WorldWideScience

Sample records for asymptotic iteration method

  1. The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Rabian Wangkeeree

    2012-01-01

    Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

  2. A connection between the asymptotic iteration method and the continued fractions formalism

    International Nuclear Information System (INIS)

    Matamala, A.R.; Gutierrez, F.A.; Diaz-Valdes, J.

    2007-01-01

    In this work, we show that there is a connection between the asymptotic iteration method (a method to solve second order linear ordinary differential equations) and the older method of continued fractions to solve differential equations

  3. On iterative procedures of asymptotic inference

    NARCIS (Netherlands)

    K.O. Dzhaparidze (Kacha)

    1983-01-01

    textabstractAbstract  An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then

  4. Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

    International Nuclear Information System (INIS)

    Arum Sari, Resita; Suparmi, A; Cari, C

    2016-01-01

    The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number n r causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. (paper)

  5. Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

    International Nuclear Information System (INIS)

    Yahiaoui, S.-A.; Bentaiba, M.

    2011-01-01

    We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

  6. Asymptotic iteration method solutions to the d-dimensional Schroedinger equation with position-dependent mass

    International Nuclear Information System (INIS)

    Yasuk, F.; Tekin, S.; Boztosun, I.

    2010-01-01

    In this study, the exact solutions of the d-dimensional Schroedinger equation with a position-dependent mass m(r)=1/(1+ζ 2 r 2 ) is presented for a free particle, V(r)=0, by using the method of point canonical transformations. The energy eigenvalues and corresponding wavefunctions for the effective potential which is to be a generalized Poeschl-Teller potential are obtained within the framework of the asymptotic iteration method.

  7. Asymptotic convergence for iterative optimization in electronic structure

    International Nuclear Information System (INIS)

    Lippert, Ross A.; Sears, Mark P.

    2000-01-01

    There have recently been a number of proposals for solving large electronic structure problems (local-density approximation, Hartree-Fock, and tight-binding methods) iteratively with a computational effort proportional to the size of the system. The effort needed to perform a single iteration in these schemes is well understood but the convergence rate has been an empirical matter. This paper will show that many of the proposed methods have a single underlying geometrical structure, which has a specific asymptotic convergence behavior, and that behavior can be understood in terms of some simple condition numbers based on the spectrum of the Hamiltonian. (c) 2000 The American Physical Society

  8. Advances in iterative methods

    International Nuclear Information System (INIS)

    Beauwens, B.; Arkuszewski, J.; Boryszewicz, M.

    1981-01-01

    Results obtained in the field of linear iterative methods within the Coordinated Research Program on Transport Theory and Advanced Reactor Calculations are summarized. The general convergence theory of linear iterative methods is essentially based on the properties of nonnegative operators on ordered normed spaces. The following aspects of this theory have been improved: new comparison theorems for regular splittings, generalization of the notions of M- and H-matrices, new interpretations of classical convergence theorems for positive-definite operators. The estimation of asymptotic convergence rates was developed with two purposes: the analysis of model problems and the optimization of relaxation parameters. In the framework of factorization iterative methods, model problem analysis is needed to investigate whether the increased computational complexity of higher-order methods does not offset their increased asymptotic convergence rates, as well as to appreciate the effect of standard relaxation techniques (polynomial relaxation). On the other hand, the optimal use of factorization iterative methods requires the development of adequate relaxation techniques and their optimization. The relative performances of a few possibilities have been explored for model problems. Presently, the best results have been obtained with optimal diagonal-Chebyshev relaxation

  9. Analytical Investigation of Beam Deformation Equation using Perturbation, Homotopy Perturbation, Variational Iteration and Optimal Homotopy Asymptotic Methods

    DEFF Research Database (Denmark)

    Farrokhzad, F.; Mowlaee, P.; Barari, Amin

    2011-01-01

    The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation......., and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...

  10. Relativistic Energy Analysis of Five-Dimensional q-Deformed Radial Rosen-Morse Potential Combined with q-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

    International Nuclear Information System (INIS)

    Pramono, Subur; Suparmi, A.; Cari, Cari

    2016-01-01

    We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separable q-deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equation l_D_-_1 have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum number n causes the increase of bound state relativistic energy level in both dimensions D=5 and D=3. The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number n_l.

  11. Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

    Science.gov (United States)

    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.

  12. Analysis of D Dimensional Dirac equation for q -deformed Posch-Teller combined with q -deformed trigonometric Manning Rosen Non-Central potential using Asymptotic Iteration Method (AIM)

    International Nuclear Information System (INIS)

    Alam, Y.; Suparmi; Cari; Anwar, F.

    2016-01-01

    In this study, we used asymptotic iteration method (AIM) to obtain the relativistic energy spectra and wavefunctions for D Dimensional Dirac equation. Solution of the D Dimensional Dirac equation using asymptotic iteration method was done by four steps. The first step, we substitutied q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential into D dimensional Dirac equation. And then, general term of D dimensioanl Dirac equation for q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential was reduced into one dimensioanal Dirac equation, consist of radial part and angular part. The second step, both of one dimensional part must be reduced to hypergeometric type differential equation by suitable parameter change. And then, hypergeometric type differential equation was transformed into AIM type differential equation. For the last step, AIM type differential equation can be solved to obtain the relativistic energy and wavefunctions of Dirac equation. Relativistic energy and wavefunctions were visualized by using Matlab software. (paper)

  13. Iterative Runge–Kutta-type methods for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Böckmann, C; Pornsawad, P

    2008-01-01

    We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge–Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule. Some particular iterative regularization methods are numerically implemented. Numerical results of the examples show that the developed Runge–Kutta-type regularization methods yield stable solutions and that particular implicit methods are very efficient in saving iteration steps

  14. Properties of a class of block-iterative methods

    International Nuclear Information System (INIS)

    Elfving, Tommy; Nikazad, Touraj

    2009-01-01

    We study a class of block-iterative (BI) methods proposed in image reconstruction for solving linear systems. A subclass, symmetric block-iteration (SBI), is derived such that for this subclass both semi-convergence analysis and stopping-rules developed for fully simultaneous iteration apply. Also results on asymptotic convergence are given, e.g., BI exhibit cyclic convergence irrespective of the consistency of the linear system. Further it is shown that the limit points of SBI satisfy a weighted least-squares problem. We also present numerical results obtained using a trained stopping rule on SBI

  15. On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

    Directory of Open Access Journals (Sweden)

    Xiaolong Qin

    2011-01-01

    Full Text Available An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

  16. New methods of testing nonlinear hypothesis using iterative NLLS estimator

    Science.gov (United States)

    Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

    2017-11-01

    This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

  17. An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation

    Directory of Open Access Journals (Sweden)

    Hakeem Ullah

    2014-01-01

    Full Text Available We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM. We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM and homotopy perturbation method (HPM solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

  18. Globally asymptotically stable analysis in a discrete time eco-epidemiological system

    International Nuclear Information System (INIS)

    Hu, Zengyun; Teng, Zhidong; Zhang, Tailei; Zhou, Qiming; Chen, Xi

    2017-01-01

    Highlights: • Dynamical behaviors of a discrete time eco-epidemiological system are discussed. • Global asymptotical stability of this system is obtained by an iteration scheme which can be expended to general dimensional discrete system. • More complex dynamical behaviors are obtained by numerical simulations. - Abstract: In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

  19. On Strong Convergence by the Hybrid Method for Equilibrium and Fixed Point Problems for an Inifnite Family of Asymptotically Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Cai Gang

    2009-01-01

    Full Text Available We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results announced by many others.

  20. Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

    Directory of Open Access Journals (Sweden)

    Gurucharan Singh Saluja

    2010-01-01

    Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.

  1. Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    E.U. Ofoedu

    2015-11-01

    Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$.  Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.

  2. Large Deviations and Asymptotic Methods in Finance

    CERN Document Server

    Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef

    2015-01-01

    Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...

  3. Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Juguo Su

    2012-01-01

    Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

  4. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

    Directory of Open Access Journals (Sweden)

    Marinca Vasile

    2017-10-01

    Full Text Available Dynamic response time is an important feature for determining the performance of magnetorheological (MR dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

  5. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

    Science.gov (United States)

    Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu

    2017-10-01

    Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

  6. A method for summing nonalternating asymptotic series

    International Nuclear Information System (INIS)

    Kazakov, D.I.

    1980-01-01

    A method for reconstructing a function from its nonalternating asymptotic series is proposed. It can also be applied when only a limited number of coefficients and their high order asymptotic behaviour are known. The method is illustrated by examples of the ordinary simple integral simulating a functional integral in a theory with degenerate minimum and of the double-well unharmonic oscillator

  7. Robust methods and asymptotic theory in nonlinear econometrics

    CERN Document Server

    Bierens, Herman J

    1981-01-01

    This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

  8. An iterative method for the canard explosion in general planar systems

    DEFF Research Database (Denmark)

    Brøns, Morten

    2013-01-01

    The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are a...... on the van der Pol equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system....... are also observed in systems where no such parameter can obviously be identied. Here we show how the iterative method of Roussel and Fraser, devised to construct regular slow manifolds, can be used to determine a canard point in a general planar system of nonlinear ODEs. We demonstrate the method...

  9. Asymptotic evolution of quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

    2012-07-01

    The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

  10. Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

    International Nuclear Information System (INIS)

    Pratiwi, B N; Suparmi, A; Cari, C; Yunianto, M; Husein, A S

    2016-01-01

    We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number n_r causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions. (paper)

  11. High frequency asymptotic methods

    International Nuclear Information System (INIS)

    Bouche, D.; Dessarce, R.; Gay, J.; Vermersch, S.

    1991-01-01

    The asymptotic methods allow us to compute the interaction of high frequency electromagnetic waves with structures. After an outline of their foundations with emphasis on the geometrical theory of diffraction, it is shown how to use these methods to evaluate the radar cross section (RCS) of complex tri-dimensional objects of great size compared to the wave-length. The different stages in simulating phenomena which contribute to the RCS are reviewed: physical theory of diffraction, multiple interactions computed by shooting rays, research for creeping rays. (author). 7 refs., 6 figs., 3 insets

  12. Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review

    Directory of Open Access Journals (Sweden)

    Mahmoud Bayat

    Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.

  13. Electromagnetic simulations of JET ICRF ITER-like antenna with TOPICA and SSWICH asymptotic codes

    Directory of Open Access Journals (Sweden)

    Křivská Alena

    2017-01-01

    Full Text Available Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF heating is routinely used in the JET tokamak. To increase the ICRF heating power available from the A2 antennas, the ICRF ITER-Like Antenna (ILA was reinstalled for the 2015 JET ITER-like wall experimental campaign. The application of high levels of ICRF power typically results in increased plasma wall interaction which leads to the observation of enhanced influx of metallic impurities in the plasma edge. It is assumed that the impurity production is mainly driven by the parallel component of the Radio-Frequency (RF antenna electric near-field, E// (parallel to the confinement magnetic field of the tokamak, that is rectified in a thin boundary layer (RF sheath. Torino Polytechnic Ion Cyclotron Antenna (TOPICA code was used to compute E// field maps in front of the ILA and between its poloidal limiters in the presence of plasma using measured density profiles and various antenna feedings. E// field maps calculated between the poloidal limiters were used to estimate the poloidal distribution of RF-sheath Direct Current (DC potential in this private region of the ILA and make relative comparison of various antenna electrical settings. For this purpose we used the asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating Slow-Wave (SSWICH-SW code. These estimations can help to study the formation of RF sheaths around the antenna and even at distant locations (∼3m away.

  14. Colorado Conference on iterative methods. Volume 1

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1994-12-31

    The conference provided a forum on many aspects of iterative methods. Volume I topics were:Session: domain decomposition, nonlinear problems, integral equations and inverse problems, eigenvalue problems, iterative software kernels. Volume II presents nonsymmetric solvers, parallel computation, theory of iterative methods, software and programming environment, ODE solvers, multigrid and multilevel methods, applications, robust iterative methods, preconditioners, Toeplitz and circulation solvers, and saddle point problems. Individual papers are indexed separately on the EDB.

  15. A note on iterated function systems with discontinuous probabilities

    International Nuclear Information System (INIS)

    Jaroszewska, Joanna

    2013-01-01

    Highlights: ► Certain iterated function system with discontinuous probabilities is discussed. ► Existence of an invariant measure via the Schauder–Tychonov theorem is established. ► Asymptotic stability of the system under examination is proved. -- Abstract: We consider an example of an iterated function system with discontinuous probabilities. We prove that it posses an invariant probability measure. We also prove that it is asymptotically stable provided probabilities are positive

  16. Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations

    Directory of Open Access Journals (Sweden)

    Bahman Ghazanfari

    2013-08-01

    Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.

  17. Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

    Science.gov (United States)

    Yi, Taishan; Chen, Yuming

    2017-12-01

    In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

  18. Asymptotic analysis of the Forward Search

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Bent

    The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made...

  19. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  20. Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Watcharaporn Cholamjiak

    2009-01-01

    Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.

  1. A multiscale asymptotic analysis of time evolution equations on the complex plane

    Energy Technology Data Exchange (ETDEWEB)

    Braga, Gastão A., E-mail: gbraga@mat.ufmg.br [Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG (Brazil); Conti, William R. P., E-mail: wrpconti@gmail.com [Departamento de Ciências do Mar, Universidade Federal de São Paulo, Rua Dr. Carvalho de Mendonça 144, 11070-100 Santos, SP (Brazil)

    2016-07-15

    Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.

  2. Asymptotic solving method for sea-air coupled oscillator ENSO model

    International Nuclear Information System (INIS)

    Zhou Xian-Chun; Yao Jing-Sun; Mo Jia-Qi

    2012-01-01

    The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction. In this article, we create an asymptotic solving method for the nonlinear system of the ENSO model. The asymptotic solution is obtained. And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO. (general)

  3. Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems

    Directory of Open Access Journals (Sweden)

    Lu-Chuan Ceng

    2014-01-01

    Full Text Available We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions.

  4. Milestones in the Development of Iterative Solution Methods

    Directory of Open Access Journals (Sweden)

    Owe Axelsson

    2010-01-01

    Full Text Available Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.

  5. The asymptotic expansion method via symbolic computation

    OpenAIRE

    Navarro, Juan F.

    2012-01-01

    This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

  6. Iterative Brinkman penalization for remeshed vortex methods

    DEFF Research Database (Denmark)

    Hejlesen, Mads Mølholm; Koumoutsakos, Petros; Leonard, Anthony

    2015-01-01

    We introduce an iterative Brinkman penalization method for the enforcement of the no-slip boundary condition in remeshed vortex methods. In the proposed method, the Brinkman penalization is applied iteratively only in the neighborhood of the body. This allows for using significantly larger time...

  7. A linear iterative unfolding method

    International Nuclear Information System (INIS)

    László, András

    2012-01-01

    A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of removing this smearing effect from the measured distribution is called unfolding, and is a delicate problem in signal processing, due to the well-known numerical ill behavior of this task. Various methods were invented which, given some assumptions on the initial probability distribution, try to regularize the unfolding problem. Most of these methods definitely introduce bias into the estimate of the initial probability distribution. We propose a linear iterative method (motivated by the Neumann series / Landweber iteration known in functional analysis), which has the advantage that no assumptions on the initial probability distribution is needed, and the only regularization parameter is the stopping order of the iteration, which can be used to choose the best compromise between the introduced bias and the propagated statistical and systematic errors. The method is consistent: 'binwise' convergence to the initial probability distribution is proved in absence of measurement errors under a quite general condition on the response function. This condition holds for practical applications such as convolutions, calorimeter response functions, momentum reconstruction response functions based on tracking in magnetic field etc. In presence of measurement errors, explicit formulae for the propagation of the three important error terms is provided: bias error (distance from the unknown to-be-reconstructed initial distribution at a finite iteration order), statistical error, and systematic error. A trade-off between these three error terms can be used to define an optimal iteration stopping criterion, and the errors can be estimated there. We provide a numerical C library for the implementation of the method, which incorporates automatic

  8. The Asymptotic Expansion Method via Symbolic Computation

    Directory of Open Access Journals (Sweden)

    Juan F. Navarro

    2012-01-01

    Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

  9. Selected asymptotic methods with applications to electromagnetics and antennas

    CERN Document Server

    Fikioris, George; Bakas, Odysseas N

    2013-01-01

    This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som

  10. New concurrent iterative methods with monotonic convergence

    Energy Technology Data Exchange (ETDEWEB)

    Yao, Qingchuan [Michigan State Univ., East Lansing, MI (United States)

    1996-12-31

    This paper proposes the new concurrent iterative methods without using any derivatives for finding all zeros of polynomials simultaneously. The new methods are of monotonic convergence for both simple and multiple real-zeros of polynomials and are quadratically convergent. The corresponding accelerated concurrent iterative methods are obtained too. The new methods are good candidates for the application in solving symmetric eigenproblems.

  11. Multi-Level iterative methods in computational plasma physics

    International Nuclear Information System (INIS)

    Knoll, D.A.; Barnes, D.C.; Brackbill, J.U.; Chacon, L.; Lapenta, G.

    1999-01-01

    Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD

  12. Multicore Performance of Block Algebraic Iterative Reconstruction Methods

    DEFF Research Database (Denmark)

    Sørensen, Hans Henrik B.; Hansen, Per Christian

    2014-01-01

    Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely on semiconv......Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely...... on semiconvergence. Block versions of these methods, based on a partitioning of the linear system, are able to combine the fast semiconvergence of ART with the better multicore properties of SIRT. These block methods separate into two classes: those that, in each iteration, access the blocks in a sequential manner...... a fixed relaxation parameter in each method, namely, the one that leads to the fastest semiconvergence. Computational results show that for multicore computers, the sequential approach is preferable....

  13. Various Newton-type iterative methods for solving nonlinear equations

    Directory of Open Access Journals (Sweden)

    Manoj Kumar

    2013-10-01

    Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.

  14. Probabilistic methods for physics

    International Nuclear Information System (INIS)

    Cirier, G

    2013-01-01

    We present an asymptotic method giving a probability of presence of the iterated spots of R d by a polynomial function f. We use the well-known Perron Frobenius operator (PF) that lets certain sets and measure invariant by f. Probabilistic solutions can exist for the deterministic iteration. If the theoretical result is already known, here we quantify these probabilities. This approach seems interesting to use for computing situations when the deterministic methods don't run. Among the examined applications, are asymptotic solutions of Lorenz, Navier-Stokes or Hamilton's equations. In this approach, linearity induces many difficult problems, all of whom we have not yet resolved.

  15. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

    2012-01-01

    Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

  16. Non-asymptotic fractional order differentiators via an algebraic parametric method

    KAUST Repository

    Liu, Dayan

    2012-08-01

    Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

  17. Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria

    Directory of Open Access Journals (Sweden)

    Lu-Chuan Ceng

    2014-01-01

    Full Text Available We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.

  18. Iterative Refinement Methods for Time-Domain Equalizer Design

    Directory of Open Access Journals (Sweden)

    Evans Brian L

    2006-01-01

    Full Text Available Commonly used time domain equalizer (TEQ design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread.

  19. Conformable variational iteration method

    Directory of Open Access Journals (Sweden)

    Omer Acan

    2017-02-01

    Full Text Available In this study, we introduce the conformable variational iteration method based on new defined fractional derivative called conformable fractional derivative. This new method is applied two fractional order ordinary differential equations. To see how the solutions of this method, linear homogeneous and non-linear non-homogeneous fractional ordinary differential equations are selected. Obtained results are compared the exact solutions and their graphics are plotted to demonstrate efficiency and accuracy of the method.

  20. Estimation of POL-iteration methods in fast running DNBR code

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Hyuk; Kim, S. J.; Seo, K. W.; Hwang, D. H. [KAERI, Daejeon (Korea, Republic of)

    2016-05-15

    In this study, various root finding methods are applied to the POL-iteration module in SCOMS and POLiteration efficiency is compared with reference method. On the base of these results, optimum algorithm of POL iteration is selected. The POL requires the iteration until present local power reach limit power. The process to search the limiting power is equivalent with a root finding of nonlinear equation. POL iteration process involved in online monitoring system used a variant bisection method that is the most robust algorithm to find the root of nonlinear equation. The method including the interval accelerating factor and escaping routine out of ill-posed condition assured the robustness of SCOMS system. POL iteration module in SCOMS shall satisfy the requirement which is a minimum calculation time. For this requirement of calculation time, non-iterative algorithm, few channel model, simple steam table are implemented into SCOMS to improve the calculation time. MDNBR evaluation at a given operating condition requires the DNBR calculation at all axial locations. An increasing of POL-iteration number increased a calculation load of SCOMS significantly. Therefore, calculation efficiency of SCOMS is strongly dependent on the POL iteration number. In case study, the iterations of the methods have a superlinear convergence for finding limiting power but Brent method shows a quardratic convergence speed. These methods are effective and better than the reference bisection algorithm.

  1. Asymptotics and Borel summability

    CERN Document Server

    Costin, Ovidiu

    2008-01-01

    Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us

  2. Quantum defect theory and asymptotic methods

    International Nuclear Information System (INIS)

    Seaton, M.J.

    1982-01-01

    It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)

  3. Advances in iterative methods for nonlinear equations

    CERN Document Server

    Busquier, Sonia

    2016-01-01

    This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...

  4. Iterative methods for weighted least-squares

    Energy Technology Data Exchange (ETDEWEB)

    Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)

    1996-12-31

    A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.

  5. Leapfrog variants of iterative methods for linear algebra equations

    Science.gov (United States)

    Saylor, Paul E.

    1988-01-01

    Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

  6. Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

    2001-01-01

    The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

  7. Iteration of ultrasound aberration correction methods

    Science.gov (United States)

    Maasoey, Svein-Erik; Angelsen, Bjoern; Varslot, Trond

    2004-05-01

    Aberration in ultrasound medical imaging is usually modeled by time-delay and amplitude variations concentrated on the transmitting/receiving array. This filter process is here denoted a TDA filter. The TDA filter is an approximation to the physical aberration process, which occurs over an extended part of the human body wall. Estimation of the TDA filter, and performing correction on transmit and receive, has proven difficult. It has yet to be shown that this method works adequately for severe aberration. Estimation of the TDA filter can be iterated by retransmitting a corrected signal and re-estimate until a convergence criterion is fulfilled (adaptive imaging). Two methods for estimating time-delay and amplitude variations in receive signals from random scatterers have been developed. One method correlates each element signal with a reference signal. The other method use eigenvalue decomposition of the receive cross-spectrum matrix, based upon a receive energy-maximizing criterion. Simulations of iterating aberration correction with a TDA filter have been investigated to study its convergence properties. A weak and strong human-body wall model generated aberration. Both emulated the human abdominal wall. Results after iteration improve aberration correction substantially, and both estimation methods converge, even for the case of strong aberration.

  8. Variational iteration method for one dimensional nonlinear thermoelasticity

    International Nuclear Information System (INIS)

    Sweilam, N.H.; Khader, M.M.

    2007-01-01

    This paper applies the variational iteration method to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity. The advantage of this method is to overcome the difficulty of calculation of Adomian's polynomials in the Adomian's decomposition method. The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that the variational iteration method is a powerful mathematical tool for solving nonlinear problems

  9. Asymptotic behaviour near extinction of continuous-state branching processes

    OpenAIRE

    Berzunza, Gabriel; Pardo, Juan Carlos

    2016-01-01

    In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a continuous state branching process whose branching mechanism satisfies a given condition and its reflected process at its infimum.

  10. An Iterative Brinkman penalization for particle vortex methods

    DEFF Research Database (Denmark)

    Walther, Jens Honore; Hejlesen, Mads Mølholm; Leonard, A.

    2013-01-01

    We present an iterative Brinkman penalization method for the enforcement of the no-slip boundary condition in vortex particle methods. This is achieved by implementing a penalization of the velocity field using iteration of the penalized vorticity. We show that using the conventional Brinkman...... condition. These are: the impulsively started flow past a cylinder, the impulsively started flow normal to a flat plate, and the uniformly accelerated flow normal to a flat plate. The iterative penalization algorithm is shown to give significantly improved results compared to the conventional penalization...

  11. Iterative Two- and One-Dimensional Methods for Three-Dimensional Neutron Diffusion Calculations

    International Nuclear Information System (INIS)

    Lee, Hyun Chul; Lee, Deokjung; Downar, Thomas J.

    2005-01-01

    Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications

  12. AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Saxild-Hansen, Maria

    2012-01-01

    We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are impleme......We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods...... are implemented: Algebraic Reconstruction Techniques (ART) and Simultaneous Iterative Reconstruction Techniques (SIRT). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter...

  13. A new non-iterative method for fitting Lorentzian to Moessbauer spectra

    International Nuclear Information System (INIS)

    Mukoyama, T.; Vegh, J.

    1980-01-01

    A new method for fitting a Lorentzian function without an iterative procedure is presented. The method is quicker and simpler than the previously proposed method of non-iterative fitting. Comparison with the previous method and with the conventional iterative method has been made. It is shown that the present method gives satisfactory results. (orig.)

  14. A comparison theorem for the SOR iterative method

    Science.gov (United States)

    Sun, Li-Ying

    2005-09-01

    In 1997, Kohno et al. have reported numerically that the improving modified Gauss-Seidel method, which was referred to as the IMGS method, is superior to the SOR iterative method. In this paper, we prove that the spectral radius of the IMGS method is smaller than that of the SOR method and Gauss-Seidel method, if the relaxation parameter [omega][set membership, variant](0,1]. As a result, we prove theoretically that this method is succeeded in improving the convergence of some classical iterative methods. Some recent results are improved.

  15. The danger of iteration methods

    International Nuclear Information System (INIS)

    Villain, J.; Semeria, B.

    1983-01-01

    When a Hamiltonian H depends on variables phisub(i), the values of these variables which minimize H satisfy the equations deltaH/deltaphisub(i) = O. If this set of equations is solved by iteration, there is no guarantee that the solution is the one which minimizes H. In the case of a harmonic system with a random potential periodic with respect to the phisub(i)'s, the fluctuations have been calculated by Efetov and Larkin by means of the iteration method. The result is wrong in the case of a strong disorder. Even in the weak disorder case, it is wrong for a one-dimensional system and for a finite system of 2 particles. It is argued that the results obtained by iteration are always wrong, and that between 2 and 4 dimensions, spin-pair correlation functions decay like powers of the distance, as found by Aharony and Pytte for another model

  16. AIR Tools II: algebraic iterative reconstruction methods, improved implementation

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Jørgensen, Jakob Sauer

    2017-01-01

    with algebraic iterative methods and their convergence properties. The present software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, we provide more flexible iterative methods, a column-action method...

  17. A transport synthetic acceleration method for transport iterations

    International Nuclear Information System (INIS)

    Ramone, G.L.; Adams, M.L.

