSM environmental impact and could be helpful to speed up the industrialization process of the DSM industry.
A summary of numerical computation for special functions
International Nuclear Information System (INIS)
Zhang Shanjie
1992-01-01
In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed
Yu, Jie; Liu, Yikan; Yamamoto, Masahiro
2018-04-01
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.
DEFF Research Database (Denmark)
Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter
1995-01-01
The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....
Energy Technology Data Exchange (ETDEWEB)
Hong, Z; Jiang, Q; Pei, R; Campbell, A M; Coombs, T A [Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)
2007-04-15
A finite element method code based on the critical state model is proposed to solve the AC loss problem in YBCO coated conductors. This numerical method is based on a set of partial differential equations (PDEs) in which the magnetic field is used as the state variable. The AC loss problems have been investigated both in self-field condition and external field condition. Two numerical approaches have been introduced: the first model is configured on the cross-section plane of the YBCO tape to simulate an infinitely long superconducting tape. The second model represents the plane of the critical current flowing and is able to simulate the YBCO tape with finite length where the end effect is accounted. An AC loss measurement has been done to verify the numerical results and shows a good agreement with the numerical solution.
Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method
International Nuclear Information System (INIS)
Xu, Zhang; Duo-Wang, Tan
2009-01-01
A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))
Numerical Feedback Stabilization with Applications to Networks
Directory of Open Access Journals (Sweden)
Simone Göttlich
2017-01-01
Full Text Available The focus is on the numerical consideration of feedback boundary control problems for linear systems of conservation laws including source terms. We explain under which conditions the numerical discretization can be used to design feedback boundary values for network applications such as electric transmission lines or traffic flow systems. Several numerical examples illustrate the properties of the results for different types of networks.
A New Numerical Method for Z2 Topological Insulators with Strong Disorder
Akagi, Yutaka; Katsura, Hosho; Koma, Tohru
2017-12-01
We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.
Analysis of thermal-plastic response of shells of revolution by numerical integration
International Nuclear Information System (INIS)
Leonard, J.W.
1975-01-01
A numerical method based instead on the numerical integration of the governing shell equations has been shown, for elastic cases, to be more efficient than the finite element method when applied to shells of revolution. In the numerical integration method, the governing differential equations of motions are converted into a set of initial-value problems. Each initial-value problem is integrated numerically between meridional boundary points and recombined so as to satisfy boundary conditions. For large-deflection elasto-plastic behavior, the equations are nonlinear and, hence, are recombined in an iterative manner using the Newton-Raphson procedure. Suppression techniques are incorporated in order to eliminate extraneous solutions within the numerical integration procedure. The Reissner-Meissner shell theory for shells of revolution is adopted to account for large deflection and higher-order rotation effects. The computer modelling of the equations is quite general in that specific shell segment geometries, e.g. cylindrical, spherical, toroidal, conical segments, and any combinations thereof can be handled easily. The elasto-plastic constitutive relations adopted are in accordance with currently recommended constitutive equations for inelastic design analysis of FFTF Components. The Von Mises yield criteria and associated flow rule is used and the kinematic hardening law is followed. Examples are considered in which stainless steels common to LMFBR application are used
Jylhä, Liisi; Honkamo, Johanna; Jantunen, Heli; Sihvola, Ari
2005-05-01
Effective permittivity was modeled and measured for composites that consist of up to 35vol% of titanium dioxide powder dispersed in a continuous epoxy matrix. The study demonstrates a method that enables fast and accurate numerical modeling of the effective permittivity values of ceramic/polymer composites. The model requires electrostatic Monte Carlo simulations, where randomly oriented homogeneous prism-shaped inclusions occupy random positions in the background phase. The computation cost of solving the electrostatic problem by a finite-element code is decreased by the use of an averaging method where the same simulated sample is solved three times with orthogonal field directions. This helps to minimize the artificial anisotropy that results from the pseudorandomness inherent in the limited computational domains. All the required parameters for numerical simulations are calculated from the lattice structure of titanium dioxide. The results show a very good agreement between the measured and numerically calculated effective permittivities. When the prisms are approximated by oblate spheroids with the corresponding axial ratio, a fairly good prediction for the effective permittivity of the mixture can be achieved with the use of an advanced analytical mixing formula.
Saavedra, Sebastian
2012-07-01
The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.
Daudelin, Denise H; Selker, Harry P; Leslie, Laurel K
2015-12-01
There is growing appreciation that process improvement holds promise for improving quality and efficiency across the translational research continuum but frameworks for such programs are not often described. The purpose of this paper is to present a framework and case examples of a Research Process Improvement Program implemented at Tufts CTSI. To promote research process improvement, we developed online training seminars, workshops, and in-person consultation models to describe core process improvement principles and methods, demonstrate the use of improvement tools, and illustrate the application of these methods in case examples. We implemented these methods, as well as relational coordination theory, with junior researchers, pilot funding awardees, our CTRC, and CTSI resource and service providers. The program focuses on capacity building to address common process problems and quality gaps that threaten the efficient, timely and successful completion of clinical and translational studies. © 2015 The Authors. Clinical and Translational Science published by Wiley Periodicals, Inc.
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
Tchernykh A. G.
2015-01-01
We consider the technology of application of numerical methods in the educational process in physics on the example of a study of the magnetic field induced by induction currents in a cylindrical conductor in a quasi-stationary magnetic field. Here is given the numerical calculation of the real and imaginary parts of the Bessel functions of complex argument. The listing of the program of drawing the graphs of the radial dependence of the amplitude and phase shift of the inductive currents fie...
Numerical method for the unsteady potential flow about pitching airfoils
International Nuclear Information System (INIS)
Parrouffe, J.-M.; Paraschivoiu, I.
1985-01-01
This paper presents a numerical method for the unsteady potential flow about an aerodynamic profile and in its wake. This study has many applications such as airplane wings and propellers, guide vanes, subcavitant hydrofoils and wind turbine blades. Typical of such nonstationary configurations is the rotor of the Darrieus vertical-axis wind turbine whose blades are exposed to cyclic aerodynamic loads in the operating state
Development of numerical methods for thermohydraulic problems in reactor safety
International Nuclear Information System (INIS)
Chabrillac, M.; Kavenoky, A.; Le Coq, G.; L'Heriteau, J.P.; Stewart, B.; Rousseau, J.C.
1976-01-01
Numerical methods are being developed for the LOCA calculation; the first part is devoted to the BERTHA model and the associated characteristic treatment for the first seconds of the blowdown, the second part presents the problems encountered for accounting for velocity difference between phases. The FLIRA treatment of the reflooding is presented in the last part: this treatment allows the calculation of the quenching front velocity
Numerical Simulation of Plasma Antenna with FDTD Method
International Nuclear Information System (INIS)
Chao, Liang; Yue-Min, Xu; Zhi-Jiang, Wang
2008-01-01
We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconBgurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design
Numerical simulation of plasma antenna with FDTD method
International Nuclear Information System (INIS)
Liang Chao; Xu Yuemin; Wang Zhijiang
2008-01-01
We adopt cylindrical-coordinate FDTD algorithm to simulate and analyse a 0.4-m-long column configuration plasma antenna. FDTD method is useful for solving electromagnetic problems, especially when wave characteristics and plasma properties are self-consistently related to each other. Focus on the frequency from 75 MHz to 400 MHz, the input impedance and radiation efficiency of plasma antennas are computed. Numerical results show that, different from copper antenna, the characteristics of plasma antenna vary simultaneously with plasma frequency and collision frequency. The property can be used to construct dynamically reconfigurable antenna. The investigation is meaningful and instructional for the optimization of plasma antenna design. (authors)
International Nuclear Information System (INIS)
Faucher, V.
2014-01-01
This HDR is dedicated to the research in the framework of fast transient dynamics for industrial fluid-structure systems carried in the Laboratory of Dynamic Studies from CEA, implementing new numerical methods for the modelling of complex systems and the parallel solution of large coupled problems on supercomputers. One key issue for the proposed approaches is the limitation to its minimum of the number of non-physical parameters, to cope with constraints arising from the area of usage of the concepts: safety for both nuclear applications (CEA, EDF) and aeronautics (ONERA), protection of the citizen (EC/JRC) in particular. Kinematic constraints strongly coupling structures (namely through unilateral contact) or fluid and structures (with both conformant or non-conformant meshes depending on the geometrical situation) are handled through exact methods including Lagrange Multipliers, with consequences on the solution strategy to be dealt with. This latter aspect makes EPX, the simulation code where the methods are integrated, a singular tool in the community of fast transient dynamics software. The document mainly relies on a description of the modelling needs for industrial fast transient scenarios, for nuclear applications in particular, and the proposed solutions built in the framework of the collaboration between CEA, EDF (via the LaMSID laboratory) and the LaMCoS laboratory from INSA Lyon. The main considered examples are the tearing of the fluid-filled tank after impact, the Code Disruptive Accident for a Generation IV reactor or the ruin of reinforced concrete structures under impact. Innovative models and parallel algorithms are thus proposed, allowing to carry out with robustness and performance the corresponding simulations on supercomputers made of interconnected multi-core nodes, with a strict preservation of the quality of the physical solution. This was particularly the main point of the ANR RePDyn project (2010-2013), with CEA as the pilot. (author
Numerical solution of the controlled Duffing oscillator by semi-orthogonal spline wavelets
International Nuclear Information System (INIS)
Lakestani, M; Razzaghi, M; Dehghan, M
2006-01-01
This paper presents a numerical method for solving the controlled Duffing oscillator. The method can be extended to nonlinear calculus of variations and optimal control problems. The method is based upon compactly supported linear semi-orthogonal B-spline wavelets. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique
Transportation package design using numerical optimization
International Nuclear Information System (INIS)
Harding, D.C.; Witkowski, W.R.
1991-01-01
The purpose of this overview is twofold: first, to outline the theory and basic elements of numerical optimization; and second, to show how numerical optimization can be applied to the transportation packaging industry and used to increase efficiency and safety of radioactive and hazardous material transportation packages. A more extensive review of numerical optimization and its applications to radioactive material transportation package design was performed previously by the authors (Witkowski and Harding 1992). A proof-of-concept Type B package design is also presented as a simplified example of potential improvements achievable using numerical optimization in the design process
Numerical methods and inversion algorithms in reservoir simulation based on front tracking
Energy Technology Data Exchange (ETDEWEB)
Haugse, Vidar
1999-04-01
This thesis uses front tracking to analyse laboratory experiments on multiphase flow in porous media. New methods for parameter estimation for two- and three-phase relative permeability experiments have been developed. Up scaling of heterogeneous and stochastic porous media is analysed. Numerical methods based on front tracking is developed and analysed. Such methods are efficient for problems involving steep changes in the physical quantities. Multi-dimensional problems are solved by combining front tracking with dimensional splitting. A method for adaptive grid refinement is developed.