    1997-01-01

    A family of transport synthetic acceleration (TSA) methods for iteratively solving within group scattering problems is presented. A single iteration in these schemes consists of a transport sweep followed by a low-order calculation, which itself is a simplified transport problem. The method for isotropic-scattering problems in X-Y geometry is described. The Fourier analysis of a model problem for equations with no spatial discretization shows that a previously proposed TSA method is unstable in two dimensions but that the modifications make it stable and rapidly convergent. The same procedure for discretized transport equations, using the step characteristic and two bilinear discontinuous methods, shows that discretization enhances TSA performance. A conjugate gradient algorithm for the low-order problem is described, a crude quadrature set for the low-order problem is proposed, and the number of low-order iterations per high-order sweep is limited to a relatively small value. These features lead to simple and efficient improvements to the method. TSA is tested on a series of problems, and a set of parameters is proposed for which the method behaves especially well. TSA achieves a substantial reduction in computational cost over source iteration, regardless of discretization parameters or material properties, and this reduction increases with the difficulty of the problem

  18. Iterative method for Amado's model

    International Nuclear Information System (INIS)

    Tomio, L.

    1980-01-01

    A recently proposed iterative method for solving scattering integral equations is applied to the spin doublet and spin quartet neutron-deuteron scattering in the Amado model. The method is tested numerically in the calculation of scattering lengths and phase-shifts and results are found better than those obtained by using the conventional Pade technique. (Author) [pt

  19. The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

    Directory of Open Access Journals (Sweden)

    Mehmet Tarik Atay

    2013-01-01

    Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

  20. Stopping test of iterative methods for solving PDE

    International Nuclear Information System (INIS)

    Wang Bangrong

    1991-01-01

    In order to assure the accuracy of the numerical solution of the iterative method for solving PDE (partial differential equation), the stopping test is very important. If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method for solving PDE is proposed. Several numerical examples are given to illustrate the applications of the stopping test formulas

  1. Iterative algorithm for the volume integral method for magnetostatics problems

    International Nuclear Information System (INIS)

    Pasciak, J.E.

    1980-11-01

    Volume integral methods for solving nonlinear magnetostatics problems are considered in this paper. The integral method is discretized by a Galerkin technique. Estimates are given which show that the linearized problems are well conditioned and hence easily solved using iterative techniques. Comparisons of iterative algorithms with the elimination method of GFUN3D shows that the iterative method gives an order of magnitude improvement in computational time as well as memory requirements for large problems. Computational experiments for a test problem as well as a double layer dipole magnet are given. Error estimates for the linearized problem are also derived

  2. Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

    Czech Academy of Sciences Publication Activity Database

    Morikuni, Keiichi; Hayami, K.

    2015-01-01

    Roč. 36, č. 1 (2015), s. 225-250 ISSN 0895-4798 Institutional support: RVO:67985807 Keywords : least squares problem * iterative methods * preconditioner * inner-outer iteration * GMRES method * stationary iterative method * rank-deficient problem Subject RIV: BA - General Mathematics Impact factor: 1.883, year: 2015

  3. Iterative approach as alternative to S-matrix in modal methods

    Science.gov (United States)

    Semenikhin, Igor; Zanuccoli, Mauro

    2014-12-01

    The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

  4. Extended asymptotic functions - some examples

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1981-01-01

    Several examples of extended asymptotic functions of two variables are given. This type of asymptotic functions has been introduced as an extension of continuous ordinary functions. The presented examples are realizations of some Schwartz distributions delta(x), THETA(x), P(1/xsup(n)) and can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. The examples illustrate the method of construction of extended asymptotic functions similar to the distributions. The set formed by the extended asymptotic functions is also considered. It is shown, that this set is not closed with respect to addition and multiplication

  5. Asymptotic Expansions - Methods and Applications

    International Nuclear Information System (INIS)

    Harlander, R.

    1999-01-01

    Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)

  6. Copper Mountain conference on iterative methods: Proceedings: Volume 2

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-10-01

    This volume (the second of two) contains information presented during the last two days of the Copper Mountain Conference on Iterative Methods held April 9-13, 1996 at Copper Mountain, Colorado. Topics of the sessions held these two days include domain decomposition, Krylov methods, computational fluid dynamics, Markov chains, sparse and parallel basic linear algebra subprograms, multigrid methods, applications of iterative methods, equation systems with multiple right-hand sides, projection methods, and the Helmholtz equation. Selected papers indexed separately for the Energy Science and Technology Database.

  7. Integral method for the calculation of Hawking radiation in dispersive media. II. Asymmetric asymptotics.

    Science.gov (United States)

    Robertson, Scott

    2014-11-01

    Analog gravity experiments make feasible the realization of black hole space-times in a laboratory setting and the observational verification of Hawking radiation. Since such analog systems are typically dominated by dispersion, efficient techniques for calculating the predicted Hawking spectrum in the presence of strong dispersion are required. In the preceding paper, an integral method in Fourier space is proposed for stationary 1+1-dimensional backgrounds which are asymptotically symmetric. Here, this method is generalized to backgrounds which are different in the asymptotic regions to the left and right of the scattering region.

  8. A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

    OpenAIRE

    Manton, Jonathan H.

    2012-01-01

    The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative m...

  9. Binary black hole initial data from matched asymptotic expansions

    International Nuclear Information System (INIS)

    Yunes, Nicolas; Owen, Benjamin J.; Tichy, Wolfgang; Bruegmann, Bernd

    2006-01-01

    We present an approximate metric for a binary black-hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally C ∞ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be straightforwardly iterated to obtain initial data to higher perturbative order

  10. Exponential asymptotics of homoclinic snaking

    International Nuclear Information System (INIS)

    Dean, A D; Matthews, P C; Cox, S M; King, J R

    2011-01-01

    We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319–54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement

  11. An iterative method for near-field Fresnel region polychromatic phase contrast imaging

    Science.gov (United States)

    Carroll, Aidan J.; van Riessen, Grant A.; Balaur, Eugeniu; Dolbnya, Igor P.; Tran, Giang N.; Peele, Andrew G.

    2017-07-01

    We present an iterative method for polychromatic phase contrast imaging that is suitable for broadband illumination and which allows for the quantitative determination of the thickness of an object given the refractive index of the sample material. Experimental and simulation results suggest the iterative method provides comparable image quality and quantitative object thickness determination when compared to the analytical polychromatic transport of intensity and contrast transfer function methods. The ability of the iterative method to work over a wider range of experimental conditions means the iterative method is a suitable candidate for use with polychromatic illumination and may deliver more utility for laboratory-based x-ray sources, which typically have a broad spectrum.

  12. Constructing Frozen Jacobian Iterative Methods for Solving Systems of Nonlinear Equations, Associated with ODEs and PDEs Using the Homotopy Method

    Directory of Open Access Journals (Sweden)

    Uswah Qasim

    2016-03-01

    Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.

  13. Asymptotic numbers, asymptotic functions and distributions

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1979-07-01

    The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)

  14. A fast iterative scheme for the linearized Boltzmann equation

    Science.gov (United States)

    Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

    2017-06-01

    Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

  15. A block-iterative nodal integral method for forced convection problems

    International Nuclear Information System (INIS)

    Decker, W.J.; Dorning, J.J.

    1992-01-01

    A new efficient iterative nodal integral method for the time-dependent two- and three-dimensional incompressible Navier-Stokes equations has been developed. Using the approach introduced by Azmy and Droning to develop nodal mehtods with high accuracy on coarse spatial grids for two-dimensional steady-state problems and extended to coarse two-dimensional space-time grids by Wilson et al. for thermal convection problems, we have developed a new iterative nodal integral method for the time-dependent Navier-Stokes equations for mechanically forced convection. A new, extremely efficient block iterative scheme is employed to invert the Jacobian within each of the Newton-Raphson iterations used to solve the final nonlinear discrete-variable equations. By taking advantage of the special structure of the Jacobian, this scheme greatly reduces memory requirements. The accuracy of the overall method is illustrated by appliying it to the time-dependent version of the classic two-dimensional driven cavity problem of computational fluid dynamics

  16. COMPARISON OF HOLOGRAPHIC AND ITERATIVE METHODS FOR AMPLITUDE OBJECT RECONSTRUCTION

    Directory of Open Access Journals (Sweden)

    I. A. Shevkunov

    2015-01-01

    Full Text Available Experimental comparison of four methods for the wavefront reconstruction is presented. We considered two iterative and two holographic methods with different mathematical models and algorithms for recovery. The first two of these methods do not use a reference wave recording scheme that reduces requirements for stability of the installation. A major role in phase information reconstruction by such methods is played by a set of spatial intensity distributions, which are recorded as the recording matrix is being moved along the optical axis. The obtained data are used consistently for wavefront reconstruction using an iterative procedure. In the course of this procedure numerical distribution of the wavefront between the planes is performed. Thus, phase information of the wavefront is stored in every plane and calculated amplitude distributions are replaced for the measured ones in these planes. In the first of the compared methods, a two-dimensional Fresnel transform and iterative calculation in the object plane are used as a mathematical model. In the second approach, an angular spectrum method is used for numerical wavefront propagation, and the iterative calculation is carried out only between closely located planes of data registration. Two digital holography methods, based on the usage of the reference wave in the recording scheme and differing from each other by numerical reconstruction algorithm of digital holograms, are compared with the first two methods. The comparison proved that the iterative method based on 2D Fresnel transform gives results comparable with the result of common holographic method with the Fourier-filtering. It is shown that holographic method for reconstructing of the object complex amplitude in the process of the object amplitude reduction is the best among considered ones.

  17. A hyperpower iterative method for computing the generalized Drazin ...

    Indian Academy of Sciences (India)

    A quadratically convergent Newton-type iterative scheme is proposed for approximating the generalized Drazin inverse bd of the Banach algebra element b. Further, its extension into the form of the hyperpower iterative method of arbitrary order p ≤ 2 is presented. Convergence criteria along with the estimation of error ...

  18. 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

  19. Natural Preconditioning and Iterative Methods for Saddle Point Systems

    KAUST Repository

    Pestana, Jennifer

    2015-01-01

    © 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.

  20. Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Larsen, Edward W.

    2004-01-01

    The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions

  1. Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

    International Nuclear Information System (INIS)

    McCormick, Stephen F.

    2016-01-01

    This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/

  2. Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

    Energy Technology Data Exchange (ETDEWEB)

    McCormick, Stephen F. [Front Range Scientific, Inc., Lake City, CO (United States)

    2016-03-25

    This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.

  3. Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation

    Directory of Open Access Journals (Sweden)

    Mohammad Hamarsheh

    2015-11-01

    Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.

  4. Asymptotic Method for Cladding Stress Evaluation in PCMI

    International Nuclear Information System (INIS)

    Kim, Hyungkyu; Kim, Jaeyong; Yoon, Kyungho; Lee, Kanghee; Kang, Heungseok

    2014-01-01

    A PCMI (Pellet Cladding Mechanical Interaction) failure was first reported in the GETR (General Electric Test Reactor) at Vacellitos in 1963, and such failures are still occurring. Since the high stress values in the cladding tube has been of a crucial concern in PCMI studies, there have been many researches on the stress analysis of a cladding tube pressed by a pellet. Typical works can be found in some references. It has often been assumed, however, that the cracks in the pellet were equally spaced and the pellet was a rigid body. In addition, the friction coefficient was arbitrarily chosen so that a slipping between the pellets and cladding tube could not be logically defined. Moreover, the stress intensification due to the sharp edge of a pellet fragment has never been realistically considered. These problems above drove us to launch a framework of a PCMI study particularly on stress analysis technology to improve the present analysis method incorporating the actual PCMI conditions such as the stress intensification, arbitrary distribution of the pellet cracks, material properties (esp. pellet) and slipping behavior of the pellet/cladding interface. As a first step of this work, this paper introduces an asymptotic method that was originally developed for a stress analysis in the vicinity of a sharp notch of a homogeneous body. The intrinsic reason for applying this method is to simulate the stress singularity that is expected to take place at the sharp edge of a pellet fragment due to cracking during irradiation. As a first attempt of this work, an eigenvalue problem is formulated in the case of adhered contact, and the generalized stress intensity factors are defined and evaluated. Although some works obviously remain to be accomplished, for the present framework on the PCMI analysis (e. g., slipping behaviour, contact force etc.), it was addressed that the asymptotic method can produce the stress values that cause the cladding tube failure in PCMI more

  5. Asymptotic structure of isolated systems

    International Nuclear Information System (INIS)

    Schmidt, B.G.

    1979-01-01

    The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)

  6. Asymptotic theory of two-dimensional trailing-edge flows

    Science.gov (United States)

    Melnik, R. E.; Chow, R.

    1975-01-01

    Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

  7. Asymptotic methods in mechanics of solids

    CERN Document Server

    Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi

    2015-01-01

    The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...

  8. Milestones in the Development of Iterative Solution Methods

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe

    2010-01-01

    Roč. 2010, - (2010), s. 1-33 ISSN 2090-0147 Institutional research plan: CEZ:AV0Z30860518 Keywords : iterative solution methods * convergence acceleration methods * linear systems Subject RIV: JC - Computer Hardware ; Software http://www.hindawi.com/journals/jece/2010/972794.html

  9. Iterative Regularization with Minimum-Residual Methods

    DEFF Research Database (Denmark)

    Jensen, Toke Koldborg; Hansen, Per Christian

    2007-01-01

    subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....

  10. Iterative regularization with minimum-residual methods

    DEFF Research Database (Denmark)

    Jensen, Toke Koldborg; Hansen, Per Christian

    2006-01-01

    subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES - their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....

  11. Strong Convergence to Common Fixed Points of a Countable Family of Asymptotically Strictly Quasi-ϕ-Pseudocontractions

    Directory of Open Access Journals (Sweden)

    Wei-Qi Deng

    2013-01-01

    Full Text Available Based on an original idea, namely, a specific way of choosing the indexes of the involved mappings, we propose a new hybrid shrinking iteration scheme for approximating some common fixed points of a countable family of asymptotically strictly quasi-ϕ-pseudocontractions and obtain a strong convergence theorem in the framework of Banach space. Our result extends other authors, related results existing in the current literature. As application, an iterative solution to a system of equilibrium problems is provided.

  12. Cluster monte carlo method for nuclear criticality safety calculation

    International Nuclear Information System (INIS)

    Pei Lucheng

    1984-01-01

    One of the most important applications of the Monte Carlo method is the calculation of the nuclear criticality safety. The fair source game problem was presented at almost the same time as the Monte Carlo method was applied to calculating the nuclear criticality safety. The source iteration cost may be reduced as much as possible or no need for any source iteration. This kind of problems all belongs to the fair source game prolems, among which, the optimal source game is without any source iteration. Although the single neutron Monte Carlo method solved the problem without the source iteration, there is still quite an apparent shortcoming in it, that is, it solves the problem without the source iteration only in the asymptotic sense. In this work, a new Monte Carlo method called the cluster Monte Carlo method is given to solve the problem further

  13. Preconditioning of iterative methods - theory and applications

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Blaheta, Radim; Neytcheva, M.; Pultarová, I.

    2015-01-01

    Roč. 22, č. 6 (2015), s. 901-902 ISSN 1070-5325 Institutional support: RVO:68145535 Keywords : preconditioning * iterative methods * applications Subject RIV: BA - General Mathematics Impact factor: 1.431, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/nla.2016/epdf

  14. Asymptotic analysis and boundary layers

    CERN Document Server

    Cousteix, Jean

    2007-01-01

    This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...

  15. Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

    Directory of Open Access Journals (Sweden)

    Muhammad Aslam Noor

    2008-01-01

    Full Text Available We apply the variational iteration method using He's polynomials (VIMHP for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

  16. Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”

    Directory of Open Access Journals (Sweden)

    Ji-Huan He

    2012-01-01

    boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.

  17. NUMERICAL WITHOUT ITERATION METHOD OF MODELING OF ELECTROMECHANICAL PROCESSES IN ASYNCHRONOUS ENGINES

    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.

  18. Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems

    Directory of Open Access Journals (Sweden)

    Oskar Cahueñas

    2013-05-01

    Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.

  19. On varitional iteration method for fractional calculus

    Directory of Open Access Journals (Sweden)

    Wu Hai-Gen

    2017-01-01

    Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.

  20. Workshop on Analytical Methods in Statistics

    CERN Document Server

    Jurečková, Jana; Maciak, Matúš; Pešta, Michal

    2017-01-01

    This volume collects authoritative contributions on analytical methods and mathematical statistics. The methods presented include resampling techniques; the minimization of divergence; estimation theory and regression, eventually under shape or other constraints or long memory; and iterative approximations when the optimal solution is difficult to achieve. It also investigates probability distributions with respect to their stability, heavy-tailness, Fisher information and other aspects, both asymptotically and non-asymptotically. The book not only presents the latest mathematical and statistical methods and their extensions, but also offers solutions to real-world problems including option pricing. The selected, peer-reviewed contributions were originally presented at the workshop on Analytical Methods in Statistics, AMISTAT 2015, held in Prague, Czech Republic, November 10-13, 2015.

  1. Probabilistic finite element stiffness of a laterally loaded monopile based on an improved asymptotic sampling method

    DEFF Research Database (Denmark)

    Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard

    2015-01-01

    shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates......The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....

  2. On iteration-separable method on the multichannel scattering theory

    International Nuclear Information System (INIS)

    Zubarev, A.L.; Ivlieva, I.N.; Podkopaev, A.P.

    1975-01-01

    The iteration-separable method for solving the equations of the Lippman-Schwinger type is suggested. Exponential convergency of the method of proven. Numerical convergency is clarified on the e + H scattering. Application of the method to the theory of multichannel scattering is formulated

  3. Numerov iteration method for second order integral-differential equation

    International Nuclear Information System (INIS)

    Zeng Fanan; Zhang Jiaju; Zhao Xuan

    1987-01-01

    In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics

  4. Asymptotic integration of differential and difference equations

    CERN Document Server

    Bodine, Sigrun

    2015-01-01

    This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...

  5. Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems

    Science.gov (United States)

    Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding

    2007-09-01

    In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.

  6. Discounted Markov games : generalized policy iteration method

    NARCIS (Netherlands)

    Wal, van der J.

    1978-01-01

    In this paper, we consider two-person zero-sum discounted Markov games with finite state and action spaces. We show that the Newton-Raphson or policy iteration method as presented by Pollats-chek and Avi-Itzhak does not necessarily converge, contradicting a proof of Rao, Chandrasekaran, and Nair.

  7. Iterative method of the parameter variation for solution of nonlinear functional equations

    International Nuclear Information System (INIS)

    Davidenko, D.F.

    1975-01-01

    The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

  8. Optimized iterative decoding method for TPC coded CPM

    Science.gov (United States)

    Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei

    2018-05-01

    Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.

  9. An iterative method for determination of a minimal eigenvalue

    DEFF Research Database (Denmark)

    Kristiansen, G.K.

    1968-01-01

    Kristiansen (1963) has discussed the convergence of a group of iterative methods (denoted the Equipoise methods) for the solution of reactor criticality problems. The main result was that even though the methods are said to work satisfactorily in all practical cases, examples of divergence can be...

  10. Fields Institute International Symposium on Asymptotic Methods in Stochastics

    CERN Document Server

    Kulik, Rafal; Haye, Mohamedou; Szyszkowicz, Barbara; Zhao, Yiqiang

    2015-01-01

    This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.

  11. Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Shenghua Wang

    2013-01-01

    Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.

  12. Asymptotic stability of a catalyst particle

    DEFF Research Database (Denmark)

    Wedel, Stig; Michelsen, Michael L.; Villadsen, John

    1977-01-01

    The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...

  13. Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

    Science.gov (United States)

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

  14. Projection-iteration methods for solving nonlinear operator equations

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

    1989-09-01

    In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

  15. Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

    Directory of Open Access Journals (Sweden)

    Okan Ozer

    2013-01-01

    Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

  16. Perils of Asymptotics

    International Nuclear Information System (INIS)

    Dewar, R. L.

    1995-01-01

    A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs

  17. An asymptotic preserving multidimensional ALE method for a system of two compressible flows coupled with friction

    Science.gov (United States)

    Del Pino, S.; Labourasse, E.; Morel, G.

    2018-06-01

    We present a multidimensional asymptotic preserving scheme for the approximation of a mixture of compressible flows. Fluids are modelled by two Euler systems of equations coupled with a friction term. The asymptotic preserving property is mandatory for this kind of model, to derive a scheme that behaves well in all regimes (i.e. whatever the friction parameter value is). The method we propose is defined in ALE coordinates, using a Lagrange plus remap approach. This imposes a multidimensional definition and analysis of the scheme.

  18. Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Yuan Li

    2013-01-01

    Full Text Available This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.

  19. Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

    Directory of Open Access Journals (Sweden)

    Yichao Gao

    2011-01-01

    Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

  20. Krylov iterative methods and synthetic acceleration for transport in binary statistical media

    International Nuclear Information System (INIS)

    Fichtl, Erin D.; Warsa, James S.; Prinja, Anil K.

    2009-01-01

    In particle transport applications there are numerous physical constructs in which heterogeneities are randomly distributed. The quantity of interest in these problems is the ensemble average of the flux, or the average of the flux over all possible material 'realizations.' The Levermore-Pomraning closure assumes Markovian mixing statistics and allows a closed, coupled system of equations to be written for the ensemble averages of the flux in each material. Generally, binary statistical mixtures are considered in which there are two (homogeneous) materials and corresponding coupled equations. The solution process is iterative, but convergence may be slow as either or both materials approach the diffusion and/or atomic mix limits. A three-part acceleration scheme is devised to expedite convergence, particularly in the atomic mix-diffusion limit where computation is extremely slow. The iteration is first divided into a series of 'inner' material and source iterations to attenuate the diffusion and atomic mix error modes separately. Secondly, atomic mix synthetic acceleration is applied to the inner material iteration and S 2 synthetic acceleration to the inner source iterations to offset the cost of doing several inner iterations per outer iteration. Finally, a Krylov iterative solver is wrapped around each iteration, inner and outer, to further expedite convergence. A spectral analysis is conducted and iteration counts and computing cost for the new two-step scheme are compared against those for a simple one-step iteration, to which a Krylov iterative method can also be applied.

  1. Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription

    Directory of Open Access Journals (Sweden)

    Humin Lei

    2017-01-01

    Full Text Available An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.

  2. Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

    Science.gov (United States)

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

  3. Iterative and range test methods for an inverse source problem for acoustic waves

    International Nuclear Information System (INIS)

    Alves, Carlos; Kress, Rainer; Serranho, Pedro

    2009-01-01

    We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples

  4. Variable aperture-based ptychographical iterative engine method

    Science.gov (United States)

    Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

    2018-02-01

    A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches.

  5. Iterative methods for tomography problems: implementation to a cross-well tomography problem

    Science.gov (United States)

    Karadeniz, M. F.; Weber, G. W.

    2018-01-01

    The velocity distribution between two boreholes is reconstructed by cross-well tomography, which is commonly used in geology. In this paper, iterative methods, Kaczmarz’s algorithm, algebraic reconstruction technique (ART), and simultaneous iterative reconstruction technique (SIRT), are implemented to a specific cross-well tomography problem. Convergence to the solution of these methods and their CPU time for the cross-well tomography problem are compared. Furthermore, these three methods for this problem are compared for different tolerance values.

  6. Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery

    Directory of Open Access Journals (Sweden)

    Lingjun Liu

    2017-01-01

    Full Text Available This paper presents a variant of the iterative shrinkage-thresholding (IST algorithm, called backtracking-based adaptive IST (BAIST, for image compressive sensing (CS reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the BAIST method backtracks to the previous noisy image using L2 norm minimization, i.e., minimizing the Euclidean distance between the current solution and the previous ones. Through this modification, the BAIST method achieves superior performance while maintaining the low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive regularizor to automatically detect the sparsity level of an image. Experimental results show that our algorithm outperforms the original IST method and several excellent CS techniques.

  7. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  8. Iterated interactions method. Realistic NN potential

    International Nuclear Information System (INIS)

    Gorbatov, A.M.; Skopich, V.L.; Kolganova, E.A.

    1991-01-01

    The method of iterated potential is tested in the case of realistic fermionic systems. As a base for comparison calculations of the 16 O system (using various versions of realistic NN potentials) by means of the angular potential-function method as well as operators of pairing correlation were used. The convergence of genealogical series is studied for the central Malfliet-Tjon potential. In addition the mathematical technique of microscopical calculations is improved: new equations for correlators in odd states are suggested and the technique of leading terms was applied for the first time to calculations of heavy p-shell nuclei in the basis of angular potential functions

  9. Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

    Directory of Open Access Journals (Sweden)

    Eman M. A. Hilal

    2014-01-01

    Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.

  10. An Automated Baseline Correction Method Based on Iterative Morphological Operations.

    Science.gov (United States)

    Chen, Yunliang; Dai, Liankui

    2018-05-01

    Raman spectra usually suffer from baseline drift caused by fluorescence or other reasons. Therefore, baseline correction is a necessary and crucial step that must be performed before subsequent processing and analysis of Raman spectra. An automated baseline correction method based on iterative morphological operations is proposed in this work. The method can adaptively determine the structuring element first and then gradually remove the spectral peaks during iteration to get an estimated baseline. Experiments on simulated data and real-world Raman data show that the proposed method is accurate, fast, and flexible for handling different kinds of baselines in various practical situations. The comparison of the proposed method with some state-of-the-art baseline correction methods demonstrates its advantages over the existing methods in terms of accuracy, adaptability, and flexibility. Although only Raman spectra are investigated in this paper, the proposed method is hopefully to be used for the baseline correction of other analytical instrumental signals, such as IR spectra and chromatograms.

  11. Three dimensional iterative beam propagation method for optical waveguide devices

    Science.gov (United States)

    Ma, Changbao; Van Keuren, Edward

    2006-10-01

    The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

  12. Variation Iteration Method for The Approximate Solution of Nonlinear ...

    African Journals Online (AJOL)

    In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...

  13. SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

    International Nuclear Information System (INIS)

    Wu, P; Mao, T; Gong, S; Wang, J; Niu, T; Sheng, K; Xie, Y

    2016-01-01

    Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R

  14. SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

    Energy Technology Data Exchange (ETDEWEB)

    Wu, P; Mao, T; Gong, S; Wang, J; Niu, T [Sir Run Run Shaw Hospital, Zhejiang University School of Medicine, Institute of Translational Medicine, Zhejiang University, Hangzhou, Zhejiang (China); Sheng, K [Department of Radiation Oncology, University of California, Los Angeles, Los Angeles, CA (United States); Xie, Y [Institute of Biomedical and Health Engineering, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong (China)

    2016-06-15

    Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R

  15. Variable aperture-based ptychographical iterative engine method.

    Science.gov (United States)

    Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

    2018-02-01

    A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

  16. A New Iterative Method for Equilibrium Problems and Fixed Point Problems

    Directory of Open Access Journals (Sweden)

    Abdul Latif

    2013-01-01

    Full Text Available Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012, Cianciaruso et al. (2010, and many others.

  17. Quasi-extended asymptotic functions

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1979-01-01

    The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta 2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example

  18. Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

    Directory of Open Access Journals (Sweden)

    Mohammad Almousa

    2013-01-01

    Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.

  19. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  20. An asymptotic expression for the eigenvalues of the normalization kernel of the resonating group method

    International Nuclear Information System (INIS)

    Lomnitz-Adler, J.; Brink, D.M.

    1976-01-01

    A generating function for the eigenvalues of the RGM Normalization Kernel is expressed in terms of the diagonal matrix elements of thw GCM Overlap Kernel. An asymptotic expression for the eigenvalues is obtained by using the Method of Steepest Descent. (Auth.)

  1. Parallel computation of multigroup reactivity coefficient using iterative method

    Science.gov (United States)

    Susmikanti, Mike; Dewayatna, Winter

    2013-09-01

    One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium.

  2. Comments on new iterative methods for solving linear systems

    Directory of Open Access Journals (Sweden)

    Wang Ke

    2017-06-01

    Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.

  3. A fast method to emulate an iterative POCS image reconstruction algorithm.

    Science.gov (United States)

    Zeng, Gengsheng L

    2017-10-01

    Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

  4. Asymptotic expansion of the Keesom integral

    International Nuclear Information System (INIS)

    Abbott, Paul C

    2007-01-01

    The asymptotic evaluation and expansion of the Keesom integral, K(a), is discussed at some length in Battezzati and Magnasco (2004 J. Phys. A: Math. Gen. 37 9677; 2005 J. Phys. A: Math. Gen. 38 6715). Here, using standard identities, it is shown that this triple integral can be reduced to a single integral from which the asymptotic behaviour is readily obtained using Laplace's method. (comment)

  5. Application of the perturbation iteration method to boundary layer type problems.

    Science.gov (United States)

    Pakdemirli, Mehmet

    2016-01-01

    The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

  6. Iterative Methods for the Non-LTE Transfer of Polarized Radiation: Resonance Line Polarization in One-dimensional Atmospheres

    Science.gov (United States)

    Trujillo Bueno, Javier; Manso Sainz, Rafael

    1999-05-01

    This paper shows how to generalize to non-LTE polarization transfer some operator splitting methods that were originally developed for solving unpolarized transfer problems. These are the Jacobi-based accelerated Λ-iteration (ALI) method of Olson, Auer, & Buchler and the iterative schemes based on Gauss-Seidel and successive overrelaxation (SOR) iteration of Trujillo Bueno and Fabiani Bendicho. The theoretical framework chosen for the formulation of polarization transfer problems is the quantum electrodynamics (QED) theory of Landi Degl'Innocenti, which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. This first paper establishes the grounds of our numerical approach to non-LTE polarization transfer by concentrating on the standard case of scattering line polarization in a gas of two-level atoms, including the Hanle effect due to a weak microturbulent and isotropic magnetic field. We begin demonstrating that the well-known Λ-iteration method leads to the self-consistent solution of this type of problem if one initializes using the ``exact'' solution corresponding to the unpolarized case. We show then how the above-mentioned splitting methods can be easily derived from this simple Λ-iteration scheme. We show that our SOR method is 10 times faster than the Jacobi-based ALI method, while our implementation of the Gauss-Seidel method is 4 times faster. These iterative schemes lead to the self-consistent solution independently of the chosen initialization. The convergence rate of these iterative methods is very high; they do not require either the construction or the inversion of any matrix, and the computing time per iteration is similar to that of the Λ-iteration method.

  7. ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

    Directory of Open Access Journals (Sweden)

    Kuzmina Ludmila Ivanovna

    2017-11-01

    Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

  8. Asymptotic work distributions in driven bistable systems

    International Nuclear Information System (INIS)

    Nickelsen, D; Engel, A

    2012-01-01

    The asymptotic tails of the probability distributions of thermodynamic quantities convey important information about the physics of nanoscopic systems driven out of equilibrium. We apply a recently proposed method to analytically determine the asymptotics of work distributions in Langevin systems to an one-dimensional model of single-molecule force spectroscopy. The results are in excellent agreement with numerical simulations, even in the centre of the distributions. We compare our findings with a recent proposal for an universal form of the asymptotics of work distributions in single-molecule experiments.

  9. Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models

    KAUST Repository

    Elsheikh, Ahmed H.

    2013-06-01

    A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.

  10. Revisiting r > g-The asymptotic dynamics of wealth inequality

    Science.gov (United States)

    Berman, Yonatan; Shapira, Yoash

    2017-02-01

    Studying the underlying mechanisms of wealth inequality dynamics is essential for its understanding and for policy aiming to regulate its level. We apply a heterogeneous non-interacting agent-based modeling approach, solved using iterated maps to model the dynamics of wealth inequality based on 3 parameters-the economic output growth rate g, the capital value change rate a and the personal savings rate s and show that for a income distribution. If a > g, the wealth distribution constantly becomes more and more inegalitarian. We also show that when a economic output, which also implies that the wealth-disposable income ratio asymptotically converges to s /(g - a) .

  11. Numerical Asymptotic Solutions Of Differential Equations

    Science.gov (United States)

    Thurston, Gaylen A.

    1992-01-01

    Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

  12. Iterative reconstruction methods for Thermo-acoustic Tomography

    International Nuclear Information System (INIS)

    Marinesque, Sebastien

    2012-01-01

    We define, study and implement various iterative reconstruction methods for Thermo-acoustic Tomography (TAT): the Back and Forth Nudging (BFN), easy to implement and to use, a variational technique (VT) and the Back and Forth SEEK (BF-SEEK), more sophisticated, and a coupling method between Kalman filter (KF) and Time Reversal (TR). A unified formulation is explained for the sequential techniques aforementioned that defines a new class of inverse problem methods: the Back and Forth Filters (BFF). In addition to existence and uniqueness (particularly for backward solutions), we study many frameworks that ensure and characterize the convergence of the algorithms. Thus we give a general theoretical framework for which the BFN is a well-posed problem. Then, in application to TAT, existence and uniqueness of its solutions and geometrical convergence of the algorithm are proved, and an explicit convergence rate and a description of its numerical behaviour are given. Next, theoretical and numerical studies of more general and realistic framework are led, namely different objects, speeds (with or without trapping), various sensor configurations and samplings, attenuated equations or external sources. Then optimal control and best estimate tools are used to characterize the BFN convergence and converging feedbacks for BFF, under observability assumptions. Finally, we compare the most flexible and efficient current techniques (TR and an iterative variant) with our various BFF and the VT in several experiments. Thus, robust, with different possible complexities and flexible, the methods that we propose are very interesting reconstruction techniques, particularly in TAT and when observations are degraded. (author) [fr

  13. A Nonmonotone Trust Region Method for Nonlinear Programming with Simple Bound Constraints

    International Nuclear Information System (INIS)

    Chen, Z.-W.; Han, J.-Y.; Xu, D.-C.

    2001-01-01

    In this paper we propose a nonmonotone trust region algorithm for optimization with simple bound constraints. Under mild conditions, we prove the global convergence of the algorithm. For the monotone case it is also proved that the correct active set can be identified in a finite number of iterations if the strict complementarity slackness condition holds, and so the proposed algorithm reduces finally to an unconstrained minimization method in a finite number of iterations, allowing a fast asymptotic rate of convergence. Numerical experiments show that the method is efficient

  14. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST

  15. Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods

    DEFF Research Database (Denmark)

    Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.

    2010-01-01

    In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...

  16. Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

    Directory of Open Access Journals (Sweden)

    Wu Guo-Cheng

    2012-01-01

    Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

  17. Iterative resonance self-shielding methods using resonance integral table in heterogeneous transport lattice calculations

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Kim, Kang-Seog

    2011-01-01

    This paper describes the iteration methods using resonance integral tables to estimate the effective resonance cross sections in heterogeneous transport lattice calculations. Basically, these methods have been devised to reduce an effort to convert resonance integral table into subgroup data to be used in the physical subgroup method. Since these methods do not use subgroup data but only use resonance integral tables directly, these methods do not include an error in converting resonance integral into subgroup data. The effective resonance cross sections are estimated iteratively for each resonance nuclide through the heterogeneous fixed source calculations for the whole problem domain to obtain the background cross sections. These methods have been implemented in the transport lattice code KARMA which uses the method of characteristics (MOC) to solve the transport equation. The computational results show that these iteration methods are quite promising in the practical transport lattice calculations.

  18. An iterative method for selecting degenerate multiplex PCR primers.

    Science.gov (United States)

    Souvenir, Richard; Buhler, Jeremy; Stormo, Gary; Zhang, Weixiong

    2007-01-01

    Single-nucleotide polymorphism (SNP) genotyping is an important molecular genetics process, which can produce results that will be useful in the medical field. Because of inherent complexities in DNA manipulation and analysis, many different methods have been proposed for a standard assay. One of the proposed techniques for performing SNP genotyping requires amplifying regions of DNA surrounding a large number of SNP loci. To automate a portion of this particular method, it is necessary to select a set of primers for the experiment. Selecting these primers can be formulated as the Multiple Degenerate Primer Design (MDPD) problem. The Multiple, Iterative Primer Selector (MIPS) is an iterative beam-search algorithm for MDPD. Theoretical and experimental analyses show that this algorithm performs well compared with the limits of degenerate primer design. Furthermore, MIPS outperforms an existing algorithm that was designed for a related degenerate primer selection problem.

  19. Formulations to overcome the divergence of iterative method of fixed-point in nonlinear equations solution

    Directory of Open Access Journals (Sweden)

    Wilson Rodríguez Calderón

    2015-04-01

    Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.

  20. A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data

    KAUST Repository

    Liang, Faming

    2013-03-01

    The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation. Since the proposed method makes use of only a small proportion of the data at each iteration, it avoids inverting large covariance matrices and thus is scalable to large datasets. The proposed method also leads to a general parameter estimation approach, maximum mean log-likelihood estimation, which includes the popular maximum (log)-likelihood estimation (MLE) approach as a special case and is expected to play an important role in analyzing large datasets. Under mild conditions, it is shown that the estimator resulting from the proposed method converges in probability to a set of parameter values of equivalent Gaussian probability measures, and that the estimator is asymptotically normally distributed. To the best of the authors\\' knowledge, the present study is the first one on asymptotic normality under infill asymptotics for general covariance functions. The proposed method is illustrated with large datasets, both simulated and real. Supplementary materials for this article are available online. © 2013 American Statistical Association.

  1. Contribution to regularizing iterative method development for attenuation correction in gamma emission tomography

    International Nuclear Information System (INIS)

    Cao, A.

    1981-07-01

    This study is concerned with the transverse axial gamma emission tomography. The problem of self-attenuation of radiations in biologic tissues is raised. The regularizing iterative method is developed, as a reconstruction method of 3 dimensional images. The different steps from acquisition to results, necessary to its application, are described. Organigrams relative to each step are explained. Comparison notion between two reconstruction methods is introduced. Some methods used for the comparison or to bring about the characteristics of a reconstruction technique are defined. The studies realized to test the regularizing iterative method are presented and results are analyzed [fr

  2. Numerical algorithms for uniform Airy-type asymptotic expansions

    NARCIS (Netherlands)

    N.M. Temme (Nico)

    1997-01-01

    textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing

  3. Plasma flow to a surface using the iterative Monte Carlo method

    International Nuclear Information System (INIS)

    Pitcher, C.S.

    1994-01-01

    The iterative Monte Carlo (IMC) method is applied to a number of one-dimensional plasma flow problems, which encompass a wide range of conditions typical of those present in the boundary of magnetic fusion devices. The kinetic IMC method of solving plasma flow to a surface consists of launching and following particles within a grid of 'bins' into which weights are left according to the time a particle spends within a bin. The density and potential distributions within the plasma are iterated until the final solution is arrived at. The IMC results are compared with analytical treatments of these problems and, in general, good agreement is obtained. (author)

  4. Conformal mapping and convergence of Krylov iterations

    Energy Technology Data Exchange (ETDEWEB)

    Driscoll, T.A.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

    1994-12-31

    Connections between conformal mapping and matrix iterations have been known for many years. The idea underlying these connections is as follows. Suppose the spectrum of a matrix or operator A is contained in a Jordan region E in the complex plane with 0 not an element of E. Let {phi}(z) denote a conformal map of the exterior of E onto the exterior of the unit disk, with {phi}{infinity} = {infinity}. Then 1/{vert_bar}{phi}(0){vert_bar} is an upper bound for the optimal asymptotic convergence factor of any Krylov subspace iteration. This idea can be made precise in various ways, depending on the matrix iterations, on whether A is finite or infinite dimensional, and on what bounds are assumed on the non-normality of A. This paper explores these connections for a variety of matrix examples, making use of a new MATLAB Schwarz-Christoffel Mapping Toolbox developed by the first author. Unlike the earlier Fortran Schwarz-Christoffel package SCPACK, the new toolbox computes exterior as well as interior Schwarz-Christoffel maps, making it easy to experiment with spectra that are not necessarily symmetric about an axis.

  5. Detailed Design and Fabrication Method of the ITER Vacuum Vessel Ports

    International Nuclear Information System (INIS)

    Hee-Jae Ahn; Kwon, T.H.; Hong, Y.S.

    2006-01-01

    The engineering design of the ITER vacuum vessel (VV) has been progressed by the ITER International Team (IT) with the cooperation of several participant teams (PT). The VV and ports are the components allocated to Korea for the construction of the ITER. Hyundai Heavy Industries has been involved in the structural analysis, detailed design and development of the fabrication method of the upper and lower ports within the framework of the ITER transitional arrangements (ITA). The design of the port structures has been investigated to validate and to improve the conceptual designs of the ITER IT and other PT. The special emphasis was laid on the flange joint between the port extension and the in-port plug to develop the design of the upper port. The modified design with a pure friction type flange with forty-eight pieces of bolts instead of the tangential key is recommended. Furthermore, the alternative flange designs developed by the ITER IT have been analyzed in detail to simplify the lip seal maintenance into the port flange. The structural analyses of the lower RH port have been also performed to verify the capacity for supporting the VV. The maximum stress exceeds the allowable value at the reinforcing block and basement. More elaborate local models have been developed to mitigate the stress concentration and to modify the component design. The fabrication method and the sequence of the detailed fabrication for the ports are developed focusing on the cost reduction as well as the simplification. A typical port structure includes a port stub, a stub extension and a port extension with a connecting duct. The fabrication sequence consists of surface treatment, cutting, forming, cleaning, welding, machining, and non-destructive inspection and test. Tolerance study has been performed to avoid the mismatch of each fabricated component and to obtain the suitable tolerances in the assembly at the shop and site. This study is based on the experience in the fabrication of

  6. Reducing the effects of acoustic heterogeneity with an iterative reconstruction method from experimental data in microwave induced thermoacoustic tomography

    International Nuclear Information System (INIS)

    Wang, Jinguo; Zhao, Zhiqin; Song, Jian; Chen, Guoping; Nie, Zaiping; Liu, Qing-Huo

    2015-01-01

    Purpose: An iterative reconstruction method has been previously reported by the authors of this paper. However, the iterative reconstruction method was demonstrated by solely using the numerical simulations. It is essential to apply the iterative reconstruction method to practice conditions. The objective of this work is to validate the capability of the iterative reconstruction method for reducing the effects of acoustic heterogeneity with the experimental data in microwave induced thermoacoustic tomography. Methods: Most existing reconstruction methods need to combine the ultrasonic measurement technology to quantitatively measure the velocity distribution of heterogeneity, which increases the system complexity. Different to existing reconstruction methods, the iterative reconstruction method combines time reversal mirror technique, fast marching method, and simultaneous algebraic reconstruction technique to iteratively estimate the velocity distribution of heterogeneous tissue by solely using the measured data. Then, the estimated velocity distribution is used subsequently to reconstruct the highly accurate image of microwave absorption distribution. Experiments that a target placed in an acoustic heterogeneous environment are performed to validate the iterative reconstruction method. Results: By using the estimated velocity distribution, the target in an acoustic heterogeneous environment can be reconstructed with better shape and higher image contrast than targets that are reconstructed with a homogeneous velocity distribution. Conclusions: The distortions caused by the acoustic heterogeneity can be efficiently corrected by utilizing the velocity distribution estimated by the iterative reconstruction method. The advantage of the iterative reconstruction method over the existing correction methods is that it is successful in improving the quality of the image of microwave absorption distribution without increasing the system complexity

  7. Iterative methods for photoacoustic tomography in attenuating acoustic media

    Science.gov (United States)

    Haltmeier, Markus; Kowar, Richard; Nguyen, Linh V.

    2017-11-01

    The development of efficient and accurate reconstruction methods is an important aspect of tomographic imaging. In this article, we address this issue for photoacoustic tomography. To this aim, we use models for acoustic wave propagation accounting for frequency dependent attenuation according to a wide class of attenuation laws that may include memory. We formulate the inverse problem of photoacoustic tomography in attenuating medium as an ill-posed operator equation in a Hilbert space framework that is tackled by iterative regularization methods. Our approach comes with a clear convergence analysis. For that purpose we derive explicit expressions for the adjoint problem that can efficiently be implemented. In contrast to time reversal, the employed adjoint wave equation is again damping and, thus has a stable solution. This stability property can be clearly seen in our numerical results. Moreover, the presented numerical results clearly demonstrate the efficiency and accuracy of the derived iterative reconstruction algorithms in various situations including the limited view case.

  8. On a new iterative method for solving linear systems and comparison results

    Science.gov (United States)

    Jing, Yan-Fei; Huang, Ting-Zhu

    2008-10-01

    In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

  9. Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in -Uniformly Smooth and Strictly Convex Banach Spaces

    Directory of Open Access Journals (Sweden)

    Meng Wen

    2012-01-01

    Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

  10. Computation of saddle-type slow manifolds using iterative methods

    DEFF Research Database (Denmark)

    Kristiansen, Kristian Uldall

    2015-01-01

    with respect to , appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples, including a model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables, and the computation of homoclinic connections in the Fitz......This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence...

  11. Asymptotic series and functional integrals in quantum field theory

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    1979-01-01

    Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)

  12. Design and fabrication methods of FW/blanket and vessel for ITER-FEAT

    Energy Technology Data Exchange (ETDEWEB)

    Ioki, K. E-mail: iokik@itereu.de; Barabash, V.; Cardella, A.; Elio, F.; Kalinin, G.; Miki, N.; Onozuka, M.; Osaki, T.; Rozov, V.; Sannazzaro, G.; Utin, Y.; Yamada, M.; Yoshimura, H

    2001-11-01

    Design has progressed on the vacuum vessel and FW/blanket for ITER-FEAT. The basic functions and structures are the same as for the 1998 ITER design. Detailed blanket module designs of the radially cooled shield block with flat separable FW panels have been developed. The ITER blanket R and D program covers different materials and fabrication methods in order make a final selection based on the results. Separate manifolds have been designed and analysed for the blanket cooling. The vessel design with flexible support housings has been improved to minimise the number of continuous poloidal ribs. Most of the R and D performed so far during EDA are still applicable.

  13. Design and fabrication methods of FW/blanket and vessel for ITER-FEAT

    International Nuclear Information System (INIS)

    Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Kalinin, G.; Miki, N.; Onozuka, M.; Osaki, T.; Rozov, V.; Sannazzaro, G.; Utin, Y.; Yamada, M.; Yoshimura, H.

    2001-01-01

    Design has progressed on the vacuum vessel and FW/blanket for ITER-FEAT. The basic functions and structures are the same as for the 1998 ITER design. Detailed blanket module designs of the radially cooled shield block with flat separable FW panels have been developed. The ITER blanket R and D program covers different materials and fabrication methods in order make a final selection based on the results. Separate manifolds have been designed and analysed for the blanket cooling. The vessel design with flexible support housings has been improved to minimise the number of continuous poloidal ribs. Most of the R and D performed so far during EDA are still applicable

  14. Variational iteration method for solving coupled-KdV equations

    International Nuclear Information System (INIS)

    Assas, Laila M.B.

    2008-01-01

    In this paper, the He's variational iteration method is applied to solve the non-linear coupled-KdV equations. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converge to the exact solution of the coupled-KdV equations. This procedure is a powerful tool for solving coupled-KdV equations

  15. Solution of problems in calculus of variations via He's variational iteration method

    International Nuclear Information System (INIS)

    Tatari, Mehdi; Dehghan, Mehdi

    2007-01-01

    In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years He's variational iteration method has been attracted a lot of attention of the researchers for solving nonlinear problems. This method finds the solution of the problem without any discretization of the equation. Since this method gives a closed form solution of the problem and avoids the round off errors, it can be considered as an efficient method for solving various kinds of problems. In this research He's variational iteration method will be employed for solving some problems in calculus of variations. Some examples are presented to show the efficiency of the proposed technique

  16. Parallel framework for topology optimization using the method of moving asymptotes

    DEFF Research Database (Denmark)

    Aage, Niels; Lazarov, Boyan Stefanov

    2013-01-01

    and simple to implement linear solvers and optimization algorithms. However, to ensure generality, the code is developed to be easily extendable in terms of physical models as well as in terms of solution methods, without compromising the parallel scalability. The widely used Method of Moving Asymptotes......The complexity of problems attacked in topology optimization has increased dramatically during the past decade. Examples include fully coupled multiphysics problems in thermo-elasticity, fluid-structure interaction, Micro-Electro Mechanical System (MEMS) design and large-scale three dimensional...... optimization algorithm is parallelized and included as a fundamental part of the code. The capabilities of the presented approaches are demonstrated on topology optimization of a Stokes flow problem with target outflow constraints as well as the minimum compliance problem with a volume constraint from linear...

  17. MO-DE-207A-07: Filtered Iterative Reconstruction (FIR) Via Proximal Forward-Backward Splitting: A Synergy of Analytical and Iterative Reconstruction Method for CT

    International Nuclear Information System (INIS)

    Gao, H

    2016-01-01

    Purpose: This work is to develop a general framework, namely filtered iterative reconstruction (FIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality. Methods: FIR is formulated as a combination of filtered data fidelity and sparsity regularization, and then solved by proximal forward-backward splitting (PFBS) algorithm. As a result, the image reconstruction decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected to the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is in turn weighted together with previous image iterate to form next image iterate. Since the eigenvalues of AR-projection operator are close to the unity, PFBS based FIR has a fast convergence. Results: The proposed FIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts. Conclusion: FIR is proposed to incorporate AR into IR, with an efficient image reconstruction algorithm based on PFBS. The CBCT results suggest that FIR synergizes AR and IR with improved image quality and reduced axial and half-fan artifacts. The authors was partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).

  18. A non-iterative method for fitting decay curves with background

    International Nuclear Information System (INIS)

    Mukoyama, T.

    1982-01-01

    A non-iterative method for fitting a decay curve with background is presented. The sum of an exponential function and a constant term is linearized by the use of the difference equation and parameters are determined by the standard linear least-squares fitting. The validity of the present method has been tested against pseudo-experimental data. (orig.)

  19. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

    Czech Academy of Sciences Publication Activity Database

    Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

    2014-01-01

    Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

  20. On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians

    International Nuclear Information System (INIS)

    O'Reilly, E.P.; Weaire, D.

    1984-01-01

    The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)

  1. Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

    Science.gov (United States)

    Jin, Qinian; Wang, Wei

    2018-03-01

    The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

  2. Numerical integration of asymptotic solutions of ordinary differential equations

    Science.gov (United States)

    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.

  3. Asymptotic Solutions of Serial Radial Fuel Shuffling

    Directory of Open Access Journals (Sweden)

    Xue-Nong Chen

    2015-12-01

    Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.

  4. A novel iterative energy calibration method for composite germanium detectors

    International Nuclear Information System (INIS)

    Pattabiraman, N.S.; Chintalapudi, S.N.; Ghugre, S.S.

    2004-01-01

    An automatic method for energy calibration of the observed experimental spectrum has been developed. The method presented is based on an iterative algorithm and presents an efficient way to perform energy calibrations after establishing the weights of the calibration data. An application of this novel technique for data acquired using composite detectors in an in-beam γ-ray spectroscopy experiment is presented

  5. A novel iterative energy calibration method for composite germanium detectors

    Energy Technology Data Exchange (ETDEWEB)

    Pattabiraman, N.S.; Chintalapudi, S.N.; Ghugre, S.S. E-mail: ssg@alpha.iuc.res.in

    2004-07-01

    An automatic method for energy calibration of the observed experimental spectrum has been developed. The method presented is based on an iterative algorithm and presents an efficient way to perform energy calibrations after establishing the weights of the calibration data. An application of this novel technique for data acquired using composite detectors in an in-beam {gamma}-ray spectroscopy experiment is presented.

  6. Asymptotic Solution of the Theory of Shells Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    I. V. Andrianov

    2007-01-01

    Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

  7. Asymptotically Safe Dark Matter

    DEFF Research Database (Denmark)

    Sannino, Francesco; Shoemaker, Ian M.

    2015-01-01

    We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....

  8. Asymptotic stability of a genetic network under impulsive control

    International Nuclear Information System (INIS)

    Li Fangfei; Sun Jitao

    2010-01-01

    The study of the stability of genetic network is an important motif for the understanding of the living organism at both molecular and cellular levels. In this Letter, we provide a theoretical method for analyzing the asymptotic stability of a genetic network under impulsive control. And the sufficient conditions of its asymptotic stability under impulsive control are obtained. Finally, an example is given to illustrate the effectiveness of the obtained method.

  9. A hyperpower iterative method for computing the generalized Drazin ...

    Indian Academy of Sciences (India)

    Shwetabh Srivastava

    [6, 7]. A number of direct and iterative methods for com- putation of the Drazin inverse were developed in [8–12]. Its extension to Banach algebras is known as the generalized Drazin inverse and was established in [13]. Let J denote the complex. Banach algebra with the unit 1. The generalized Drazin inverse of an element ...

  10. Copper Mountain conference on iterative methods: Proceedings: Volume 1

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-10-01

    This volume (one of two) contains information presented during the first three days of the Copper Mountain Conference on Iterative Methods held April 9-13, 1996 at Copper Mountain, Colorado. Topics of the sessions held these three days included nonlinear systems, parallel processing, preconditioning, sparse matrix test collections, first-order system least squares, Arnoldi`s method, integral equations, software, Navier-Stokes equations, Euler equations, Krylov methods, and eigenvalues. The top three papers from a student competition are also included. Selected papers indexed separately for the Energy Science and Technology Database.

  11. Asymptotic time dependent neutron transport in multidimensional systems

    International Nuclear Information System (INIS)

    Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.

    1983-01-01

    A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated

  12. An asymptotic formula of the divergent bilateral basic hypergeometric series

    OpenAIRE

    Morita, Takeshi

    2012-01-01

    We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.

  13. Polynomial factor models : non-iterative estimation via method-of-moments

    NARCIS (Netherlands)

    Schuberth, Florian; Büchner, Rebecca; Schermelleh-Engel, Karin; Dijkstra, Theo K.

    2017-01-01

    We introduce a non-iterative method-of-moments estimator for non-linear latent variable (LV) models. Under the assumption of joint normality of all exogenous variables, we use the corrected moments of linear combinations of the observed indicators (proxies) to obtain consistent path coefficient and

  14. Methods and Algorithms for Approximating the Gamma Function and Related Functions. A survey. Part I: Asymptotic Series

    Directory of Open Access Journals (Sweden)

    Cristinel Mortici

    2015-01-01

    Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.

  15. An iterative method for the canard explosion in general planar systems

    DEFF Research Database (Denmark)

    Brøns, Morten

    2012-01-01

    The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are a...... equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system....

  16. Methods in half-linear asymptotic theory

    Directory of Open Access Journals (Sweden)

    Pavel Rehak

    2016-10-01

    Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.

  17. Asymptotic Eigenstructures

    Science.gov (United States)

    Thompson, P. M.; Stein, G.

    1980-01-01

    The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

  18. Note: interpreting iterative methods convergence with diffusion point of view

    OpenAIRE

    Hong, Dohy

    2013-01-01

    In this paper, we explain the convergence speed of different iteration schemes with the fluid diffusion view when solving a linear fixed point problem. This interpretation allows one to better understand why power iteration or Jacobi iteration may converge faster or slower than Gauss-Seidel iteration.

  19. A New General Iterative Method for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Singthong Urailuk

    2010-01-01

    Full Text Available We introduce a new general iterative method by using the -mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert spaces. A strong convergence theorem of the purposed iterative method is established under some certain control conditions. Our results improve and extend the results announced by many others.

  20. More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

    Directory of Open Access Journals (Sweden)

    Jen-Yuan Chen

    2014-01-01

    Full Text Available Continuing from the works of Li et al. (2014, Li (2007, and Kincaid et al. (2000, we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.

  1. A multigroup flux-limited asymptotic diffusion Fokker-Planck equation

    International Nuclear Information System (INIS)

    Liu Chengan

    1987-01-01

    A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems

  2. Gauss-Seidel Iterative Method as a Real-Time Pile-Up Solver of Scintillation Pulses

    Science.gov (United States)

    Novak, Roman; Vencelj, Matja¿

    2009-12-01

    The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

  3. Asymptotics of relativistic spin networks

    International Nuclear Information System (INIS)

    Barrett, John W; Steele, Christopher M

    2003-01-01

    The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol

  4. A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

    Energy Technology Data Exchange (ETDEWEB)

    Melboe, Hallgeir

    2001-10-01

    This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

  5. Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method

    International Nuclear Information System (INIS)

    Langemann, Dirk; Tasche, Manfred

    2008-01-01

    In this paper we consider the numerical solution of a phase retrieval problem for a compactly supported, linear spline f : R → C with the Fourier transform f-circumflex, where values of |f| and |f-circumflex| at finitely many equispaced nodes are given. The unknown phases of complex spline coefficients fulfil a well-structured system of nonlinear equations. Thus the phase reconstruction leads to a nonlinear inverse problem, which is solved by a multilevel strategy and iterative Tikhonov regularization. The multilevel strategy concentrates the main effort of the solution of the phase retrieval problem in the coarse, less expensive levels and provides convenient initial guesses at the next finer level. On each level, the corresponding nonlinear system is solved by an iteratively regularized Gauss–Newton method. The multilevel strategy is motivated by convergence results of IRGN. This method is applicable to a wide range of examples as shown in several numerical tests for noiseless and noisy data

  6. Regge asymptotics of scattering with flavour exchange in QCD

    International Nuclear Information System (INIS)

    Kirschner, R.

    1994-06-01

    The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated. (orig.)

  7. Study of a Biparametric Family of Iterative Methods

    Directory of Open Access Journals (Sweden)

    B. Campos

    2014-01-01

    Full Text Available The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c with clear stable and unstable behaviors.

  8. Non-iterative method to calculate the periodical distribution of temperature in reactors with thermal regeneration

    International Nuclear Information System (INIS)

    Sanchez de Alsina, O.L.; Scaricabarozzi, R.A.

    1982-01-01

    A matrix non-iterative method to calculate the periodical distribution in reactors with thermal regeneration is presented. In case of exothermic reaction, a source term will be included. A computer code was developed to calculate the final temperature distribution in solids and in the outlet temperatures of the gases. The results obtained from ethane oxidation calculation in air, using the Dietrich kinetic data are presented. This method is more advantageous than iterative methods. (E.G.) [pt

  9. Asymptotic and geometrical quantization

    International Nuclear Information System (INIS)

    Karasev, M.V.; Maslov, V.P.

    1984-01-01

    The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered

  10. Asymptotically Optimal Agents

    OpenAIRE

    Lattimore, Tor; Hutter, Marcus

    2011-01-01

    Artificial general intelligence aims to create agents capable of learning to solve arbitrary interesting problems. We define two versions of asymptotic optimality and prove that no agent can satisfy the strong version while in some cases, depending on discounting, there does exist a non-computable weak asymptotically optimal agent.

  11. Analyzing the Impacts of Alternated Number of Iterations in Multiple Imputation Method on Explanatory Factor Analysis

    Directory of Open Access Journals (Sweden)

    Duygu KOÇAK

    2017-11-01

    Full Text Available The study aims to identify the effects of iteration numbers used in multiple iteration method, one of the methods used to cope with missing values, on the results of factor analysis. With this aim, artificial datasets of different sample sizes were created. Missing values at random and missing values at complete random were created in various ratios by deleting data. For the data in random missing values, a second variable was iterated at ordinal scale level and datasets with different ratios of missing values were obtained based on the levels of this variable. The data were generated using “psych” program in R software, while “dplyr” program was used to create codes that would delete values according to predetermined conditions of missing value mechanism. Different datasets were generated by applying different iteration numbers. Explanatory factor analysis was conducted on the datasets completed and the factors and total explained variances are presented. These values were first evaluated based on the number of factors and total variance explained of the complete datasets. The results indicate that multiple iteration method yields a better performance in cases of missing values at random compared to datasets with missing values at complete random. Also, it was found that increasing the number of iterations in both missing value datasets decreases the difference in the results obtained from complete datasets.

  12. On calculating double logarithmical asymptotics of vertex functions defined on the mass shell

    International Nuclear Information System (INIS)

    Belokurov, V.V.; Usyukina, N.I.

    1981-01-01

    The essence of the calculation method of double logarithmical asymptotics of vertex functions defined on the mass shell is presented. Using the method the asymptotics of the form-factor of electron is calculated. The ladder and cross-ladder diagrams are asymptotically considerable in every order of the perturbation theory. The way in which the asymptotics of the 4-order diagrams is calculated has been shown. The diagrams of this order and reduction procedures for them are given in a graphic form. The photon mass μ 2 not equal to 0 plays the role of a regulator, removing infrared divergencies. The double logarithmical asymptotics of the form-factor of electron on the mass shell is calculated rigorously in an arbitrary order of the perturbation theory [ru

  13. Iteratively-coupled propagating exterior complex scaling method for electron-hydrogen collisions

    International Nuclear Information System (INIS)

    Bartlett, Philip L; Stelbovics, Andris T; Bray, Igor

    2004-01-01

    A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schroedinger equation, for L ≤ 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources. (letter to the editor)

  14. Newton-sor iterative method for solving the two-dimensional porous ...

    African Journals Online (AJOL)

    In this paper, we consider the application of the Newton-SOR iterative method in obtaining the approximate solution of the two-dimensional porous medium equation (2D PME). The nonlinear finite difference approximation equation to the 2D PME is derived by using the implicit finite difference scheme. The developed ...

  15. Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

    International Nuclear Information System (INIS)

    Zhang, Jia-Fang; Chen, Heshan

    2014-01-01

    This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution

  16. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    OpenAIRE

    Darzi R; Neamaty A

    2010-01-01

    We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

  17. A sparsity-regularized Born iterative method for reconstruction of two-dimensional piecewise continuous inhomogeneous domains

    KAUST Repository

    Sandhu, Ali Imran; Desmal, Abdulla; Bagci, Hakan

    2016-01-01

    A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile's derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.

  18. Method of asymptotic expansions and qualitative analysis of finite-dimensional models in the nonlinear field theory

    International Nuclear Information System (INIS)

    Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.

    1984-01-01

    The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed

  19. An iterative method for the solution of nonlinear systems using the Faber polynomials for annular sectors

    Energy Technology Data Exchange (ETDEWEB)

    Myers, N.J. [Univ. of Durham (United Kingdom)

    1994-12-31

    The author gives a hybrid method for the iterative solution of linear systems of equations Ax = b, where the matrix (A) is nonsingular, sparse and nonsymmetric. As in a method developed by Starke and Varga the method begins with a number of steps of the Arnoldi method to produce some information on the location of the spectrum of A. This method then switches to an iterative method based on the Faber polynomials for an annular sector placed around these eigenvalue estimates. The Faber polynomials for an annular sector are used because, firstly an annular sector can easily be placed around any eigenvalue estimates bounded away from zero, and secondly the Faber polynomials are known analytically for an annular sector. Finally the author gives three numerical examples, two of which allow comparison with Starke and Varga`s results. The third is an example of a matrix for which many iterative methods would fall, but this method converges.

  20. ITER radio frequency systems

    International Nuclear Information System (INIS)

    Bosia, G.

    1998-01-01

    Neutral Beam Injection and RF heating are two of the methods for heating and current drive in ITER. The three ITER RF systems, which have been developed during the EDA, offer several complementary services and are able to fulfil ITER operational requirements

  1. Environmental dose rate assessment of ITER using the Monte Carlo method

    Directory of Open Access Journals (Sweden)

    Karimian Alireza

    2014-01-01

    Full Text Available Exposure to radiation is one of the main sources of risk to staff employed in reactor facilities. The staff of a tokamak is exposed to a wide range of neutrons and photons around the tokamak hall. The International Thermonuclear Experimental Reactor (ITER is a nuclear fusion engineering project and the most advanced experimental tokamak in the world. From the radiobiological point of view, ITER dose rates assessment is particularly important. The aim of this study is the assessment of the amount of radiation in ITER during its normal operation in a radial direction from the plasma chamber to the tokamak hall. To achieve this goal, the ITER system and its components were simulated by the Monte Carlo method using the MCNPX 2.6.0 code. Furthermore, the equivalent dose rates of some radiosensitive organs of the human body were calculated by using the medical internal radiation dose phantom. Our study is based on the deuterium-tritium plasma burning by 14.1 MeV neutron production and also photon radiation due to neutron activation. As our results show, the total equivalent dose rate on the outside of the bioshield wall of the tokamak hall is about 1 mSv per year, which is less than the annual occupational dose rate limit during the normal operation of ITER. Also, equivalent dose rates of radiosensitive organs have shown that the maximum dose rate belongs to the kidney. The data may help calculate how long the staff can stay in such an environment, before the equivalent dose rates reach the whole-body dose limits.

  2. A novel EMD selecting thresholding method based on multiple iteration for denoising LIDAR signal

    Science.gov (United States)

    Li, Meng; Jiang, Li-hui; Xiong, Xing-long

    2015-06-01

    Empirical mode decomposition (EMD) approach has been believed to be potentially useful for processing the nonlinear and non-stationary LIDAR signals. To shed further light on its performance, we proposed the EMD selecting thresholding method based on multiple iteration, which essentially acts as a development of EMD interval thresholding (EMD-IT), and randomly alters the samples of noisy parts of all the corrupted intrinsic mode functions to generate a better effect of iteration. Simulations on both synthetic signals and LIDAR signals from real world support this method.

  3. Variationally Asymptotically Stable Difference Systems

    Directory of Open Access Journals (Sweden)

    Goo YoonHoe

    2007-01-01

    Full Text Available We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.

  4. Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

    Science.gov (United States)

    Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

    2018-01-01

    Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

  5. Chatter suppression methods of a robot machine for ITER vacuum vessel assembly and maintenance

    International Nuclear Information System (INIS)

    Wu, Huapeng; Wang, Yongbo; Li, Ming; Al-Saedi, Mazin; Handroos, Heikki

    2014-01-01

    Highlights: •A redundant 10-DOF serial-parallel hybrid robot for ITER assembly and maintains is presented. •A dynamic model of the robot is developed. •A feedback and feedforward controller is presented to suppress machining vibration of the robot. -- Abstract: In the process of assembly and maintenance of ITER vacuum vessel (ITER VV), various machining tasks including threading, milling, welding-defects cutting and flexible hose boring are required to be performed from inside of ITER VV by on-site machining tools. Robot machine is a promising option for these tasks, but great chatter (machine vibration) would happen in the machining process. The chatter vibration will deteriorate the robot accuracy and surface quality, and even cause some damages on the end-effector tools and the robot structure itself. This paper introduces two vibration control methods, one is passive and another is active vibration control. For the passive vibration control, a parallel mechanism is presented to increase the stiffness of robot machine; for the active vibration control, a hybrid control method combining feedforward controller and nonlinear feedback controller is introduced for chatter suppression. A dynamic model and its chatter vibration phenomena of a hybrid robot is demonstrated. Simulation results are given based on the proposed hybrid robot machine which is developed for the ITER VV assembly and maintenance

  6. Chatter suppression methods of a robot machine for ITER vacuum vessel assembly and maintenance

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Huapeng; Wang, Yongbo, E-mail: yongbo.wang@lut.fi; Li, Ming; Al-Saedi, Mazin; Handroos, Heikki

    2014-10-15

    Highlights: •A redundant 10-DOF serial-parallel hybrid robot for ITER assembly and maintains is presented. •A dynamic model of the robot is developed. •A feedback and feedforward controller is presented to suppress machining vibration of the robot. -- Abstract: In the process of assembly and maintenance of ITER vacuum vessel (ITER VV), various machining tasks including threading, milling, welding-defects cutting and flexible hose boring are required to be performed from inside of ITER VV by on-site machining tools. Robot machine is a promising option for these tasks, but great chatter (machine vibration) would happen in the machining process. The chatter vibration will deteriorate the robot accuracy and surface quality, and even cause some damages on the end-effector tools and the robot structure itself. This paper introduces two vibration control methods, one is passive and another is active vibration control. For the passive vibration control, a parallel mechanism is presented to increase the stiffness of robot machine; for the active vibration control, a hybrid control method combining feedforward controller and nonlinear feedback controller is introduced for chatter suppression. A dynamic model and its chatter vibration phenomena of a hybrid robot is demonstrated. Simulation results are given based on the proposed hybrid robot machine which is developed for the ITER VV assembly and maintenance.

  7. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    Directory of Open Access Journals (Sweden)

    R. Darzi

    2010-01-01

    Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

  8. On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis.

    Science.gov (United States)

    Yamazaki, Keisuke

    2012-07-01

    Parametric models for sequential data, such as hidden Markov models, stochastic context-free grammars, and linear dynamical systems, are widely used in time-series analysis and structural data analysis. Computation of the likelihood function is one of primary considerations in many learning methods. Iterative calculation of the likelihood such as the model selection is still time-consuming though there are effective algorithms based on dynamic programming. The present paper studies parameter learning in a simplified feature space to reduce the computational cost. Simplifying data is a common technique seen in feature selection and dimension reduction though an oversimplified space causes adverse learning results. Therefore, we mathematically investigate a condition of the feature map to have an asymptotically equivalent convergence point of estimated parameters, referred to as the vicarious map. As a demonstration to find vicarious maps, we consider the feature space, which limits the length of data, and derive a necessary length for parameter learning in hidden Markov models. Copyright © 2012 Elsevier Ltd. All rights reserved.

  9. An iterative method for obtaining the optimum lightning location on a spherical surface

    Science.gov (United States)

    Chao, Gao; Qiming, MA

    1991-01-01

    A brief introduction to the basic principles of an eigen method used to obtain the optimum source location of lightning is presented. The location of the optimum source is obtained by using multiple direction finders (DF's) on a spherical surface. An improvement of this method, which takes the distance of source-DF's as a constant, is presented. It is pointed out that using a weight factor of signal strength is not the most ideal method because of the inexact inverse signal strength-distance relation and the inaccurate signal amplitude. An iterative calculation method is presented using the distance from the source to the DF as a weight factor. This improved method has higher accuracy and needs only a little more calculation time. Some computer simulations for a 4DF system are presented to show the improvement of location through use of the iterative method.

  10. Discrete fourier transform (DFT) analysis for applications using iterative transform methods

    Science.gov (United States)

    Dean, Bruce H. (Inventor)

    2012-01-01

    According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

  11. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    Science.gov (United States)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  12. Polynomial Asymptotes of the Second Kind

    Science.gov (United States)

    Dobbs, David E.

    2011-01-01

    This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

  13. Worst-case Analysis of Strategy Iteration and the Simplex Method

    DEFF Research Database (Denmark)

    Hansen, Thomas Dueholm

    In this dissertation we study strategy iteration (also known as policy iteration) algorithms for solving Markov decision processes (MDPs) and two-player turn-based stochastic games (2TBSGs). MDPs provide a mathematical model for sequential decision making under uncertainty. They are widely used...... to model stochastic optimization problems in various areas ranging from operations research, machine learning, artificial intelligence, economics and game theory. The class of two-player turn-based stochastic games is a natural generalization of Markov decision processes that is obtained by introducing...... in the size of the problem (the bounds have subexponential form). Utilizing a tight connection between MDPs and linear programming, it is shown that the same bounds apply to the corresponding pivoting rules for the simplex method for solving linear programs. Prior to this result no super-polynomial lower...

  14. Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

    Science.gov (United States)

    Hudson, H M; Ma, J; Green, P

    1994-01-01

    Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

  15. An efficient iterative method for the generalized Stokes problem

    Energy Technology Data Exchange (ETDEWEB)

    Sameh, A. [Univ. of Minnesota, Twin Cities, MN (United States); Sarin, V. [Univ. of Illinois, Urbana, IL (United States)

    1996-12-31

    This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.

  16. He's variational iteration method applied to the solution of the prey and predator problem with variable coefficients

    International Nuclear Information System (INIS)

    Yusufoglu, Elcin; Erbas, Baris

    2008-01-01

    In this Letter, a mathematical model of the problem of prey and predator is presented and He's variational iteration method is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Comparison of the methods show that He's variational iteration method is a powerful method for obtaining approximate solutions to nonlinear equations and their systems

  17. A sparsity-regularized Born iterative method for reconstruction of two-dimensional piecewise continuous inhomogeneous domains

    KAUST Repository

    Sandhu, Ali Imran

    2016-04-10

    A sparsity-regularized Born iterative method (BIM) is proposed for efficiently reconstructing two-dimensional piecewise-continuous inhomogeneous dielectric profiles. Such profiles are typically not spatially sparse, which reduces the efficiency of the sparsity-promoting regularization. To overcome this problem, scattered fields are represented in terms of the spatial derivative of the dielectric profile and reconstruction is carried out over samples of the dielectric profile\\'s derivative. Then, like the conventional BIM, the nonlinear problem is iteratively converted into a sequence of linear problems (in derivative samples) and sparsity constraint is enforced on each linear problem using the thresholded Landweber iterations. Numerical results, which demonstrate the efficiency and accuracy of the proposed method in reconstructing piecewise-continuous dielectric profiles, are presented.

  18. Asymptotic theory of weakly dependent random processes

    CERN Document Server

    Rio, Emmanuel

    2017-01-01

    Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...

  19. Conference on Boundary and Interior Layers : Computational and Asymptotic Methods

    CERN Document Server

    Stynes, Martin; Zhang, Zhimin

    2017-01-01

    This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed diffe...

  20. Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

    KAUST Repository

    Xu, Zhiqiang

    2017-02-16

    Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

  1. Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

    KAUST Repository

    Xu, Zhiqiang; Cheng, James; Xiao, Xiaokui; Fujimaki, Ryohei; Muraoka, Yusuke

    2017-01-01

    Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

  2. Asymptotics of bivariate generating functions with algebraic singularities

    Science.gov (United States)

    Greenwood, Torin

    Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

  3. Asymptotic numbers: Pt.1

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1980-01-01

    The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

  4. Generalized heat kernel coefficients for a new asymptotic expansion

    International Nuclear Information System (INIS)

    Osipov, Alexander A.; Hiller, Brigitte

    2003-01-01

    The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified

  5. Asymptotic Safety Guaranteed in Supersymmetry

    Science.gov (United States)

    Bond, Andrew D.; Litim, Daniel F.

    2017-11-01

    We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

  6. Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

    Science.gov (United States)

    Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

    2017-12-01

    We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

  7. AN ITERATIVE SEGMENTATION METHOD FOR REGION OF INTEREST EXTRACTION

    Directory of Open Access Journals (Sweden)

    Volkan CETIN

    2013-01-01

    Full Text Available In this paper, a method is presented for applications which include mammographic image segmentation and region of interest extraction. Segmentation is a very critical and difficult stage to accomplish in computer aided detection systems. Although the presented segmentation method is developed for mammographic images, it can be used for any medical image which resembles the same statistical characteristics with mammograms. Fundamentally, the method contains iterative automatic thresholding and masking operations which is applied to the original or enhanced mammograms. Also the effect of image enhancement to the segmentation process was observed. A version of histogram equalization was applied to the images for enhancement. Finally, the results show that enhanced version of the proposed segmentation method is preferable because of its better success rate.

  8. A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position

    Science.gov (United States)

    Zhou, Wenjie; Wei, Xuesong; Wang, Leqin; Wu, Guangkuan

    2017-05-01

    Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method-twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

  9. Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

    Science.gov (United States)

    Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M.

    2000-12-01

    Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve ˜50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R&D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R&D is being performed.

  10. Iterative convergence acceleration of neutral particle transport methods via adjacent-cell preconditioners

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    1999-01-01

    The author proposes preconditioning as a viable acceleration scheme for the inner iterations of transport calculations in slab geometry. In particular he develops Adjacent-Cell Preconditioners (AP) that have the same coupling stencil as cell-centered diffusion schemes. For lowest order methods, e.g., Diamond Difference, Step, and 0-order Nodal Integral Method (ONIM), cast in a Weighted Diamond Difference (WDD) form, he derives AP for thick (KAP) and thin (NAP) cells that for model problems are unconditionally stable and efficient. For the First-Order Nodal Integral Method (INIM) he derives a NAP that possesses similarly excellent spectral properties for model problems. The two most attractive features of the new technique are:(1) its cell-centered coupling stencil, which makes it more adequate for extension to multidimensional, higher order situations than the standard edge-centered or point-centered Diffusion Synthetic Acceleration (DSA) methods; and (2) its decreasing spectral radius with increasing cell thickness to the extent that immediate pointwise convergence, i.e., in one iteration, can be achieved for problems with sufficiently thick cells. He implemented these methods, augmented with appropriate boundary conditions and mixing formulas for material heterogeneities, in the test code APID that he uses to successfully verify the analytical spectral properties for homogeneous problems. Furthermore, he conducts numerical tests to demonstrate the robustness of the KAP and NAP in the presence of sharp mesh or material discontinuities. He shows that the AP for WDD is highly resilient to such discontinuities, but for INIM a few cases occur in which the scheme does not converge; however, when it converges, AP greatly reduces the number of iterations required to achieve convergence

  11. A study on linear and nonlinear Schrodinger equations by the variational iteration method

    International Nuclear Information System (INIS)

    Wazwaz, Abdul-Majid

    2008-01-01

    In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

  12. The Davidson Method as an alternative to power iterations for criticality calculations

    International Nuclear Information System (INIS)

    Subramanian, C.; Van Criekingen, S.; Heuveline, V.; Nataf, F.; Have, P.

    2011-01-01

    The Davidson method is implemented within the neutron transport core solver parafish to solve k-eigenvalue criticality transport problems. The parafish solver is based on domain decomposition, uses spherical harmonics (P_N method) for angular discretization, and nonconforming finite elements for spatial discretization. The Davidson method is compared to the traditional power iteration method in that context. Encouraging numerical results are obtained with both sequential and parallel calculations. (author)

  13. Iterative solutions of finite difference diffusion equations

    International Nuclear Information System (INIS)

    Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

    1981-01-01

    The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

  14. Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

    International Nuclear Information System (INIS)

    Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

    2016-01-01

    Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

  15. Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

    Science.gov (United States)

    Nikazad, T; Davidi, R; Herman, G T

    2012-03-01

    We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.

  16. An iterative stochastic ensemble method for parameter estimation of subsurface flow models

    International Nuclear Information System (INIS)

    Elsheikh, Ahmed H.; Wheeler, Mary F.; Hoteit, Ibrahim

    2013-01-01

    Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates

  17. An iterative stochastic ensemble method for parameter estimation of subsurface flow models

    KAUST Repository

    Elsheikh, Ahmed H.

    2013-06-01

    Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss-Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier Inc.

  18. Double folding model of nucleus-nucleus potential: formulae, iteration method and computer code

    International Nuclear Information System (INIS)

    Luk'yanov, K.V.

    2008-01-01

    Method of construction of the nucleus-nucleus double folding potential is described. Iteration procedure for the corresponding integral equation is presented. Computer code and numerical results are presented

  19. Joint 2D-DOA and Frequency Estimation for L-Shaped Array Using Iterative Least Squares Method

    Directory of Open Access Journals (Sweden)

    Ling-yun Xu

    2012-01-01

    Full Text Available We introduce an iterative least squares method (ILS for estimating the 2D-DOA and frequency based on L-shaped array. The ILS iteratively finds direction matrix and delay matrix, then 2D-DOA and frequency can be obtained by the least squares method. Without spectral peak searching and pairing, this algorithm works well and pairs the parameters automatically. Moreover, our algorithm has better performance than conventional ESPRIT algorithm and propagator method. The useful behavior of the proposed algorithm is verified by simulations.

  20. An asymptotic solution of large-N QCD

    Directory of Open Access Journals (Sweden)

    Bochicchio Marco

    2014-01-01

    Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.

  1. Multiscale optical simulation settings: challenging applications handled with an iterative ray-tracing FDTD interface method.

    Science.gov (United States)

    Leiner, Claude; Nemitz, Wolfgang; Schweitzer, Susanne; Kuna, Ladislav; Wenzl, Franz P; Hartmann, Paul; Satzinger, Valentin; Sommer, Christian

    2016-03-20

    We show that with an appropriate combination of two optical simulation techniques-classical ray-tracing and the finite difference time domain method-an optical device containing multiple diffractive and refractive optical elements can be accurately simulated in an iterative simulation approach. We compare the simulation results with experimental measurements of the device to discuss the applicability and accuracy of our iterative simulation procedure.

  2. A holistic calibration method with iterative distortion compensation for stereo deflectometry

    Science.gov (United States)

    Xu, Yongjia; Gao, Feng; Zhang, Zonghua; Jiang, Xiangqian

    2018-07-01

    This paper presents a novel holistic calibration method for stereo deflectometry system to improve the system measurement accuracy. The reconstruction result of stereo deflectometry is integrated with the calculated normal data of the measured surface. The calculation accuracy of the normal data is seriously influenced by the calibration accuracy of the geometrical relationship of the stereo deflectometry system. Conventional calibration approaches introduce form error to the system due to inaccurate imaging model and distortion elimination. The proposed calibration method compensates system distortion based on an iterative algorithm instead of the conventional distortion mathematical model. The initial value of the system parameters are calculated from the fringe patterns displayed on the systemic LCD screen through a reflection of a markless flat mirror. An iterative algorithm is proposed to compensate system distortion and optimize camera imaging parameters and system geometrical relation parameters based on a cost function. Both simulation work and experimental results show the proposed calibration method can significantly improve the calibration and measurement accuracy of a stereo deflectometry. The PV (peak value) of measurement error of a flat mirror can be reduced to 69.7 nm by applying the proposed method from 282 nm obtained with the conventional calibration approach.

  3. ITMETH, Iterative Routines for Linear System

    International Nuclear Information System (INIS)

    Greenbaum, A.

    1989-01-01

    1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

  4. Application of He's variational iteration method to the fifth-order boundary value problems

    International Nuclear Information System (INIS)

    Shen, S

    2008-01-01

    Variational iteration method is introduced to solve the fifth-order boundary value problems. This method provides an efficient approach to solve this type of problems without discretization and the computation of the Adomian polynomials. Numerical results demonstrate that this method is a promising and powerful tool for solving the fifth-order boundary value problems

  5. Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

    International Nuclear Information System (INIS)

    Ioki, K.; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M.

    2000-01-01

    Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve ∼50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R and D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R and D is being performed

  6. Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

    International Nuclear Information System (INIS)

    Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist

    2007-01-01

    This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable

  7. Design and fabrication methods of FW/blanket, divertor and vacuum vessel for ITER

    Energy Technology Data Exchange (ETDEWEB)

    Ioki, K. E-mail: iokik@itereu.deiokik@ipp.mpg.de; Barabash, V.; Cardella, A.; Elio, F.; Ibbott, C.; Janeschitz, G.; Johnson, G.; Kalinin, G.; Miki, N.; Onozuka, M.; Sannazzaro, G.; Tivey, R.; Utin, Y.; Yamada, M

    2000-12-01

    Design has progressed on the vacuum vessel, FW/blanket and Divertor for the Reduced Technical Objective/Reduced Cost (RTO/RC) ITER. The basic functions and structures are the same as for the 1998 ITER design [K. Ioki et al., J. Nucl. Mater. 258-263 (1998) 74]. Design and fabrication methods of the components have been improved to achieve {approx}50% reduction of the construction cost. Detailed blanket module designs with flat separable FW panels have been developed to reduce the fabrication cost and the future radioactive waste. Most of the R and D performed so far during the Engineering Design Activities (EDAs) are still applicable. Further cost reduction methods are also being investigated and additional R and D is being performed.

  8. Maxwell iteration for the lattice Boltzmann method with diffusive scaling

    Science.gov (United States)

    Zhao, Weifeng; Yong, Wen-An

    2017-03-01

    In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

  9. The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg

    2007-01-01

    This paper describes new extensions to the previously published multivariate alteration detection (MAD) method for change detection in bi-temporal, multi- and hypervariate data such as remote sensing imagery. Much like boosting methods often applied in data mining work, the iteratively reweighted...... to observations that show little change, i.e., for which the sum of squared, standardized MAD variates is small, and small weights are assigned to observations for which the sum is large. Like the original MAD method, the iterative extension is invariant to linear (affine) transformations of the original...... an agricultural region in Kenya, and hyperspectral airborne HyMap data from a small rural area in southeastern Germany are given. The latter case demonstrates the need for regularization....

  10. A mutually profitable alliance - Asymptotic expansions and numerical computations

    Science.gov (United States)

    Euvrard, D.

    Problems including the flow past a wing airfoil at Mach 1, and the two-dimensional flow past a partially immersed body are used to show the advantages of coupling a standard numerical method for the whole domain where everything is of the order of 1, with an appropriate asymptotic expansion in the vicinity of some singular point. Cases more closely linking the two approaches are then considered. In the localized finite element method, the asymptotic expansion at infinity becomes a convergent series and the problem reduces to a variational form. Combined analytical and numerical methods are used in the singularity distribution method and in the various couplings of finite elements and a Green integral representation to design a subroutine to compute the Green function and its derivatives.

  11. Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

    Science.gov (United States)

    Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

    2017-10-01

    This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

  12. Improved fixed point iterative method for blade element momentum computations

    DEFF Research Database (Denmark)

    Sun, Zhenye; Shen, Wen Zhong; Chen, Jin

    2017-01-01

    The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...... are addressed through both theoretical analysis and numerical tests. A term from the BEM equations equals to zero at a critical inflow angle is the source of the convergence problems. When the initial inflow angle is set larger than the critical inflow angle and the relaxation methodology is adopted...

  13. Acceleration of the AFEN method by two-node nonlinear iteration

    Energy Technology Data Exchange (ETDEWEB)

    Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

    1999-12-31

    A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

  14. Acceleration of the AFEN method by two-node nonlinear iteration

    Energy Technology Data Exchange (ETDEWEB)

    Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

    1998-12-31

    A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

  15. Iterative methods for dose reduction and image enhancement in tomography

    Science.gov (United States)

    Miao, Jianwei; Fahimian, Benjamin Pooya

    2012-09-18

    A system and method for creating a three dimensional cross sectional image of an object by the reconstruction of its projections that have been iteratively refined through modification in object space and Fourier space is disclosed. The invention provides systems and methods for use with any tomographic imaging system that reconstructs an object from its projections. In one embodiment, the invention presents a method to eliminate interpolations present in conventional tomography. The method has been experimentally shown to provide higher resolution and improved image quality parameters over existing approaches. A primary benefit of the method is radiation dose reduction since the invention can produce an image of a desired quality with a fewer number projections than seen with conventional methods.

  16. Generating asymptotically plane wave spacetimes

    International Nuclear Information System (INIS)

    Hubeny, Veronika E.; Rangamani, Mukund

    2003-01-01

    In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)

  17. Asymptotic twistor theory and the Kerr theorem

    International Nuclear Information System (INIS)

    Newman, Ezra T

    2006-01-01

    We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

  18. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x = Ax2α + Bx2

    Directory of Open Access Journals (Sweden)

    N. Al Sdran

    2016-06-01

    Full Text Available The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x = Ax2α + Bx2, (A>0, B<0, with (α = 2 for quadratic, (α =3 for sextic and (α =4 for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x by a piecewise-linear potential v(x, while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  19. Asymptotic behaviour of Feynman integrals

    International Nuclear Information System (INIS)

    Bergere, M.C.

    1980-01-01

    In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)

  20. An iterative method for Tikhonov regularization with a general linear regularization operator

    NARCIS (Netherlands)

    Hochstenbach, M.E.; Reichel, L.

    2010-01-01

    Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan

  1. Nonminimal hints for asymptotic safety

    Science.gov (United States)

    Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran

    2018-01-01

    In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

  2. ITER...ation

    International Nuclear Information System (INIS)

    Troyon, F.

    1997-01-01

    Recurrent attacks against ITER, the new generation of tokamak are a mix of political and scientific arguments. This short article draws a historical review of the European fusion program. This program has allowed to build and manage several installations in the aim of getting experimental results necessary to lead the program forwards. ITER will bring together a fusion reactor core with technologies such as materials, superconductive coils, heating devices and instrumentation in order to validate and delimit the operating range. ITER will be a logical and decisive step towards the use of controlled fusion. (A.C.)

  3. Asymptotic functions and multiplication of distributions

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1979-01-01

    Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory

  4. MUSIC imaging method for electromagnetic inspection of composite multi-layers

    Science.gov (United States)

    Rodeghiero, Giacomo; Ding, Ping-Ping; Zhong, Yu; Lambert, Marc; Lesselier, Dominique

    2015-03-01

    A first-order asymptotic formulation of the electric field scattered by a small inclusion (with respect to the wavelength in dielectric regime or to the skin depth in conductive regime) embedded in composite material is given. It is validated by comparison with results obtained using a Method of Moments (MoM). A non-iterative MUltiple SIgnal Classification (MUSIC) imaging method is utilized in the same configuration to locate the position of small defects. The effectiveness of the imaging algorithm is illustrated through some numerical examples.

  5. Preconditioned iterations to calculate extreme eigenvalues

    Energy Technology Data Exchange (ETDEWEB)

    Brand, C.W.; Petrova, S. [Institut fuer Angewandte Mathematik, Leoben (Austria)

    1994-12-31

    Common iterative algorithms to calculate a few extreme eigenvalues of a large, sparse matrix are Lanczos methods or power iterations. They converge at a rate proportional to the separation of the extreme eigenvalues from the rest of the spectrum. Appropriate preconditioning improves the separation of the eigenvalues. Davidson`s method and its generalizations exploit this fact. The authors examine a preconditioned iteration that resembles a truncated version of Davidson`s method with a different preconditioning strategy.

  6. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    Science.gov (United States)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  7. Comparing performance of standard and iterative linear unmixing methods for hyperspectral signatures

    Science.gov (United States)

    Gault, Travis R.; Jansen, Melissa E.; DeCoster, Mallory E.; Jansing, E. David; Rodriguez, Benjamin M.

    2016-05-01

    Linear unmixing is a method of decomposing a mixed signature to determine the component materials that are present in sensor's field of view, along with the abundances at which they occur. Linear unmixing assumes that energy from the materials in the field of view is mixed in a linear fashion across the spectrum of interest. Traditional unmixing methods can take advantage of adjacent pixels in the decomposition algorithm, but is not the case for point sensors. This paper explores several iterative and non-iterative methods for linear unmixing, and examines their effectiveness at identifying the individual signatures that make up simulated single pixel mixed signatures, along with their corresponding abundances. The major hurdle addressed in the proposed method is that no neighboring pixel information is available for the spectral signature of interest. Testing is performed using two collections of spectral signatures from the Johns Hopkins University Applied Physics Laboratory's Signatures Database software (SigDB): a hand-selected small dataset of 25 distinct signatures from a larger dataset of approximately 1600 pure visible/near-infrared/short-wave-infrared (VIS/NIR/SWIR) spectra. Simulated spectra are created with three and four material mixtures randomly drawn from a dataset originating from SigDB, where the abundance of one material is swept in 10% increments from 10% to 90%with the abundances of the other materials equally divided amongst the remainder. For the smaller dataset of 25 signatures, all combinations of three or four materials are used to create simulated spectra, from which the accuracy of materials returned, as well as the correctness of the abundances, is compared to the inputs. The experiment is expanded to include the signatures from the larger dataset of almost 1600 signatures evaluated using a Monte Carlo scheme with 5000 draws of three or four materials to create the simulated mixed signatures. The spectral similarity of the inputs to the

  8. Asymptotic chaos expansions in finance theory and practice

    CERN Document Server

    Nicolay, David

    2014-01-01

    Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...

  9. The steady performance prediction of propeller-rudder-bulb system based on potential iterative method

    International Nuclear Information System (INIS)

    Liu, Y B; Su, Y M; Ju, L; Huang, S L

    2012-01-01

    A new numerical method was developed for predicting the steady hydrodynamic performance of propeller-rudder-bulb system. In the calculation, the rudder and bulb was taken into account as a whole, the potential based surface panel method was applied both to propeller and rudder-bulb system. The interaction between propeller and rudder-bulb was taken into account by velocity potential iteration in which the influence of propeller rotation was considered by the average influence coefficient. In the influence coefficient computation, the singular value should be found and deleted. Numerical results showed that the method presented is effective for predicting the steady hydrodynamic performance of propeller-rudder system and propeller-rudder-bulb system. Comparing with the induced velocity iterative method, the method presented can save programming and calculation time. Changing dimensions, the principal parameter—bulb size that affect energy-saving effect was studied, the results show that the bulb on rudder have a optimal size at the design advance coefficient.

  10. A convergence analysis of the iteratively regularized Gauss–Newton method under the Lipschitz condition

    International Nuclear Information System (INIS)

    Jin Qinian

    2008-01-01

    In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense

  11. Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

    Science.gov (United States)

    Faria, Luiz; Rosales, Rodolfo

    2017-11-01

    We introduce an alternative to the method of matched asymptotic expansions. In the ``traditional'' implementation, approximate solutions, valid in different (but overlapping) regions are matched by using ``intermediate'' variables. Here we propose to match at the level of the equations involved, via a ``uniform expansion'' whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the ``simplest'' set of equations that capture the behavior. Ruben Rosales work was partially supported by NSF Grants DMS-1614043 and DMS-1719637.

  12. Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

    OpenAIRE

    Cury , Claire; Glaunès , Joan Alexis; Colliot , Olivier

    2014-01-01

    International audience; A common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centr...

  13. Iterative Method of Regularization with Application of Advanced Technique for Detection of Contours

    International Nuclear Information System (INIS)

    Niedziela, T.; Stankiewicz, A.

    2000-01-01

    This paper proposes a novel iterative method of regularization with application of an advanced technique for detection of contours. To eliminate noises, the properties of convolution of functions are utilized. The method can be accomplished in a simple neural cellular network, which creates the possibility of extraction of contours by automatic image recognition equipment. (author)

  14. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax{sup 2α} + Bx{sup 2}

    Energy Technology Data Exchange (ETDEWEB)

    Al Sdran, N. [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Najran University, Faculty of Sciences and Arts, Najran (Saudi Arabia); Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Thermal Process Laboratory Research and Technologies Centre of Energy, BP 95, 2050 Hammam-lif (Tunisia)

    2016-06-15

    The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x) = Ax{sup 2α} + Bx{sup 2}, (A>0, B<0), with (α = 2) for quadratic, (α =3) for sextic and (α =4) for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x) by a piecewise-linear potential v(x), while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  15. Iterative numerical solution of scattering problems

    International Nuclear Information System (INIS)

    Tomio, L.; Adhikari, S.K.

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10 10 after some-8-10 iterations. (author). 31 refs, 2 tabs

  16. Iterative methods used in overlap astrometric reduction techniques do not always converge

    Science.gov (United States)

    Rapaport, M.; Ducourant, C.; Colin, J.; Le Campion, J. F.

    1993-04-01

    In this paper we prove that the classical Gauss-Seidel type iterative methods used for the solution of the reduced normal equations occurring in overlapping reduction methods of astrometry do not always converge. We exhibit examples of divergence. We then analyze an alternative algorithm proposed by Wang (1985). We prove the consistency of this algorithm and verify that it can be convergent while the Gauss-Seidel method is divergent. We conjecture the convergence of Wang method for the solution of astrometric problems using overlap techniques.

  17. Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

    Science.gov (United States)

    Lavery, N.; Taylor, C.

    1999-07-01

    Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

  18. A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

    Science.gov (United States)

    Wu, S. T.; Sun, M. T.; Sakurai, Takashi

    1990-01-01

    This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

  19. Asymptotic expansion and statistical description of turbulent systems

    International Nuclear Information System (INIS)

    Hagan, W.K. III.

    1986-01-01

    A new approach to studying turbulent systems is presented in which an asymptotic expansion of the general dynamical equations is performed prior to the application of statistical methods for describing the evolution of the system. This approach has been applied to two specific systems: anomalous drift wave turbulence in plasmas and homogeneous, isotropic turbulence in fluids. For the plasma case, the time and length scales of the turbulent state result in the asymptotic expansion of the Vlasov/Poisson equations taking the form of nonlinear gyrokinetic theory. Questions regarding this theory and modern Hamiltonian perturbation methods are discussed and resolved. A new alternative Hamiltonian method is described. The Eulerian Direct Interaction Approximation (EDIA) is slightly reformulated and applied to the equations of nonlinear gyrokinetic theory. Using a similarity transformation technique, expressions for the thermal diffusivity are derived from the EDIA equations for various geometries, including a tokamak. In particular, the unique result for generalized geometry may be of use in evaluating fusion reactor designs and theories of anomalous thermal transport in tokamaks. Finally, a new and useful property of the EDIA is pointed out. For the fluid case, an asymptotic expansion is applied to the Navier-Stokes equation and the results lead to the speculation that such an approach may resolve the problem of predicting the Kolmogorov inertial range energy spectrum for homogeneous, isotropic turbulence. 45 refs., 3 figs

  20. Asymptotic iteration method for the modified Pöschl–Teller potential ...

    Indian Academy of Sciences (India)

    2017-01-04

    Jan 4, 2017 ... Relativistic energy equation is calculated numerically by the Matlab soft- ware. The increase in the radial quantum number nr causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical.

  1. Asymptotic iteration method for the modified Pöschl–Teller potential ...

    Indian Academy of Sciences (India)

    Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number nr causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system ...

  2. Iterative numerical solution of scattering problems

    Energy Technology Data Exchange (ETDEWEB)

    Tomio, L; Adhikari, S K

    1995-05-01

    An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10{sup 10} after some-8-10 iterations. (author). 31 refs, 2 tabs.

  3. Asymptotic symmetries of Rindler space at the horizon and null infinity

    International Nuclear Information System (INIS)

    Chung, Hyeyoun

    2010-01-01

    We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

  4. Nonlinear adaptive control system design with asymptotically stable parameter estimation error

    Science.gov (United States)

    Mishkov, Rumen; Darmonski, Stanislav

    2018-01-01

    The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

  5. International Conference on Boundary and Interior Layers : Computational and Asymptotic Methods

    CERN Document Server

    Kopteva, Natalia; O'Riordan, Eugene; Stynes, Martin

    2009-01-01

    These Proceedings contain a selection of the lectures given at the conference BAIL 2008: Boundary and Interior Layers – Computational and Asymptotic Methods, which was held from 28th July to 1st August 2008 at the University of Limerick, Ireland. The ?rst three BAIL conferences (1980, 1982, 1984) were organised by Professor John Miller in Trinity College Dublin, Ireland. The next seven were held in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth (2002),Toulouse(2004),and Got ¨ tingen(2006).With BAIL 2008the series returned to Ireland. BAIL 2010 is planned for Zaragoza. The BAIL conferences strive to bring together mathematicians and engineers whose research involves layer phenomena,as these two groups often pursue largely independent paths. BAIL 2008, at which both communities were well represented, succeeded in this regard. The lectures given were evenly divided between app- cations and theory, exposing all conference participants to a broad spectrum of research into problems e...

  6. Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well.

    Science.gov (United States)

    Du, Miao; Tian, Lixin; Wang, Jun; Zhang, Fubao

    2016-03-01

    In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V , K , a , and f , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.

  7. Dynamic RCS Simulation of a Missile Target Group Based on the High-frequency Asymptotic Method

    Directory of Open Access Journals (Sweden)

    Zhao Tao

    2014-04-01

    Full Text Available To simulate dynamic Radar Cross Section (RCS of missile target group, an efficient RCS prediction approach is proposed based on the high-frequency asymptotic theory. The minimal energy trajectory and coordinate transformation is used to get trajectories of the missile, decoys and roll booster, and establish the dynamic scene for the separate procedure of the target group, and the dynamic RCS including specular reflection, edge diffraction and multi-reflection from the target group are obtained by Physical Optics (PO, Equivalent Edge Currents (EEC and Shooting-and-Bouncing Ray (SBR methods. Compared with the dynamic RCS result with the common interpolation method, the proposed method is consistent with the common method when the targets in the scene are far away from each other and each target is not sheltered by others in the incident direction. When the target group is densely distributed and the shelter effect can not be neglected, the interpolation method is extremely difficult to realize, whereas the proposed method is successful.

  8. On the asymptotic stability of nonlinear mechanical switched systems

    Science.gov (United States)

    Platonov, A. V.

    2018-05-01

    Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

  9. ITER-FEAT operation

    International Nuclear Information System (INIS)

    Shimomura, Y.; Huguet, M.; Mizoguchi, T.; Murakami, Y.; Polevoi, A.R.; Shimada, M.; Aymar, R.; Chuyanov, V.A.; Matsumoto, H.

    2001-01-01

    ITER is planned to be the first fusion experimental reactor in the world operating for research in physics and engineering. The first ten years of operation will be devoted primarily to physics issues at low neutron fluence and the following ten years of operation to engineering testing at higher fluence. ITER can accommodate various plasma configurations and plasma operation modes, such as inductive high Q modes, long pulse hybrid modes and non-inductive steady state modes, with large ranges of plasma current, density, beta and fusion power, and with various heating and current drive methods. This flexibility will provide an advantage for coping with uncertainties in the physics database, in studying burning plasmas, in introducing advanced features and in optimizing the plasma performance for the different programme objectives. Remote sites will be able to participate in the ITER experiment. This concept will provide an advantage not only in operating ITER for 24 hours a day but also in involving the worldwide fusion community and in promoting scientific competition among the ITER Parties. (author)

  10. Asymptotic normalization coefficients and astrophysical factors

    International Nuclear Information System (INIS)

    Mukhamedzhanov, A.M.; Azhari, A.; Clark, H.L.; Gagliardi, C.A.; Lui, Y.-W.; Sattarov, A.; Trache, L.; Tribble, R.E.; Burjan, V.; Kroha, V.; Carstoiu, F.

    2000-01-01

    The S factor for the direct capture reaction 7 Be(p,γ) 8 B can be found at astrophysical energies from the asymptotic normalization coefficients (ANC's) which provide the normalization of the tails of the overlap functions for 8 B → 7 Be + p. Peripheral transfer reactions offer a technique to determine these ANC's. Using this technique, the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions have been used to measure the asymptotic normalization coefficient for 7 Be(p, γ) 8 B. These results provide an indirect determination of S 17 (0). Analysis of the existing 9 Be(p, γ) 10 B experimental data within the framework of the R-matrix method demonstrates that experimentally measured ANC's can provide a reasonable determination of direct radiative capture rates. (author)

  11. Statistics of electron multiplication in multiplier phototube: iterative method

    International Nuclear Information System (INIS)

    Grau Malonda, A.; Ortiz Sanchez, J.F.

    1985-01-01

    An iterative method is applied to study the variation of dynode response in the multiplier phototube. Three different situations are considered that correspond to the following ways of electronic incidence on the first dynode: incidence of exactly one electron, incidence of exactly r electrons and incidence of an average anti-r electrons. The responses are given for a number of steps between 1 and 5, and for values of the multiplication factor of 2.1, 2.5, 3 and 5. We study also the variance, the skewness and the excess of jurtosis for different multiplication factors. (author)

  12. Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories

    International Nuclear Information System (INIS)

    Gusynin, V.P.; Miranskij, V.A.

    1986-01-01

    An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed

  13. An iterative method for the analysis of Cherenkov rings in the HERA-B RICH

    International Nuclear Information System (INIS)

    Staric, M.; Krizan, P.

    1999-01-01

    A new method is presented for the analysis of data recorded with a Ring Imaging Cherenkov (RICH) counter. The method, an iterative sorting of hits on the photon detector, is particularly useful for events where rings overlap considerably. The algorithm was tested on simulated data for the HERA-B experiment

  14. Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Farouq, S.; Neytcheva, M.

    2017-01-01

    Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

  15. Monte Carlo methods in PageRank computation: When one iteration is sufficient

    NARCIS (Netherlands)

    Avrachenkov, K.; Litvak, Nelli; Nemirovsky, D.; Osipova, N.

    2005-01-01

    PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method which requires

  16. Monte Carlo methods in PageRank computation: When one iteration is sufficient

    NARCIS (Netherlands)

    Avrachenkov, K.; Litvak, Nelli; Nemirovsky, D.; Osipova, N.

    PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer, and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method, which requires

  17. Iterative raw measurements restoration method with penalized weighted least squares approach for low-dose CT

    Science.gov (United States)

    Takahashi, Hisashi; Goto, Taiga; Hirokawa, Koichi; Miyazaki, Osamu

    2014-03-01

    Statistical iterative reconstruction and post-log data restoration algorithms for CT noise reduction have been widely studied and these techniques have enabled us to reduce irradiation doses while maintaining image qualities. In low dose scanning, electronic noise becomes obvious and it results in some non-positive signals in raw measurements. The nonpositive signal should be converted to positive signal so that it can be log-transformed. Since conventional conversion methods do not consider local variance on the sinogram, they have difficulty of controlling the strength of the filtering. Thus, in this work, we propose a method to convert the non-positive signal to the positive signal by mainly controlling the local variance. The method is implemented in two separate steps. First, an iterative restoration algorithm based on penalized weighted least squares is used to mitigate the effect of electronic noise. The algorithm preserves the local mean and reduces the local variance induced by the electronic noise. Second, smoothed raw measurements by the iterative algorithm are converted to the positive signal according to a function which replaces the non-positive signal with its local mean. In phantom studies, we confirm that the proposed method properly preserves the local mean and reduce the variance induced by the electronic noise. Our technique results in dramatically reduced shading artifacts and can also successfully cooperate with the post-log data filter to reduce streak artifacts.

  18. A new ART iterative method and a comparison of performance among various ART methods

    International Nuclear Information System (INIS)

    Tan, Yufeng; Sato, Shunsuke

    1993-01-01

    Many algebraic reconstruction techniques (ART) image reconstruction algorithms, for instance, simultaneous iterative reconstruction technique (SIRT), the relaxation method and multiplicative ART (MART), have been proposed and their convergent properties have been studied. SIRT and the underrelaxed relaxation method converge to the least-squares solution, but the convergent speeds are very slow. The Kaczmarz method converges very quickly, but the reconstructed images contain a lot of noise. The comparative studies between these algorithms have been done by Gilbert and others, but are not adequate. In this paper, we (1) propose a new method which is a modified Kaczmarz method and prove its convergence property, (2) study performance of 7 algorithms including the one proposed here by computer simulation for 3 kinds of typical phantoms. The method proposed here does not give the least-square solution, but the root mean square errors of its reconstructed images decrease very quickly after few interations. The result shows that the method proposed here gives a better reconstructed image. (author)

  19. Asymptotic solution for the El Niño time delay sea—air oscillator model

    International Nuclear Information System (INIS)

    Mo Jia-Qi; Lin Wan-Tao; Lin Yi-Hua

    2011-01-01

    A sea—air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Niño-southern oscillation (ENSO) model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities. (general)

  20. Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

    International Nuclear Information System (INIS)

    Griffin, J.J.; Dworzecka, M.

    1982-01-01

    The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

  1. Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Farouq, S.; Neytcheva, M.

    2017-01-01

    Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution method s * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

  2. An iterative method for accelerated degradation testing data of smart electricity meter

    Science.gov (United States)

    Wang, Xiaoming; Xie, Jinzhe

    2017-01-01

    In order to evaluate the performance of smart electricity meter (SEM), we must spend a lot of time censoring its status. For example, if we assess to the meter stability of the SEM which needs several years at least according to the standards. So accelerated degradation testing (ADT) is a useful method to assess the performance of the SEM. As we known, the Wiener process is a prevalent method to interpret the performance degradation. This paper proposes an iterative method for ADT data of SEM. The simulation study verifies the application and superiority of the proposed model than other ADT methods.

  3. Development of an iterative 3D reconstruction method for the control of heavy-ion oncotherapy with PET

    International Nuclear Information System (INIS)

    Lauckner, K.

    1999-06-01

    The dissertation reports the approach and work for developing and implementing an image space reconstruction method that allows to check the 3D activity distribution and detect possible deviations from irradiation planning data. Other than usual PET scanners, the BASTEI instrument is equipped with two detectors positioned at opposite sides above and below the patient, so that there is enough space for suitable positioning of patient and radiation source. Due to the restricted field of view of the positron camera, the 3D imaging process is subject to displacement-dependent variations, creating bad reconstruction conditions. In addition, the counting rate is lower by two or three orders of magnitude than the usual counting rates of nuclear-medicine PET applications. This is why an iterative 3D algorithm is needed. Two iterative methods known from conventional PET were examined for their suitability and compared with respect to results. The MLEM algorithm proposed by Shepp and Vardi interprets the measured data as a random sample of independent variables of Poisson distributions, to be used for assessing the unknown activity distribution. A disadvantage of this algorithm is the considerable calculation effort required. For minimizing the calculation effort, and in order to make iterative statistical methods applicable to measured 3D data, Daube-Whitherspoon and Muehllehner developed the Iterative Image Space Reconstruction Algorithm, ISRA, derived through modification of the sequence of development steps of the MLEM algorithm. Problem solution with ISRA is based on least square deviation method, other than with the MLEM algorithm which uses the best probability method. (orig./CB) [de

  4. Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...

    African Journals Online (AJOL)

    Asymptotic representation theorems for poverty indices ... Statistical asymptotic laws for these indices, particularly asymptotic normality, on which statistical inference on the ... population of individuals, each of which having a random income or ...

  5. Asymptotic safety, emergence and minimal length

    International Nuclear Information System (INIS)

    Percacci, Roberto; Vacca, Gian Paolo

    2010-01-01

    There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that (1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and (2) there is a sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.

  6. Solving Ratio-Dependent Predatorprey System with Constant Effort Harvesting Using Variational Iteration Method

    DEFF Research Database (Denmark)

    Ghotbi, Abdoul R; Barari, Amin

    2009-01-01

    Due to wide range of interest in use of bio-economic models to gain insight in to the scientific management of renewable resources like fisheries and forestry, variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort...

  7. Asymptotic Poincare lemma and its applications

    International Nuclear Information System (INIS)

    Ziolkowski, R.W.; Deschamps, G.A.

    1984-01-01

    An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures

  8. Renormalization group and asymptotic freedom

    International Nuclear Information System (INIS)

    Morris, J.R.

    1978-01-01

    Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

  9. Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations

    Science.gov (United States)

    Hoogenboom, J. Eduard; Dufek, Jan

    2014-06-01

    This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.

  10. Optimized iteration in coupled Monte-Carlo - Thermal-hydraulics calculations

    International Nuclear Information System (INIS)

    Hoogenboom, J.E.; Dufek, J.

    2013-01-01

    This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration methods are also tested and it is concluded that the presented iteration method is near optimal. (authors)

  11. A Comparison of Iterative 2D-3D Pose Estimation Methods for Real-Time Applications

    DEFF Research Database (Denmark)

    Grest, Daniel; Krüger, Volker; Petersen, Thomas

    2009-01-01

    This work compares iterative 2D-3D Pose Estimation methods for use in real-time applications. The compared methods are available for public as C++ code. One method is part of the openCV library, namely POSIT. Because POSIT is not applicable for planar 3Dpoint congurations, we include the planar P...

  12. Asymptotic Stabilization of Non-holonomic Port-controlled Hamiltonian Systems

    DEFF Research Database (Denmark)

    Sørensen, Mathias Jesper; Bendtsen, Jan Dimon; Andersen, Palle

    2004-01-01

    A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mob...

  13. A necessary and sufficient condition for the convergence of an AOR iterative method

    International Nuclear Information System (INIS)

    Hu Jiagan

    1992-01-01

    In this paper, a necessary and sufficient condition for the convergence of an AOR iterative method is given under the condition that the coefficient matrix A is consistently ordered and the eigenvalues of the Jacobi matrix of A are all real. With the same method the condition for the convergence of t he extrapolation Gauss-Seidel (EGS) method is also obtained. As an example, the conditions for the model problem are given. The rate of convergence of the EGS method is about twice that of the GS method

  14. The structure analysis of ITER cryostat based on the finite element method

    International Nuclear Information System (INIS)

    Liang Chao; Ye, M.Y.; Yao, D.M.; Cao, Lei; Zhou, Z.B.; Xu, Teijun; Wang Jian

    2013-01-01

    In the ITER project the cryostat is one of the most important components. Cryostat shall transfer all the loads that derive from the TOKAMAK inner basic machine, and from the cryostat itself, to the floor of the TOKAMAK pit (during the normal and off-normal operational regimes, and at specified accidental conditions). This paper researches the dynamic structure strength of the ITER cryostat during the operation of TOKAMAK. Firstly the paper introduces the types of loads and the importance of every type load to the research. Then it gives out the method of building model and principle of simplified model, boundary conditions and the way of applying loads on the cryostat. Finally the author discussed the analysis result and the strength questions of cryostat, also, the author pointed out the opinions according to the analysis results.

  15. Modeling broadband poroelastic propagation using an asymptotic approach

    Energy Technology Data Exchange (ETDEWEB)

    Vasco, Donald W.

    2009-05-01

    An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.

  16. Experimental results and validation of a method to reconstruct forces on the ITER test blanket modules

    International Nuclear Information System (INIS)

    Zeile, Christian; Maione, Ivan A.

    2015-01-01

    Highlights: • An in operation force measurement system for the ITER EU HCPB TBM has been developed. • The force reconstruction methods are based on strain measurements on the attachment system. • An experimental setup and a corresponding mock-up have been built. • A set of test cases representing ITER relevant excitations has been used for validation. • The influence of modeling errors on the force reconstruction has been investigated. - Abstract: In order to reconstruct forces on the test blanket modules in ITER, two force reconstruction methods, the augmented Kalman filter and a model predictive controller, have been selected and developed to estimate the forces based on strain measurements on the attachment system. A dedicated experimental setup with a corresponding mock-up has been designed and built to validate these methods. A set of test cases has been defined to represent possible excitation of the system. It has been shown that the errors in the estimated forces mainly depend on the accuracy of the identified model used by the algorithms. Furthermore, it has been found that a minimum of 10 strain gauges is necessary to allow for a low error in the reconstructed forces.

  17. Asymptotics of Laplace-Dirichlet integrals

    International Nuclear Information System (INIS)

    Kozlov, S.M.

    1990-01-01

    Here we consider the problem of the asymptotic expansion of the Laplace-Dirichlet integral. In homogenization theory such an integral represents the energy, and in general depends on the cohomology class. Here the asymptotic behaviour of this integral is found. The full text will appear in Functional Analysis and Applications, 1990, No.2. (author). 3 refs

  18. Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

    International Nuclear Information System (INIS)

    Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

    2009-01-01

    The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

  19. On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Bai, Z.-Z.; Rozložník, Miroslav

    2015-01-01

    Roč. 53, č. 4 (2015), s. 1716-1737 ISSN 0036-1429 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : matrix splitting * stationary iteration method * backward error * rounding error analysis Subject RIV: BA - General Mathematics Impact factor: 1.899, year: 2015

  20. Asymptotic conditions and conserved quantities

    International Nuclear Information System (INIS)

    Koul, R.K.

    1990-01-01

    Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C 1 . In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q ab , P ab ) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background

  1. Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-01-01

    Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

  2. Asymptotic mass degeneracies in conformal field theories

    International Nuclear Information System (INIS)

    Kani, I.; Vafa, C.

    1990-01-01

    By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli. (orig.)

  3. Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

    Directory of Open Access Journals (Sweden)

    A. A. Hemeda

    2013-01-01

    Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

  4. Asymptotic boundary conditions for dissipative waves: General theory

    Science.gov (United States)

    Hagstrom, Thomas

    1990-01-01

    An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

  5. Asymptotic boundary conditions for dissipative waves - General theory

    Science.gov (United States)

    Hagstrom, Thomas

    1991-01-01

    An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

  6. Trinucleon asymptotic normalization constants including Coulomb effects

    International Nuclear Information System (INIS)

    Friar, J.L.; Gibson, B.F.; Lehman, D.R.; Payne, G.L.

    1982-01-01

    Exact theoretical expressions for calculating the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Coordinate-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the D-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the 3 He S-wave asymptotic norm by less than 1% relative to that of 3 H, that Coulomb effects decrease the 3 He D-wave asymptotic norm by approximately 8% relative to that of 3 H, and that the distorted-wave Born approximation D-state parameter, D 2 , is only 1% smaller in magnitude for 3 He than for 3 H due to compensating Coulomb effects

  7. Asymptotic solutions and spectral theory of linear wave equations

    International Nuclear Information System (INIS)

    Adam, J.A.

    1982-01-01

    This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

  8. Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

    Directory of Open Access Journals (Sweden)

    G. M. N’Guérékata

    2018-01-01

    Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

  9. Analysis of Iterated Hard Decision Decoding of Product Codes with Reed-Solomon Component Codes

    DEFF Research Database (Denmark)

    Justesen, Jørn; Høholdt, Tom

    2007-01-01

    Products of Reed-Solomon codes are important in applications because they offer a combination of large blocks, low decoding complexity, and good performance. A recent result on random graphs can be used to show that with high probability a large number of errors can be corrected by iterating...... minimum distance decoding. We present an analysis related to density evolution which gives the exact asymptotic value of the decoding threshold and also provides a closed form approximation to the distribution of errors in each step of the decoding of finite length codes....

  10. Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

    International Nuclear Information System (INIS)

    Costa, Carlos A N; Campos, Itamara S; Costa, Jessé C; Neto, Francisco A; Schleicher, Jörg; Novais, Amélia

    2013-01-01

    Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality. (paper)

  11. A non-iterative twin image elimination method with two in-line digital holograms

    Science.gov (United States)

    Kim, Jongwu; Lee, Heejung; Jeon, Philjun; Kim, Dug Young

    2018-02-01

    We propose a simple non-iterative in-line holographic measurement method which can effectively eliminate a twin image in digital holographic 3D imaging. It is shown that a twin image can be effectively eliminated with only two measured holograms by using a simple numerical propagation algorithm and arithmetic calculations.

  12. Iterative regularization in intensity-modulated radiation therapy optimization

    International Nuclear Information System (INIS)

    Carlsson, Fredrik; Forsgren, Anders

    2006-01-01

    A common way to solve intensity-modulated radiation therapy (IMRT) optimization problems is to use a beamlet-based approach. The approach is usually employed in a three-step manner: first a beamlet-weight optimization problem is solved, then the fluence profiles are converted into step-and-shoot segments, and finally postoptimization of the segment weights is performed. A drawback of beamlet-based approaches is that beamlet-weight optimization problems are ill-conditioned and have to be regularized in order to produce smooth fluence profiles that are suitable for conversion. The purpose of this paper is twofold: first, to explain the suitability of solving beamlet-based IMRT problems by a BFGS quasi-Newton sequential quadratic programming method with diagonal initial Hessian estimate, and second, to empirically show that beamlet-weight optimization problems should be solved in relatively few iterations when using this optimization method. The explanation of the suitability is based on viewing the optimization method as an iterative regularization method. In iterative regularization, the optimization problem is solved approximately by iterating long enough to obtain a solution close to the optimal one, but terminating before too much noise occurs. Iterative regularization requires an optimization method that initially proceeds in smooth directions and makes rapid initial progress. Solving ten beamlet-based IMRT problems with dose-volume objectives and bounds on the beamlet-weights, we find that the considered optimization method fulfills the requirements for performing iterative regularization. After segment-weight optimization, the treatments obtained using 35 beamlet-weight iterations outperform the treatments obtained using 100 beamlet-weight iterations, both in terms of objective value and of target uniformity. We conclude that iterating too long may in fact deteriorate the quality of the deliverable plan

  13. Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems

    DEFF Research Database (Denmark)

    Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

    2011-01-01

    The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...

  14. Novel manufacturing method by using stainless steel pipes expanded into aluminium profiles for the ITER Neutral Beam cryopumps

    Energy Technology Data Exchange (ETDEWEB)

    Dremel, Matthias, E-mail: matthias.dremel@iter.org; Boissin, Jean-Claude; Déléage, Vincent; Quinn, Eamonn; Pearce, Robert

    2015-10-15

    This paper describes the novel engineering and manufacturing solution of stainless steel pipe expansion into aluminium extrusion profiles for use at cryogenic temperatures up to 400 K. This fabrication method will be used for the thermal radiation shields and the cryopanels of the ITER Neutral Beam cryopumps. The use of stainless steel pipes expanded into aluminium extrusion profiles is a solution that combines standard stainless steel welding procedures for the manifolds of the cooling circuits with extended aluminium structures taking advantage of the high thermal conductivity of aluminium. The cryogenic cooling circuits of the pump are a first confinement barrier in the ITER vacuum vessel and the risk of a leakage needs to be minimized as far as possible. The expansion method avoids the need of joints of dissimilar materials in the primary confinement barrier. The fabrication method and results of the prototyping of full scaled components for the ITER Neutral Beam cryopumps are outlined in this paper.

  15. Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Mashinchi Joubari

    2015-01-01

    Full Text Available In this paper, we implemented the Modified Iteration Perturbation Method (MIPM for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need to complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.

  16. A Method for Speeding Up Value Iteration in Partially Observable Markov Decision Processes

    OpenAIRE

    Zhang, Nevin Lianwen; Lee, Stephen S.; Zhang, Weihong

    2013-01-01

    We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov decision processes (MDPs). The technique can be easily incorporated into any existing POMDP value iteration algorithms. Experiments have been conducted on several test problems with one POMDP value iteration algorithm called incremental pruning. We find that th...

  17. On maximal surfaces in asymptotically flat space-times

    International Nuclear Information System (INIS)

    Bartnik, R.; Chrusciel, P.T.; O Murchadha, N.

    1990-01-01

    Existence of maximal and 'almost maximal' hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurface can be used to 'partially fix' an asymptotic Poincare group. (orig.)

  18. Modified variational iteration method for an El Niño Southern Oscillation delayed oscillator

    International Nuclear Information System (INIS)

    Cao Xiao-Qun; Song Jun-Qiang; Zhu Xiao-Qian; Zhang Li-Lun; Zhang Wei-Min; Zhao Jun

    2012-01-01

    This paper studies a delayed air—sea coupled oscillator describing the physical mechanism of El Niño Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model. (general)

  19. Numerical doubly-periodic solution of the (2+1)-dimensional Boussinesq equation with initial conditions by the variational iteration method

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2007-01-01

    In this Letter, a scheme is developed to study numerical doubly-periodic solutions of the (2+1)-dimensional Boussinesq equation with initial condition by the variational iteration method. As a result, the approximate and exact doubly-periodic solutions are obtained. For different modulus m, comparison between the approximate solution and the exact solution is made graphically, revealing that the variational iteration method is a powerful and effective tool to non-linear problems

  20. Computation of fields in an arbitrarily shaped heterogeneous dielectric or biological body by an iterative conjugate gradient method

    International Nuclear Information System (INIS)

    Wang, J.J.H.; Dubberley, J.R.

    1989-01-01

    Electromagnetic (EM) fields in a three-dimensional, arbitrarily shaped heterogeneous dielectric or biological body illuminated by a plane wave are computed by an iterative conjugate gradient method. The method is a generalized method of moments applied to the volume integral equation. Because no matrix is explicitly involved or stored, the present iterative method is capable of computing EM fields in objects an order of magnitude larger than those that can be handled by the conventional method of moments. Excellent numerical convergence is achieved. Perfect convergence to the result of the conventional moment method using the same basis and weighted with delta functions is consistently achieved in all the cases computed, indicating that these two algorithms (direct and interactive) are equivalent

  1. NITSOL: A Newton iterative solver for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)

    1996-12-31

    Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

  2. New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

    Directory of Open Access Journals (Sweden)

    Mohamed S. Al-luhaibi

    2015-01-01

    Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

  3. The Asymptotic Behavior of Particle Size Distribution Undergoing Brownian Coagulation Based on the Spline-Based Method and TEMOM Model

    Directory of Open Access Journals (Sweden)

    Qing He

    2018-01-01

    Full Text Available In this paper, the particle size distribution is reconstructed using finite moments based on a converted spline-based method, in which the number of linear system of equations to be solved reduced from 4m × 4m to (m + 3 × (m + 3 for (m + 1 nodes by using cubic spline compared to the original method. The results are verified by comparing with the reference firstly. Then coupling with the Taylor-series expansion moment method, the evolution of particle size distribution undergoing Brownian coagulation and its asymptotic behavior are investigated.

  4. On asymptotic continuity of functions of quantum states

    International Nuclear Information System (INIS)

    Synak-Radtke, Barbara; Horodecki, Michal

    2006-01-01

    A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this letter, we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called robustness under admixture. This allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous. Subsequently, we consider arrowing-a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples. (letter to the editor)

  5. Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

    Science.gov (United States)

    Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

    2017-11-01

    Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

  6. Dose rate evaluation of body phantom behind ITER bio-shield wall using Monte Carlo method

    International Nuclear Information System (INIS)

    Beheshti, A.; Jabbari, I.; Karimian, A.; Abdi, M.

    2012-01-01

    One of the most critical risks to humans in reactors environment is radiation exposure. Around the tokamak hall personnel are exposed to a wide range of particles, including neutrons and photons. International Thermonuclear Experimental Reactor (ITER) is a nuclear fusion research and engineering project, which is the most advanced experimental tokamak nuclear fusion reactor. Dose rates assessment and photon radiation due to the neutron activation of the solid structures in ITER is important from the radiological point of view. Therefore, the dosimetry considered in this case is based on the Deuterium-Tritium (DT) plasma burning with neutrons production rate at 14.1 MeV. The aim of this study is assessment the amount of radiation behind bio-shield wall that a human received during normal operation of ITER by considering neutron activation and delay gammas. To achieve the aim, the ITER system and its components were simulated by Monte Carlo method. Also to increase the accuracy and precision of the absorbed dose assessment a body phantom were considered in the simulation. The results of this research showed that total dose rates level near the outside of bio-shield wall of the tokamak hall is less than ten percent of the annual occupational dose limits during normal operation of ITER and It is possible to learn how long human beings can remain in that environment before the body absorbs dangerous levels of radiation. (authors)

  7. A successive over-relaxation for slab geometry Simplified SN method with interface flux iteration

    International Nuclear Information System (INIS)

    Yavuz, M.

    1995-01-01

    A Successive Over-Relaxation scheme is proposed for speeding up the solution of one-group slab geometry transport problems using a Simplified S N method. The solution of the Simplified S N method that is completely free from all spatial truncation errors is based on the expansion of the angular flux in spherical-harmonics solutions. One way to obtain the (numerical) solution of the Simplified S N method is to use Interface Flux Iteration, which can be considered as the Gauss-Seidel relaxation scheme; the new information is immediately used in the calculations. To accelerate the convergence, an over relaxation parameter is employed in the solution algorithm. The over relaxation parameters for a number of cases depending on scattering ratios and mesh sizes are determined by Fourier analyzing infinite-medium Simplified S 2 equations. Using such over relaxation parameters in the iterative scheme, a significant increase in the convergence of transport problems can be achieved for coarse spatial cells whose spatial widths are greater than one mean-free-path

  8. Asymptotic techniques in elastic-plastic analysis of structures

    International Nuclear Information System (INIS)

    Sayir, M.

    1983-01-01

    Elastic-plastic structures can nowadays be analyzed with the powerful numerical procedures of the finite element method. Nevertheless, in many engineering applications, analytical expressions capable of predicting with sufficient accuracy the stress distributions, the extent of the plastic zones and the load displacement behaviour could be of great practical value. For simple structures and loading stages not too far from the elastic limit, such analytical expressions may be obtained by using perturbation methods and asymptotic expansions. A small dimensionless parameter epsilon is defined as the ratio of a length characterizing the extent of the narrow plastic zone, to a conveniently chosen typical dimension of the structure. Stresses and displacements are formally expanded as asymptotic series in terms of powers of epsilon. For each order of magnitude, the exact basic relations lead to a separate set of simplified differential equations which can be integrated analytically or numerically by using standard procedures. The method is very general and can be applied to several classes of plastic behaviour and of structural problems. Three examples of very simple structures are chosen in particular to illustrate the applicability of the perturbation method to engineering problems. (orig./RW)

  9. Direct deterministic method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor

    International Nuclear Information System (INIS)

    Terry, W.K.; Gougar, H.D.; Ougouag, A.M.

    2002-01-01

    A new deterministic method has been developed for the neutronics analysis of a pebble-bed reactor (PBR). The method accounts for the flow of pebbles explicitly and couples the flow to the neutronics. The method allows modeling of once-through cycles as well as cycles in which pebbles are recirculated through the core an arbitrary number of times. This new work is distinguished from older methods by the systematically semi-analytical approach it takes. In particular, whereas older methods use the finite-difference approach (or an equivalent one) for the discretization and the solution of the burnup equation, the present work integrates the relevant differential equation analytically in discrete and complementary sub-domains of the reactor. Like some of the finite-difference codes, the new method obtains the asymptotic fuel-loading pattern directly, without modeling any intermediate loading pattern. This is a significant advantage for the design and optimization of the asymptotic fuel-loading pattern. The new method is capable of modeling directly both the once-through-then-out fuel cycle and the pebble recirculating fuel cycle. Although it currently includes a finite-difference neutronics solver, the new method has been implemented into a modular code that incorporates the framework for the future coupling to an efficient solver such as a nodal method and to modern cross section preparation capabilities. In its current state, the deterministic method presented here is capable of quick and efficient design and optimization calculations for the in-core PBR fuel cycle. The method can also be used as a practical 'scoping' tool. It could, for example, be applied to determine the potential of the PBR for resisting nuclear-weapons proliferation and to optimize proliferation-resistant features. However, the purpose of this paper is to show that the method itself is viable. Refinements to the code are under way, with the objective of producing a powerful reactor physics

  10. Stationary solutions and asymptotic flatness I

    International Nuclear Information System (INIS)

    Reiris, Martin

    2014-01-01

    In general relativity, a stationary isolated system is defined as an asymptotically flat (AF) stationary spacetime with compact material sources. Other definitions that are less restrictive on the type of asymptotic could in principle be possible. Between this article and its sequel, we show that under basic assumptions, asymptotic flatness indeed follows as a consequence of Einstein's theory. In particular, it is proved that any vacuum stationary spacetime-end whose (quotient) manifold is diffeomorphic to R 3 minus a ball and whose Killing field has its norm bounded away from zero, is necessarily AF with Schwarzschildian fall off. The ‘excised’ ball would contain (if any) the actual material body, but this information is unnecessary to reach the conclusion. In this first article, we work with weakly asymptotically flat (WAF) stationary ends, a notion that generalizes as much as possible that of the AF end, and prove that WAF ends are AF with Schwarzschildian fall off. Physical and mathematical implications are also discussed. (paper)

  11. Asymptotic variance of grey-scale surface area estimators

    DEFF Research Database (Denmark)

    Svane, Anne Marie

    Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....

  12. ITER-FEAT operation

    International Nuclear Information System (INIS)

    Shimomura, Y.; Huget, M.; Mizoguchi, T.; Murakami, Y.; Polevoi, A.; Shimada, M.; Aymar, R.; Chuyanov, V.; Matsumoto, H.

    2001-01-01

    ITER is planned to be the first fusion experimental reactor in the world operating for research in physics and engineering. The first 10 years' operation will be devoted primarily to physics issues at low neutron fluence and the following 10 years' operation to engineering testing at higher fluence. ITER can accommodate various plasma configurations and plasma operation modes such as inductive high Q modes, long pulse hybrid modes, non-inductive steady-state modes, with large ranges of plasma current, density, beta and fusion power, and with various heating and current drive methods. This flexibility will provide an advantage for coping with uncertainties in the physics database, in studying burning plasmas, in introducing advanced features and in optimizing the plasma performance for the different programme objectives. Remote sites will be able to participate in the ITER experiment. This concept will provide an advantage not only in operating ITER for 24 hours per day but also in involving the world-wide fusion communities and in promoting scientific competition among the Parties. (author)

  13. Radiation pattern synthesis of planar antennas using the iterative sampling method

    Science.gov (United States)

    Stutzman, W. L.; Coffey, E. L.

    1975-01-01

    A synthesis method is presented for determining an excitation of an arbitrary (but fixed) planar source configuration. The desired radiation pattern is specified over all or part of the visible region. It may have multiple and/or shaped main beams with low sidelobes. The iterative sampling method is used to find an excitation of the source which yields a radiation pattern that approximates the desired pattern to within a specified tolerance. In this paper the method is used to calculate excitations for line sources, linear arrays (equally and unequally spaced), rectangular apertures, rectangular arrays (arbitrary spacing grid), and circular apertures. Examples using these sources to form patterns with shaped main beams, multiple main beams, shaped sidelobe levels, and combinations thereof are given.

  14. Performance Analysis of Fission and Surface Source Iteration Method for Domain Decomposed Monte Carlo Whole-Core Calculation

    International Nuclear Information System (INIS)

    Jo, Yu Gwon; Oh, Yoo Min; Park, Hyang Kyu; Park, Kang Soon; Cho, Nam Zin

    2016-01-01

    In this paper, two issues in the FSS iteration method, i.e., the waiting time for surface source data and the variance biases in local tallies are investigated for the domain decomposed, 3-D continuous-energy whole-core calculation. The fission sources are provided as usual, while the surface sources are provided by banking MC particles crossing local domain boundaries. The surface sources serve as boundary conditions for nonoverlapping local problems, so that each local problem can be solved independently. In this paper, two issues in the FSS iteration are investigated. One is quantifying the waiting time of processors to receive surface source data. By using nonblocking communication, 'time penalty' to wait for the arrival of the surface source data is reduced. The other important issue is underestimation of the sample variance of the tally because of additional inter-iteration correlations in surface sources. From the numerical results on a 3-D whole-core test problem, it is observed that the time penalty is negligible in the FSS iteration method and that the real variances of both pin powers and assembly powers are estimated by the HB method. For those purposes, three cases; Case 1 (1 local domain), Case 2 (4 local domains), Case 3 (16 local domains) are tested. For both Cases 2 and 3, the time penalties for waiting are negligible compared to the source-tracking times. However, for finer divisions of local domains, the loss of parallel efficiency caused by the different number of sources for local domains in symmetric locations becomes larger due to the stochastic errors in source distributions. For all test cases, the HB method very well estimates the real variances of local tallies. However, it is also noted that the real variances of local tallies estimated by the HB method show slightly smaller than the real variances obtained from 30 independent batch runs and the deviations become larger for finer divisions of local domains. The batch size used for the HB

  15. Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

    Directory of Open Access Journals (Sweden)

    Zhanhua Yu

    2011-01-01

    Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

  16. Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

    Directory of Open Access Journals (Sweden)

    Maria Crespo

    2017-08-01

    Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

  17. Globally Asymptotic Stability of Stochastic Nonlinear Systems by the Output Feedback

    Directory of Open Access Journals (Sweden)

    Wenwen Cheng

    2015-01-01

    the traditional mathematical induction method. Indeed, we develop a new method to study the globally asymptotic stability by introducing a series of specific inequalities. Moreover, an example and its simulations are given to illustrate the theoretical result.

  18. Statistics of electron multiplication in a multiplier phototube; Iterative method

    International Nuclear Information System (INIS)

    Ortiz, J. F.; Grau, A.

    1985-01-01

    In the present paper an iterative method is applied to study the variation of dynode response in the multiplier phototube. Three different situation are considered that correspond to the following ways of electronic incidence on the first dynode: incidence of exactly one electron, incidence of exactly r electrons and incidence of an average r electrons. The responses are given for a number of steps between 1 and 5, and for values of the multiplication factor of 2.1, 2.5, 3 and 5. We study also the variance, the skewness and the excess of jurtosis for different multiplication factors. (Author) 11 refs

  19. The ITER remote maintenance system

    International Nuclear Information System (INIS)

    Tesini, A.; Palmer, J.

    2008-01-01

    The aim of this paper is to summarize the ITER approach to machine components maintenance. A major objective of the ITER project is to demonstrate that a future power producing fusion device can be maintained effectively and offer practical levels of plant availability. During its operational lifetime, many systems of the ITER machine will require maintenance and modification; this can be achieved using remote handling methods. The need for timely, safe and effective remote operations on a machine as complex as ITER and within one of the world's most hostile remote handling environments represents a major challenge at every level of the ITER Project organization, engineering and technology. The basic principles of fusion reactor maintenance are presented. An updated description of the ITER remote maintenance system is provided. This includes the maintenance equipment used inside the vacuum vessel, inside the hot cell and the hot cell itself. The correlation between the functions of the remote handling equipment, of the hot cell and of the radwaste processing system is also described. The paper concludes that ITER has equipped itself with a good platform to tackle the challenges presented by its own maintenance and upgrade needs

  20. Deep inelastic scattering in an asymptotically free gauge theory

    International Nuclear Information System (INIS)

    Fujiwara, Tsutomu

    1977-01-01

    This paper reviews the success of the asymptotically free gauge theory which describes the deep inelastic lepton-hadron scattering. The asymptotically free gauge theory was discussed as well as the reason why the parton has the nature like free particles by the aid of the field theory. The asymptotically free gauge theory (AFGT) gives the prediction that the Bjorken scaling gives rise to logarithmic violation. The theory was applied to the exchange processes of single photon and two photons. First, this paper describes the approaches to the Bjorken scaling. The approaches are the discussion of the scaling law dependent on the model and the discussion of the scaling law independent of the model. The field theoretical treatment in described. This is called the method of the renormalization group introduced by Wilson. The asymptotically free gauge theory was formed on the basis of the Callan-Symanzik equation (CSE) and of the Weinberg's power counting theorem. The exact Bjorken scaling does not hold in the quantum field theory, at least there must be logarithmic violation. The pattern of the scaling violation cannot be clarified by the present data. Discussions concerning two gamma process are presented. The measurement of the photon-photon scattering process will give the judgement whether the prediction of the AFGT is correct or not. (Kato, T.)

  1. Asymptotic behavior and stability of second order neutral delay differential equations

    NARCIS (Netherlands)

    Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd

    2014-01-01

    We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed

  2. An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

    Science.gov (United States)

    Zhang, B.; Sang, Jun; Alam, Mohammad S.

    2013-03-01

    An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.

  3. AN AUTOMATIC OPTICAL AND SAR IMAGE REGISTRATION METHOD USING ITERATIVE MULTI-LEVEL AND REFINEMENT MODEL

    Directory of Open Access Journals (Sweden)

    C. Xu

    2016-06-01

    Full Text Available Automatic image registration is a vital yet challenging task, particularly for multi-sensor remote sensing images. Given the diversity of the data, it is unlikely that a single registration algorithm or a single image feature will work satisfactorily for all applications. Focusing on this issue, the mainly contribution of this paper is to propose an automatic optical-to-SAR image registration method using –level and refinement model: Firstly, a multi-level strategy of coarse-to-fine registration is presented, the visual saliency features is used to acquire coarse registration, and then specific area and line features are used to refine the registration result, after that, sub-pixel matching is applied using KNN Graph. Secondly, an iterative strategy that involves adaptive parameter adjustment for re-extracting and re-matching features is presented. Considering the fact that almost all feature-based registration methods rely on feature extraction results, the iterative strategy improve the robustness of feature matching. And all parameters can be automatically and adaptively adjusted in the iterative procedure. Thirdly, a uniform level set segmentation model for optical and SAR images is presented to segment conjugate features, and Voronoi diagram is introduced into Spectral Point Matching (VSPM to further enhance the matching accuracy between two sets of matching points. Experimental results show that the proposed method can effectively and robustly generate sufficient, reliable point pairs and provide accurate registration.

  4. Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Zagorodny, A.H.

    2004-01-01

    The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)

  5. AIR-MRF: Accelerated iterative reconstruction for magnetic resonance fingerprinting.

    Science.gov (United States)

    Cline, Christopher C; Chen, Xiao; Mailhe, Boris; Wang, Qiu; Pfeuffer, Josef; Nittka, Mathias; Griswold, Mark A; Speier, Peter; Nadar, Mariappan S

    2017-09-01

    Existing approaches for reconstruction of multiparametric maps with magnetic resonance fingerprinting (MRF) are currently limited by their estimation accuracy and reconstruction time. We aimed to address these issues with a novel combination of iterative reconstruction, fingerprint compression, additional regularization, and accelerated dictionary search methods. The pipeline described here, accelerated iterative reconstruction for magnetic resonance fingerprinting (AIR-MRF), was evaluated with simulations as well as phantom and in vivo scans. We found that the AIR-MRF pipeline provided reduced parameter estimation errors compared to non-iterative and other iterative methods, particularly at shorter sequence lengths. Accelerated dictionary search methods incorporated into the iterative pipeline reduced the reconstruction time at little cost of quality. Copyright © 2017 Elsevier Inc. All rights reserved.

  6. A novel iterative scheme and its application to differential equations.

    Science.gov (United States)

    Khan, Yasir; Naeem, F; Šmarda, Zdeněk

    2014-01-01

    The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

  7. Iterative solution of large linear systems

    CERN Document Server

    Young, David Matheson

    1971-01-01

    This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth

  8. Calorimetric method for current sharing temperature measurements in ITER conductor samples in SULTAN

    International Nuclear Information System (INIS)

    Bagnasco, M.

    2009-01-01

    Several Toroidal Field Conductor short samples with slight layout variations have been assembled and tested in the SULTAN facility at CRPP. The measurement campaigns started in 2007 and are still ongoing. The performance of every conductor is expressed in terms of current sharing temperature (T cs ), i.e. the temperature at which a defined electric field, 10 μV/m, is detected in the cable due to the incipient superconducting-to-normal state transition. The T cs at specific operating conditions is the key design parameter for the ITER conductors and is the main object of the qualification tests. Typically, the average electric field is measured with voltage tap pairs attached on the jacket along the conductor. The inability however to explain observed premature voltage developments opened the discussion about possible alternative measuring methods. The He flow calorimetric method is based on the measurement of the resistive power generation in the conductor. It relies on the detection of very small temperature increases along the conductor in steady state operation. The accuracy and the reliability of the calorimetric method in SULTAN are critically discussed, with particular emphasis on the instrumentation requirements and test procedures. The application of the calorimetric method to the recent SULTAN test campaigns is described with its merits and limits. For future tests of ITER conductors in SULTAN, the calorimetric method for T cs test is proposed as a routine procedure.

  9. Iterative solution of the Helmholtz equation

    Energy Technology Data Exchange (ETDEWEB)

    Larsson, E.; Otto, K. [Uppsala Univ. (Sweden)

    1996-12-31

    We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.

  10. Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

    DEFF Research Database (Denmark)

    Hoffmann, Kristoffer; Knudsen, Kim

    2014-01-01

    For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...... impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two...

  11. Asymptotic Conservation Laws in Classical Field Theory

    International Nuclear Information System (INIS)

    Anderson, I.M.; Torre, C.G.

    1996-01-01

    A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society

  12. Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems.

    Science.gov (United States)

    Wang, An; Cao, Yang; Shi, Quan

    2018-01-01

    In this paper, we demonstrate a complete version of the convergence theory of the modulus-based matrix splitting iteration methods for solving a class of implicit complementarity problems proposed by Hong and Li (Numer. Linear Algebra Appl. 23:629-641, 2016). New convergence conditions are presented when the system matrix is a positive-definite matrix and an [Formula: see text]-matrix, respectively.

  13. Information operator approach and iterative regularization methods for atmospheric remote sensing

    International Nuclear Information System (INIS)

    Doicu, A.; Hilgers, S.; Bargen, A. von; Rozanov, A.; Eichmann, K.-U.; Savigny, C. von; Burrows, J.P.

    2007-01-01

    In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO 2 retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen

  14. The methods for generating tomographic images using transmition, emission and nuclear magnetic resonance techniques. II. Fourier method and iterative methods

    International Nuclear Information System (INIS)

    Ursu, I.; Demco, D.E.; Gligor, T.D.; Pop, G.; Dollinger, R.

    1987-01-01

    In a wide variety of applications it is necessary to infer the structure of a multidimensional object from a set of its projections. Computed tomography is at present largely extended in the medical field, but the industrial application may ultimately far exceed its medical applications. Two techniques for reconstructing objects from their projections are presented: Fourier methods and iterative techniques. The paper also contains a brief comparative study of the reconstruction algorithms. (authors)

  15. Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

    Science.gov (United States)

    Nefedov, N. N.; Nikulin, E. I.

    2018-01-01

    A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

  16. Asymptotic matching of the solar-system gravitational yields

    International Nuclear Information System (INIS)

    Kopejkin, S.M.

    1989-01-01

    In the framework of the general relativity, the structure of the Solar-system gravitational fields is investigated and the relativistic formulae of transformation between nonrotating in the dynamical sense harmonic reference systems - barycentric, planetocentric and topocentric (satelite) ones - are derived by the method of the asymptotic mathing of components of the metric tensor. The derived formulae generalize the linear Poincare transformation in the case of curved space-time. With the help of the asymptotic matching formulae, the relationships between relativistic time scales inside the Solar system have been established, the equations of relativistic precession of the space axis of one reference system with respect to another one have been derived, the equations of translational motion of the center-of-mass of planets (the Sun) and their satellites have been obtained

  17. On Small Deviation Asymptotics In L2 of Some Mixed Gaussian Processes

    Directory of Open Access Journals (Sweden)

    Alexander I. Nazarov

    2018-04-01

    Full Text Available We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen–Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

  18. SU-E-I-93: Improved Imaging Quality for Multislice Helical CT Via Sparsity Regularized Iterative Image Reconstruction Method Based On Tensor Framelet

    International Nuclear Information System (INIS)

    Nam, H; Guo, M; Lee, K; Li, R; Xing, L; Gao, H

    2014-01-01

    Purpose: Inspired by compressive sensing, sparsity regularized iterative reconstruction method has been extensively studied. However, its utility pertinent to multislice helical 4D CT for radiotherapy with respect to imaging quality, dose, and time has not been thoroughly addressed. As the beginning of such an investigation, this work carries out the initial comparison of reconstructed imaging quality between sparsity regularized iterative method and analytic method through static phantom studies using a state-of-art 128-channel multi-slice Siemens helical CT scanner. Methods: In our iterative method, tensor framelet (TF) is chosen as the regularization method for its superior performance from total variation regularization in terms of reduced piecewise-constant artifacts and improved imaging quality that has been demonstrated in our prior work. On the other hand, X-ray transforms and its adjoints are computed on-the-fly through GPU implementation using our previous developed fast parallel algorithms with O(1) complexity per computing thread. For comparison, both FDK (approximate analytic method) and Katsevich algorithm (exact analytic method) are used for multislice helical CT image reconstruction. Results: The phantom experimental data with different imaging doses were acquired using a state-of-art 128-channel multi-slice Siemens helical CT scanner. The reconstructed image quality was compared between TF-based iterative method, FDK and Katsevich algorithm with the quantitative analysis for characterizing signal-to-noise ratio, image contrast, and spatial resolution of high-contrast and low-contrast objects. Conclusion: The experimental results suggest that our tensor framelet regularized iterative reconstruction algorithm improves the helical CT imaging quality from FDK and Katsevich algorithm for static experimental phantom studies that have been performed

  19. Asymptotic symmetries, holography and topological hair

    Science.gov (United States)

    Mishra, Rashmish K.; Sundrum, Raman

    2018-01-01

    Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons

  20. Laminar flow and convective transport processes scaling principles and asymptotic analysis

    CERN Document Server

    Brenner, Howard

    1992-01-01

    Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered.A unique feat

  1. Investigation of vessel visibility of iterative reconstruction method in coronary computed tomography angiography using simulated vessel phantom

    International Nuclear Information System (INIS)

    Inoue, Takeshi; Uto, Fumiaki; Ichikawa, Katsuhiro; Hara, Takanori; Urikura, Atsushi; Hoshino, Takashi; Miura, Youhei; Terakawa, Syouichi

    2012-01-01

    Iterative reconstruction methods can reduce the noise of computed tomography (CT) images, which are expected to contribute to the reduction of patient dose CT examinations. The purpose of this study was to investigate impact of an iterative reconstruction method (iDose 4 , Philips Healthcare) on vessel visibility in coronary CT angiography (CTA) by using phantom studies. A simulated phantom was scanned by a CT system (iCT, Philips Healthcare), and the axial images were reconstructed by filtered back projection (FBP) and given a level of 1 to 7 (L1-L7) of the iterative reconstruction (IR). The vessel visibility was evaluated by a quantitative analysis using profiles across a 1.5-mm diameter simulated vessel as well as visual evaluation for multi planar reformation (MPR) images and volume rendering (VR) images in terms of the normalized-rank method with analysis of variance. The peak CT value of the profiles decreased with IR level and full width at half maximum of the profile also decreased with the IR level. For normalized-rank method, there was no statistical difference between FBP and L1 (20% dose reduction) for both MPR and VR images. The IR levels higher than L1 sacrificed the spatial resolution for the 1.5-mm simulated vessel, and their visual vessel visibilities were significantly inferior to that of the FBP. (author)

  2. Asymptotics for the greatest zeros of solutions of a particular O.D.E.

    Directory of Open Access Journals (Sweden)

    Silvia Noschese

    1994-05-01

    Full Text Available This paper deals with the Liouville-Stekeloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation. From the classical tools we deduce information about the asymptotics of the greatest zeros of a class of solutions of a particular ODE, including the classical Hermite polynomials.

  3. Iterative correction method for shift-variant blurring caused by collimator aperture in SPECT

    International Nuclear Information System (INIS)

    Ogawa, Koichi; Katsu, Haruto

    1996-01-01

    A collimation system in single photon computed tomography (SPECT) induces blurring on reconstructed images. The blurring varies with the collimator aperture which is determined by the shape of the hole (its diameter and length), and with the distance between the collimator surface and the object. The blurring has shift-variant properties. This paper presents a new iterative method for correcting the shift-variant blurring. The method estimates the ratio of 'ideal projection value' to 'measured projection value' at each sample point. The term 'ideal projection value' means the number of photons which enter the hole perpendicular to the collimator surface, and the term 'measured projection value' means the number of photons which enter the hole at acute angles to the collimator aperture axis. If the estimation is accurate, ideal projection value can be obtained as the product of the measured projection value and the estimated ratio. The accuracy of the estimation is improved iteratively by comparing the measured projection value with a weighted summation of several estimated projection value. The simulation results showed that spatial resolution was improved without amplification of artifacts due to statistical noise. (author)

  4. Implementation of the multireference Brillouin-Wigner and Mukherjee’s coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism

    Energy Technology Data Exchange (ETDEWEB)

    Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus JJ; Pittner, Jiri; Kowalski, Karol

    2012-09-07

    In this paper we discuss the performance of the non-iterative State-Specific Mul- tireference Coupled Cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with the exact full configuration interaction results (FCI) for small systems (H2O, N2, and Be3). For larger systems (naphthyne isomers and -carotene), the non-iterative BW-MRCCSD(T) and Mk-MRCCSD(T) methods are compared against the results obtained with the single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of pro- cessor groups.

  5. Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense

    International Nuclear Information System (INIS)

    Chidume, C.E.; Shahzad, Naseer; Zegeye, Habtu

    2003-08-01

    Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be a non-self mapping which is asymptotically nonexpansive in the intermediate sense with F(T) := {x is an element of K : Tx x} ≠ 0. A demiclosed principle for T is proved. Moreover, if T is completely continuous, an iterative sequence {x n } is constructed which converges strongly to some x* is an element of F(T). If T is not assumed to be completely continuous but the dual E* of E is assumed to have the Kadec-Klee property, then {x n } converges weakly to some x* is an element of F(T). The operator P which plays a central role in our proofs is, in this case, the Banach space analogue of the proximity map in Hilbert spaces. (author)

  6. Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

    KAUST Repository

    Elsheikh, Ahmed H.

    2013-05-01

    A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. © 2013 Elsevier B.V.

  7. Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method

    International Nuclear Information System (INIS)

    Dehghan, Mehdi; Tatari, Mehdi

    2008-01-01

    In this research, the He's variational iteration technique is used for computing an unknown time-dependent parameter in an inverse quasilinear parabolic partial differential equation. Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and physics, as they appear in various engineering models. The He's variational iteration method is an analytical procedure for finding solutions of differential equations, is based on the use of Lagrange multipliers for identification of an optimal value of a parameter in a functional. To show the efficiency of the new approach, several test problems are presented for one-, two- and three-dimensional cases

  8. Large gauge symmetries and asymptotic states in QED

    Energy Technology Data Exchange (ETDEWEB)

    Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)

    2016-12-19

    Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.

  9. Asymptotic theory for regressions with smoothly changing parameters

    DEFF Research Database (Denmark)

    Hillebrand, Eric; Medeiros, Marcelo; Xu, Junyue

    2013-01-01

    We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual pT-rate and has...... an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

  10. On the solution of large-scale SDP problems by the modified barrier method using iterative solvers

    Czech Academy of Sciences Publication Activity Database

    Kočvara, Michal; Stingl, M.

    2007-01-01

    Roč. 109, 2-3 (2007), s. 413-444 ISSN 0025-5610 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : semidefinite programming * iterative methods * preconditioned conjugate gradient s * augmented lagrangian methods Subject RIV: BA - General Mathematics Impact factor: 1.475, year: 2007

  11. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

    KAUST Repository

    Desmal, Abdulla

    2014-07-01

    A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.

  12. Development of an automated method for in situ measurement of the geometrical properties of the ITER bolometer diagnostic

    Energy Technology Data Exchange (ETDEWEB)

    Meister, H., E-mail: meister@ipp.mpg.de; Penzel, F.; Giannone, L.; Kannamueller, M.; Kling, A.; Koll, J.; Trautmann, T.

    2011-10-15

    In order to derive the local emission profile of the plasma radiation in a fusion device using the line-integrated measurements of the bolometer diagnostic, tomographic reconstruction methods have to be applied to the measurements from many lines-of-sight. A successful reconstruction needs to take the finite sizes of detectors and apertures and the resulting non-ideal measurements into account. In ITER a method for in situ measurement of the geometrical properties of the various components of the bolometer diagnostic after installation is required as the viewing cones have to pass through narrow gaps between components. The method proposed to be used for ITER uses the beam of a laser with high intensity to illuminate the bolometer assembly from many different angles {xi} and {theta}. A light-weight robot from Kuka Robotics is used to efficiently position the laser on many points covering the complete viewing cone of each line-of-sight and to direct the beam precisely into the entrance aperture of the bolometer. Measuring the response of the bolometer allows for the calculation of the transmission function t({xi}, {theta}), the angular etendue and finally the geometric function in reconstruction space, which is required for the tomography algorithms. Measuring the transmission function for a laboratory assembly demonstrates the viability of the proposed method. Results for a collimator-type camera from a prototype envisaged for ITER are presented. The implemented procedure is discussed in detail, in particular with respect to the automatisation applied which takes the achievable positioning and alignment accuracies of the robot into account. This discussion is extended towards the definition of requirements for a remote-handling tool for ITER.

  13. A quantum kinematics for asymptotically flat gravity

    Science.gov (United States)

    Campiglia, Miguel; Varadarajan, Madhavan

    2015-07-01

    We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.

  14. Criteria for exponential asymptotic stability in the large of ...

    African Journals Online (AJOL)

    The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the ...

  15. A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

    Science.gov (United States)

    Heinkenschloss, Matthias

    2005-01-01

    We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

  16. Asymptotic Theory for Regressions with Smoothly Changing Parameters

    DEFF Research Database (Denmark)

    Hillebrand, Eric Tobias; Medeiros, Marcelo C.; Xu, Junyue

    We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual square-root-of-T rate...... and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

  17. Iterating skeletons

    DEFF Research Database (Denmark)

    Dieterle, Mischa; Horstmeyer, Thomas; Berthold, Jost

    2012-01-01

    a particular skeleton ad-hoc for repeated execution turns out to be considerably complicated, and raises general questions about introducing state into a stateless parallel computation. In addition, one would strongly prefer an approach which leaves the original skeleton intact, and only uses it as a building...... block inside a bigger structure. In this work, we present a general framework for skeleton iteration and discuss requirements and variations of iteration control and iteration body. Skeleton iteration is expressed by synchronising a parallel iteration body skeleton with a (likewise parallel) state......Skeleton-based programming is an area of increasing relevance with upcoming highly parallel hardware, since it substantially facilitates parallel programming and separates concerns. When parallel algorithms expressed by skeletons involve iterations – applying the same algorithm repeatedly...

  18. AGB [asymptotic giant branch]: Star evolution

    International Nuclear Information System (INIS)

    Becker, S.A.

    1987-01-01

    Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs

  19. Asymptotic density and effective negligibility

    Science.gov (United States)

    Astor, Eric P.

    In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both

  20. Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction

    NARCIS (Netherlands)

    Veldman, AEP

    The paper presents a personal view on the history of viscous-inviscid interaction methods, a history closely related to the evolution of the method of matched asymptotic expansions. The main challenge in solving Prandtl's boundary-layer equations has been to overcome the singularity at a point of

  1. Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences

    Directory of Open Access Journals (Sweden)

    Bipan Hazarika

    2013-01-01

    in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

  2. Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Hu Changsong

    2010-01-01

    Full Text Available We consider two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces. We proved that the proposed algorithms strongly converge to a common fixed point of a countable family of nonexpansive mappings which solves the corresponding variational inequality. Our results improve and extend the corresponding ones announced by many others.

  3. The Asymptotic Solution for the Steady Variable-Viscosity Free ...

    African Journals Online (AJOL)

    Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...

  4. Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence

    International Nuclear Information System (INIS)

    Zhang Tailei; Teng Zhidong

    2008-01-01

    In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence

  5. Asymptotic geometric analysis, part I

    CERN Document Server

    Artstein-Avidan, Shiri

    2015-01-01

    The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen

  6. Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities

    International Nuclear Information System (INIS)

    Warsa, James S.; Wareing, Todd A.; Morel, Jim E.

    2004-01-01

    A loss in the effectiveness of diffusion synthetic acceleration (DSA) schemes has been observed with certain S N discretizations on two-dimensional Cartesian grids in the presence of material discontinuities. We will present more evidence supporting the conjecture that DSA effectiveness will degrade for multidimensional problems with discontinuous total cross sections, regardless of the particular physical configuration or spatial discretization. Fourier analysis and numerical experiments help us identify a set of representative problems for which established DSA schemes are ineffective, focusing on diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look at a fully consistent and a 'partially consistent' DSA method for this discretization. The effectiveness of both methods is shown to degrade significantly. A Fourier analysis of the fully consistent DSA scheme in the limit of decreasing cell optical thickness supports the view that the DSA itself is failing when material discontinuities are present in a problem. We show that a Krylov iterative method, preconditioned with DSA, is an effective remedy that can be used to efficiently compute solutions for this class of problems. We show that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate. In fact, it is preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily. The Krylov method can be implemented in terms of the original S N source iteration coding with only slight modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration

  7. Asymptotic safety guaranteed

    DEFF Research Database (Denmark)

    Litim, Daniel F.; Sannino, Francesco

    2014-01-01

    We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...

  8. Cosmic censorship, persistent curvature and asymptotic causal pathology

    International Nuclear Information System (INIS)

    Newman, R.P.A.C.

    1984-01-01

    The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)

  9. Primal Domain Decomposition Method with Direct and Iterative Solver for Circuit-Field-Torque Coupled Parallel Finite Element Method to Electric Machine Modelling

    Directory of Open Access Journals (Sweden)

    Daniel Marcsa

    2015-01-01

    Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.

  10. Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

    Science.gov (United States)

    Banks, H T; Holm, Kathleen; Robbins, Danielle

    2010-11-01

    We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.

  11. Adaptive Asymptotical Synchronization for Stochastic Complex Networks with Time-Delay and Markovian Switching

    Directory of Open Access Journals (Sweden)

    Xueling Jiang

    2014-01-01

    Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.

  12. A new iterative triclass thresholding technique in image segmentation.

    Science.gov (United States)

    Cai, Hongmin; Yang, Zhong; Cao, Xinhua; Xia, Weiming; Xu, Xiaoyin

    2014-03-01

    We present a new method in image segmentation that is based on Otsu's method but iteratively searches for subregions of the image for segmentation, instead of treating the full image as a whole region for processing. The iterative method starts with Otsu's threshold and computes the mean values of the two classes as separated by the threshold. Based on the Otsu's threshold and the two mean values, the method separates the image into three classes instead of two as the standard Otsu's method does. The first two classes are determined as the foreground and background and they will not be processed further. The third class is denoted as a to-be-determined (TBD) region that is processed at next iteration. At the succeeding iteration, Otsu's method is applied on the TBD region to calculate a new threshold and two class means and the TBD region is again separated into three classes, namely, foreground, background, and a new TBD region, which by definition is smaller than the previous TBD regions. Then, the new TBD region is processed in the similar manner. The process stops when the Otsu's thresholds calculated between two iterations is less than a preset threshold. Then, all the intermediate foreground and background regions are, respectively, combined to create the final segmentation result. Tests on synthetic and real images showed that the new iterative method can achieve better performance than the standard Otsu's method in many challenging cases, such as identifying weak objects and revealing fine structures of complex objects while the added computational cost is minimal.

  13. Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations

    International Nuclear Information System (INIS)

    Morel, Jim E.; Brian Yang, T.-Y.; Warsa, James S.

    2007-01-01

    The linear multifrequency-grey acceleration (LMFGA) technique is used to accelerate the iterative convergence of multigroup thermal radiation diffusion calculations in high energy density simulations. Although it is effective and efficient in one-dimensional calculations, the LMFGA method has recently been observed to significantly degrade under certain conditions in multidimensional calculations with large discontinuities in material properties. To address this deficiency, we recast the LMFGA method in terms of a preconditioned system that is solved with a Krylov method (LMFGK). Results are presented demonstrating that the new LMFGK method always requires fewer iterations than the original LMFGA method. The reduction in iteration count increases with both the size of the time step and the inhomogeneity of the problem. However, for reasons later explained, the LMFGK method can cost more per iteration than the LMFGA method, resulting in lower but comparable efficiency in problems with small time steps and weak inhomogeneities. In problems with large time steps and strong inhomogeneities, the LMFGK method is significantly more efficient than the LMFGA method

  14. Multi-level iteration optimization for diffusive critical calculation

    International Nuclear Information System (INIS)

    Li Yunzhao; Wu Hongchun; Cao Liangzhi; Zheng Youqi

    2013-01-01

    In nuclear reactor core neutron diffusion calculation, there are usually at least three levels of iterations, namely the fission source iteration, the multi-group scattering source iteration and the within-group iteration. Unnecessary calculations occur if the inner iterations are converged extremely tight. But the convergence of the outer iteration may be affected if the inner ones are converged insufficiently tight. Thus, a common scheme suit for most of the problems was proposed in this work to automatically find the optimized settings. The basic idea is to optimize the relative error tolerance of the inner iteration based on the corresponding convergence rate of the outer iteration. Numerical results of a typical thermal neutron reactor core problem and a fast neutron reactor core problem demonstrate the effectiveness of this algorithm in the variational nodal method code NODAL with the Gauss-Seidel left preconditioned multi-group GMRES algorithm. The multi-level iteration optimization scheme reduces the number of multi-group and within-group iterations respectively by a factor of about 1-2 and 5-21. (authors)

  15. Evaluation of Continuation Desire as an Iterative Game Development Method

    DEFF Research Database (Denmark)

    Schoenau-Fog, Henrik; Birke, Alexander; Reng, Lars

    2012-01-01

    When developing a game it is always valuable to use feedback from players in each iteration, in order to plan the design of the next iteration. However, it can be challenging to devise a simple approach to acquiring information about a player's engagement while playing. In this paper we will thus...... concerning a crowd game which is controlled by smartphones and is intended to be played by audiences in cinemas and at venues with large screens. The case study demonstrates how the approach can be used to help improve the desire to continue when developing a game....

  16. Asymptotic expansions for high-contrast linear elasticity

    KAUST Repository

    Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

    2015-01-01

    We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

  17. Asymptotic expansions for high-contrast linear elasticity

    KAUST Repository

    Poveda, Leonardo A.

    2015-03-01

    We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

  18. On asymptotic analysis of spectral problems in elasticity

    Directory of Open Access Journals (Sweden)

    S.A. Nazarov

    Full Text Available The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.

  19. Parallel S/sub n/ iteration schemes

    International Nuclear Information System (INIS)

    Wienke, B.R.; Hiromoto, R.E.

    1986-01-01

    The iterative, multigroup, discrete ordinates (S/sub n/) technique for solving the linear transport equation enjoys widespread usage and appeal. Serial iteration schemes and numerical algorithms developed over the years provide a timely framework for parallel extension. On the Denelcor HEP, the authors investigate three parallel iteration schemes for solving the one-dimensional S/sub n/ transport equation. The multigroup representation and serial iteration methods are also reviewed. This analysis represents a first attempt to extend serial S/sub n/ algorithms to parallel environments and provides good baseline estimates on ease of parallel implementation, relative algorithm efficiency, comparative speedup, and some future directions. The authors examine ordered and chaotic versions of these strategies, with and without concurrent rebalance and diffusion acceleration. Two strategies efficiently support high degrees of parallelization and appear to be robust parallel iteration techniques. The third strategy is a weaker parallel algorithm. Chaotic iteration, difficult to simulate on serial machines, holds promise and converges faster than ordered versions of the schemes. Actual parallel speedup and efficiency are high and payoff appears substantial

  20. Geometric interpretation of optimal iteration strategies

    International Nuclear Information System (INIS)

    Jones, R.B.

    1977-01-01

    The relationship between inner and outer iteration errors is extremely complex, and even formal description of total error behavior is difficult. Inner and outer iteration error propagation is analyzed in a variational formalism for a reactor model describing multidimensional, one-group theory. In a generalization the work of Akimov and Sabek, the number of inner iterations performed during each outer serial that minimizes the total computation time is determined. The generalized analysis admits a geometric interpretation of total error behavior. The results can be applied to both transport and diffusion theory computer methods. 1 figure

  1. AIR Tools - A MATLAB Package of Algebraic Iterative Reconstruction Techniques

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Saxild-Hansen, Maria

    This collection of MATLAB software contains implementations of several Algebraic Iterative Reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods...... are implemented: Algebraic Reconstruction Techniques (ART) and Simultaneous Iterative Reconstruction Techniques (SIRT). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter...

  2. ITER plant systems

    International Nuclear Information System (INIS)

    Kolbasov, B.; Barnes, C.; Blevins, J.

    1991-01-01

    As part of a series of documents published by the IAEA that summarize the results of the Conceptual Design Activities for the ITER project, this publication describes the conceptual design of the ITER plant systems, in particular (i) the heat transport system, (ii) the electrical distribution system, (iii) the requirements for radioactive equipment handling, the hot cell, and waste management, (iv) the supply system for fluids and operational chemicals, (v) the qualitative analyses of failure scenarios and methods of burn stability control and emergency shutdown control, (vi) analyses of tokamak building functions and design requirements, (vii) a plant layout, and (viii) site requirements. Refs, figs and tabs

  3. DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

    Science.gov (United States)

    Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

    2016-10-01

    This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

  4. A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

    Directory of Open Access Journals (Sweden)

    Kamonrat Nammanee

    2012-01-01

    Full Text Available We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞. Our results improve and extend those announced by G. Marino and H.-K. Xu (2006 and many authors.

  5. An iterative method for hydrodynamic interactions in Brownian dynamics simulations of polymer dynamics

    Science.gov (United States)

    Miao, Linling; Young, Charles D.; Sing, Charles E.

    2017-07-01

    Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.

  6. Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

    KAUST Repository

    Elsheikh, Ahmed H.

    2013-06-01

    We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.

  7. Optimization of Parameters of Asymptotically Stable Systems

    Directory of Open Access Journals (Sweden)

    Anna Guerman

    2011-01-01

    Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.

  8. Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method

    Energy Technology Data Exchange (ETDEWEB)

    Fatalov, Vadim R [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2011-08-31

    We prove results on exact asymptotics as n{yields}{infinity} for the expectations E{sub a} exp{l_brace}-{theta}{Sigma}{sub k=0}{sup n-1}g(X{sub k}){r_brace} and probabilities P{sub a}{l_brace}(1/n {Sigma}{sub k=0}{sup n-1}g(X{sub k})=}1, is the corresponding random walk on R, g(x) is a positive continuous function satisfying certain conditions, and d>0, {theta}>0, a element of R are fixed numbers. Our results are obtained using a new method which is developed in this paper: the Laplace method for the occupation time of discrete-time Markov chains. For g(x) one can take |x|{sup p}, log (|x|{sup p}+1), p>0, |x| log (|x|+1), or e{sup {alpha}|x|}-1, 0<{alpha}<1/2, x element of R, for example. We give a detailed treatment of the case when g(x)=|x| using Bessel functions to make explicit calculations.

  9. Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

    DEFF Research Database (Denmark)

    Miansari, Mo; Miansari, Me; Barari, Amin

    2009-01-01

    In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

  10. On the Application of Iterative Methods of Nondifferentiable Optimization to Some Problems of Approximation Theory

    Directory of Open Access Journals (Sweden)

    Stefan M. Stefanov

    2014-01-01

    Full Text Available We consider the data fitting problem, that is, the problem of approximating a function of several variables, given by tabulated data, and the corresponding problem for inconsistent (overdetermined systems of linear algebraic equations. Such problems, connected with measurement of physical quantities, arise, for example, in physics, engineering, and so forth. A traditional approach for solving these two problems is the discrete least squares data fitting method, which is based on discrete l2-norm. In this paper, an alternative approach is proposed: with each of these problems, we associate a nondifferentiable (nonsmooth unconstrained minimization problem with an objective function, based on discrete l1- and/or l∞-norm, respectively; that is, these two norms are used as proximity criteria. In other words, the problems under consideration are solved by minimizing the residual using these two norms. Respective subgradients are calculated, and a subgradient method is used for solving these two problems. The emphasis is on implementation of the proposed approach. Some computational results, obtained by an appropriate iterative method, are given at the end of the paper. These results are compared with the results, obtained by the iterative gradient method for the corresponding “differentiable” discrete least squares problems, that is, approximation problems based on discrete l2-norm.

  11. ITER-FEAT - outline design report. Report by the ITER Director. ITER meeting, Tokyo, January 2000

    International Nuclear Information System (INIS)

    2001-01-01

    It is now possible to define the key elements of ITER-FEAT. This report provides the results, to date, of the joint work of the Special Working Group in the form of an Outline Design Report on the ITER-FEAT design which, subject to the views of ITER Council and of the Parties, will be the focus of further detailed design work and analysis in order to provide to the Parties a complete and fully integrated engineering design within the framework of the ITER EDA extension

  12. The ITER CODAC conceptual design

    International Nuclear Information System (INIS)

    Lister, J.B.; Farthing, J.W.; Greenwald, M.; Yonekawa, I.

    2007-01-01

    CODAC orchestrates the activity of 60-90 Plant Systems in normal ITER operation. Interlock Systems protect ITER from potentially damaging operating off-normal conditions. Safety Systems protect the personnel and the environment and will be subject to licensing. The principal challenges to be met in the design and implementation of CODAC include: complexity, reliability, transparent access respecting security, a high experiment data rate and data volume since ITER is an experimental reactor, scientific exploitation from multiple Participant Team Experiment Sites and the long 35-year period for construction and operation. Complexity is addressed by prescribing the communication interfaces to the Plant Systems and prescribing the technical implementation within the Plant Systems. Plant Systems export to CODAC all the information on their construction and operation as 'self-description'. Complexity is also addressed by automating the operation of ITER and of the plasma, using a structured data description of 'Operation Schedules' which encompass all non-manual control, including Plasma Control. Reliability is addressed by maximising code reuse and maximising the use of existing products thereby minimising in-house development. The design is hierarchical and modular in both hardware and software. The latter facilitates evolution of methods during the project lifetime. Guaranteeing security while maximising access is addressed by flow separation. Out-flowing data, including experimental signals and the status of ITER plant is risk-free. In-flowing commands and data originate from Experiment Sites. The Cadarache Experiment Site is equated with the Remote Experiment Sites and a rigorous 'Operation Request Gatekeeper' is provided. The high data rates and data volumes are handled with high performance networks. Global Area Networks allow Participant Teams to access all CODAC data and applications. Scientific exploitation of ITER will remain a human as well as technical

  13. Power system state estimation using an iteratively reweighted least squares method for sequential L{sub 1}-regression

    Energy Technology Data Exchange (ETDEWEB)

    Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)

    2006-02-15

    This paper presents an implementation of the least absolute value (LAV) power system state estimator based on obtaining a sequence of solutions to the L{sub 1}-regression problem using an iteratively reweighted least squares (IRLS{sub L1}) method. The proposed implementation avoids reformulating the regression problem into standard linear programming (LP) form and consequently does not require the use of common methods of LP, such as those based on the simplex method or interior-point methods. It is shown that the IRLS{sub L1} method is equivalent to solving a sequence of linear weighted least squares (LS) problems. Thus, its implementation presents little additional effort since the sparse LS solver is common to existing LS state estimators. Studies on the termination criteria of the IRLS{sub L1} method have been carried out to determine a procedure for which the proposed estimator is more computationally efficient than a previously proposed non-linear iteratively reweighted least squares (IRLS) estimator. Indeed, it is revealed that the proposed method is a generalization of the previously reported IRLS estimator, but is based on more rigorous theory. (author)

  14. Asymptotically free SU(5) models

    International Nuclear Information System (INIS)

    Kogan, Ya.I.; Ter-Martirosyan, K.A.; Zhelonkin, A.V.

    1981-01-01

    The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles [ru

  15. 8. Asymptotically Flat and Regular Cauchy Data

    Science.gov (United States)

    Dain, Sergio

    I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

  16. A practical iterative PID tuning method for mechanical systems using parameter chart

    Science.gov (United States)

    Kang, M.; Cheong, J.; Do, H. M.; Son, Y.; Niculescu, S.-I.

    2017-10-01

    In this paper, we propose a method of iterative proportional-integral-derivative parameter tuning for mechanical systems that possibly possess hidden mechanical resonances, using a parameter chart which visualises the closed-loop characteristics in a 2D parameter space. We employ a hypothetical assumption that the considered mechanical systems have their upper limit of the derivative feedback gain, from which the feasible region in the parameter chart becomes fairly reduced and thus the gain selection can be extremely simplified. Then, a two-directional parameter search is carried out within the feasible region in order to find the best set of parameters. Experimental results show the validity of the assumption used and the proposed parameter tuning method.

  17. Low-memory iterative density fitting.

    Science.gov (United States)

    Grajciar, Lukáš

    2015-07-30

    A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

  18. Involvement of the EU industry in ITER EDA

    International Nuclear Information System (INIS)

    Bogusch, E.

    2001-01-01

    Since the fifties, European industry has been involved in research and development in the field of nuclear fusion as a potential future source of energy. Early contributions mainly included deliveries of plant components and services to experimental facilities. In the Engineering Design Activities (EDA) phase of the planned multinational International Thermonuclear Experimental Reactor (ITER) in 1993 to 2001 this commitment of industry was intensified. Industries from seven European countries participated in the project with various contributions, e.g., in the development, design, and manufacture of components, and in the development of methods of planning and executing the complex ITER project. These activities were accompanied by an extensive R and D program. e.g., about materials and methods of manufacturing ITER components. In this way, European industry made an important contribution to the further development of nuclear fusion within the framework of ITER EDA activities, and will be able to continue this work intensively in the expected ITER construction phase to follow. (orig.) [de

  19. The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference

    Directory of Open Access Journals (Sweden)

    Nicholas Scott Cardell

    2013-05-01

    Full Text Available Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. In this paper we prove that the data constrained GME estimator of the general linear model is consistent and asymptotically normal. The approach we take in establishing the asymptotic properties concomitantly identifies a new computationally efficient method for calculating GME estimates. Formulae are developed to compute asymptotic variances and to perform Wald, likelihood ratio, and Lagrangian multiplier statistical tests on model parameters. Monte Carlo simulations are provided to assess the performance of the GME estimator in both large and small sample situations. Furthermore, we extend our results to maximum cross-entropy estimators and indicate a variant of the GME estimator that is unbiased. Finally, we discuss the relationship of GME estimators to Bayesian estimators, pointing out the conditions under which an unbiased GME estimator would be efficient.

  20. Noise-based tube current reduction method with iterative reconstruction for reduction of radiation exposure in coronary CT angiography

    International Nuclear Information System (INIS)

    Shen, Junlin; Du, Xiangying; Guo, Daode; Cao, Lizhen; Gao, Yan; Bai, Mei; Li, Pengyu; Liu, Jiabin; Li, Kuncheng

    2013-01-01

    Purpose: To investigate the potential of noise-based tube current reduction method with iterative reconstruction to reduce radiation exposure while achieving consistent image quality in coronary CT angiography (CCTA). Materials and methods: 294 patients underwent CCTA on a 64-detector row CT equipped with iterative reconstruction. 102 patients with fixed tube current were assigned to Group 1, which was used to establish noise-based tube current modulation formulas, where tube current was modulated by the noise of test bolus image. 192 patients with noise-based tube current were randomly assigned to Group 2 and Group 3. Filtered back projection was applied for Group 2 and iterative reconstruction for Group 3. Qualitative image quality was assessed with a 5 point score. Image noise, signal intensity, volume CT dose index, and dose-length product were measured. Results: The noise-based tube current modulation formulas were established through regression analysis using image noise measurements in Group 1. Image noise was precisely maintained at the target value of 35.00 HU with small interquartile ranges for Group 2 (34.17–35.08 HU) and Group 3 (34.34–35.03 HU), while it was from 28.41 to 36.49 HU for Group 1. All images in the three groups were acceptable for diagnosis. A relative 14% and 41% reduction in effective dose for Group 2 and Group 3 were observed compared with Group 1. Conclusion: Adequate image quality could be maintained at a desired and consistent noise level with overall 14% dose reduction using noise-based tube current reduction method. The use of iterative reconstruction further achieved approximately 40% reduction in effective dose

  1. Asymptotic dynamics of QCD, coherent states and the quark form factor

    International Nuclear Information System (INIS)

    Steiner, F.; Dahmen, H.D.

    1980-05-01

    The method of asymptotic dynamics for large times developed by Kulish and Fadde'ev for QED is applied to QCD. We study the solution and calculate the on shell quark form factor in leading logarithmic order. (orig.)

  2. Asymptotics of Wigner 3nj-symbols with small and large angular momenta: an elementary method

    International Nuclear Information System (INIS)

    Bonzom, Valentin; Fleury, Pierre

    2012-01-01

    Yu and Littlejohn recently studied in (2011 Phys. Rev. A 83 052114 (arXiv:1104.1499)) some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j-, 12j- and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano–Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron are needed, leading to new asymptotics for Wigner 3nj-symbols. As an illustration, we present 15j-symbols with one, two and four small angular momenta, and give an alternative formula to Yu’s recent 15j-symbol with three small spins. (paper)

  3. Iterative supervirtual refraction interferometry

    KAUST Repository

    Al-Hagan, Ola

    2014-05-02

    In refraction tomography, the low signal-to-noise ratio (S/N) can be a major obstacle in picking the first-break arrivals at the far-offset receivers. To increase the S/N, we evaluated iterative supervirtual refraction interferometry (ISVI), which is an extension of the supervirtual refraction interferometry method. In this method, supervirtual traces are computed and then iteratively reused to generate supervirtual traces with a higher S/N. Our empirical results with both synthetic and field data revealed that ISVI can significantly boost up the S/N of far-offset traces. The drawback is that using refraction events from more than one refractor can introduce unacceptable artifacts into the final traveltime versus offset curve. This problem can be avoided by careful windowing of refraction events.

  4. Iterative supervirtual refraction interferometry

    KAUST Repository

    Al-Hagan, Ola; Hanafy, Sherif M.; Schuster, Gerard T.

    2014-01-01

    In refraction tomography, the low signal-to-noise ratio (S/N) can be a major obstacle in picking the first-break arrivals at the far-offset receivers. To increase the S/N, we evaluated iterative supervirtual refraction interferometry (ISVI), which is an extension of the supervirtual refraction interferometry method. In this method, supervirtual traces are computed and then iteratively reused to generate supervirtual traces with a higher S/N. Our empirical results with both synthetic and field data revealed that ISVI can significantly boost up the S/N of far-offset traces. The drawback is that using refraction events from more than one refractor can introduce unacceptable artifacts into the final traveltime versus offset curve. This problem can be avoided by careful windowing of refraction events.

  5. Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations

    OpenAIRE

    Soleimani, Farahnaz; Stanimirovi´c, Predrag; Soleymani, Fazlollah

    2015-01-01

    An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the ...

  6. Asymptotics for the Kummer function of Bose plasmas

    International Nuclear Information System (INIS)

    Kowalenko, V.; Frankel, N.E.

    1993-01-01

    The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetised Bose plasmas at T = 0 K are presented for large and small values of its parameter, thereby displaying the function's asymptotic non-uniformity. The large parameter expansion plays a determining role in the behaviour of these Bose systems in the limit that the external magnetic field B →0. This particular expansion is generalised herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function. 18 refs., 1 tab., 2 figs

  7. Iterative algorithms to approximate canonieal Gabor windows: Computational aspects

    DEFF Research Database (Denmark)

    Janssen, A. J. E. M.; Søndergaard, Peter Lempel

    2007-01-01

    In this article we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g, a, b). The iterations start with the window g while the iteration steps comprise the window g, the k(th) iteran...

  8. Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

    Energy Technology Data Exchange (ETDEWEB)

    Kim, S. [Purdue Univ., West Lafayette, IN (United States)

    1994-12-31

    Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

  9. Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour

    International Nuclear Information System (INIS)

    Buckingham, Robert J; Miller, Peter D

    2014-01-01

    Rational solutions of the inhomogeneous Painlevé-II equation and of a related coupled Painlevé-II system have recently arisen in studies of fluid vortices and of the sine-Gordon equation. For the sine-Gordon application in particular it is of interest to understand the large-degree asymptotic behaviour of the rational Painlevé-II functions. We explicitly compute the leading-order large-degree asymptotics of these two families of rational functions valid in the whole complex plane with the exception of a neighbourhood of a certain piecewise-smooth closed curve. We obtain rigorous error bounds by using the Deift–Zhou nonlinear steepest-descent method for Riemann–Hilbert problems. (paper)

  10. Accelerated convergence of the steepest-descent method for magnetohydrodynamic equilibria

    International Nuclear Information System (INIS)

    Handy, C.R.; Hirshman, S.P.

    1984-06-01

    Iterative schemes based on the method of steepest descent have recently been used to obtain magnetohydrodynamic (MHD) equilibria. Such schemes generate asymptotic geometric vector sequences whose convergence rate can be improved through the use of the epsilon-algorithm. The application of this nonlinear recursive technique to stiff systems is discussed. In principle, the epsilon-algorithm is capable of yielding quadratic convergence and therefore represents an attractive alternative to other quadratic convergence schemes requiring Jacobian matrix inversion. Because the damped MHD equations have eigenvalues with negative real parts (in the neighborhood of a stable equilibrium), the epsilon-algorithm will generally be stable. Concern for residual monotonic sequences leads to consideration of alternative methods for implementing the algorithm

  11. ITER council proceedings: 2001

    International Nuclear Information System (INIS)

    2001-01-01

    Continuing the ITER EDA, two further ITER Council Meetings were held since the publication of ITER EDA documentation series no, 20, namely the ITER Council Meeting on 27-28 February 2001 in Toronto, and the ITER Council Meeting on 18-19 July in Vienna. That Meeting was the last one during the ITER EDA. This volume contains records of these Meetings, including: Records of decisions; List of attendees; ITER EDA status report; ITER EDA technical activities report; MAC report and advice; Final report of ITER EDA; and Press release

  12. Frequency sweep of the field scattered by an inhomogeneous structure using method of moments and asymptotic waveform evaluation

    DEFF Research Database (Denmark)

    Troelsen, Jens; Meincke, Peter; Breinbjerg, Olav

    2000-01-01

    into account. To the knowledge of the authors the AWE technique has not previously been applied to a MoM solution based on this kind of integral equation. It is the purpose of this paper to investigate the use of the AWE technique as a tool to obtain a fast frequency sweep of the field scattered......In many radar applications it is necessary to determine the scattering from an object over a wide frequency band. The asymptotic waveform evaluation (AWE), which is a moment matching (MM) technique, constitutes a method to this end. In general, MM techniques provide a reduced-order model...

  13. ITER and world chaos; Iter ou le bouleversement du monde

    Energy Technology Data Exchange (ETDEWEB)

    Pourcel, Eric

    2012-02-15

    ITER is the International Thermonuclear Experimental Reactor: the author here develops three scenarios linked to the control of nuclear fusion as a method of producing electrical energy that could take over from fossil fuels in the twenty-First century. His expose shows the likely strategic disarray that might result

  14. ITER safety

    International Nuclear Information System (INIS)

    Raeder, J.; Piet, S.; Buende, R.

    1991-01-01

    As part of the series of publications by the IAEA that summarize the results of the Conceptual Design Activities for the ITER project, this document describes the ITER safety analyses. It contains an assessment of normal operation effluents, accident scenarios, plasma chamber safety, tritium system safety, magnet system safety, external loss of coolant and coolant flow problems, and a waste management assessment, while it describes the implementation of the safety approach for ITER. The document ends with a list of major conclusions, a set of topical remarks on technical safety issues, and recommendations for the Engineering Design Activities, safety considerations for siting ITER, and recommendations with regard to the safety issues for the R and D for ITER. Refs, figs and tabs

  15. Application of an iterative methodology for cross-section and variance/covariance data adjustment to the analysis of fast spectrum systems accounting for non-linearity

    International Nuclear Information System (INIS)

    Pelloni, Sandro

    2014-01-01

    Highlights: • Our data adjustment is based on a Generalized Linear Least-Squares approach. • The computed sensitivity coefficients are converged within an iterative procedure. • The corresponding multistep adjustment thus accounts for non-linearity. • It provides a more accurate simulation of fast-spectrum experiments. - Abstract: The data assimilation benchmark launched by the “Subgroup 33” on “Methods and issues for the combined use of integral experiments and covariance data” of the Working Party on Evaluation Cooperation (WPEC) of the OECD Nuclear Energy Agency Nuclear Science Committee is recalculated by means of a multistep adjustment procedure using the deterministic code system ERANOS in conjunction with a dedicated Generalized Linear Least-Squares approach based on the Bayesian parameter estimation method. Nuclear data in terms of multi-group cross-sections as well as their variances and covariances, are adjusted for 11 nuclides, namely 10 B, 16 O, 23 Na, 56 Fe, 52 Cr, 58 Ni, 235 U, 238 U, 239 Pu, 240 Pu and 241 Pu and 6 nuclear reactions which are elastic and inelastic scattering, lumped (n,2n) and (n,3n), capture, fission and ν ¯ . The adjustment is carried out by making use of experimental data for 19 integral parameters obtained in 7 different fast spectrum systems. In the determination of a posteriori values for these integral parameters including effective multiplication factors, spectral indices and void effects, along with their nuclear data uncertainty, the required adjusted data for these nuclides and reactions are generated in conjunction with pre-computed sensitivity coefficients of the analytical integral parameters to the nuclear data to adjust. The suggested multistep scheme aims at accounting for non-linear effects. Correspondingly, the sensitivity coefficients are recalculated within an iterative procedure on the basis of the a posteriori analytical values and adjusted cross-sections. The adjustment is thus repeated

  16. Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

    Directory of Open Access Journals (Sweden)

    Ali Konuralp

    2014-01-01

    Full Text Available Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay function θ(t vanishes inside the integral limits such that θ(t=qt for 0

  17. The ITER Remote Maintenance Management System

    International Nuclear Information System (INIS)

    Tesini, Alessandro; Rolfe, A.C.

    2009-01-01

    A major challenge for the ITER project is to develop and implement a Remote Maintenance System, which can deliver high Tokamak availability within the constraints of the overall ITER programme objectives. Much of the maintenance of ITER will be performed using remote handling methods and some with combined manual and remote activities working together. The organization and management of the ITER remote handling facilities will be of a scale unlike any other remote handling application in the world. The ITER remote handling design and procurement activities will require co-ordination and management across many different sites throughout the world. It will be a major challenge for the ITER project to ensure a consistent quality and technical approach in all of the contributing parties. To address this issue the IO remote handling team are implementing the ITER Maintenance Management Plan (IMMP) comprising an overarching document defining the policies and methodologies (ITER Remote Maintenance Management System or IMMS) and an associated ITER remote handling code of practise (IRHCOP). The IMMS will be in document form available as a pdf file or similar. The IRHCOP will be implemented as a web based application and will provide access to the central resource of the entire code of practise from any location in the world. The IRHCOP data library will be centrally controlled in order that users can be assured of the data relevance and authenticity. This paper will describe the overall approach being taken to deal with this challenge and go on to detail the structure and content of both the IMMS and the IRHCOP.

  18. An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

    Science.gov (United States)

    Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.

    2009-12-01

    A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.

  19. Komar integrals in asymptotically anti-de Sitter space-times

    International Nuclear Information System (INIS)

    Magnon, A.

    1985-01-01

    Recently, boundary conditions governing the asymptotic behavior of the gravitational field in the presence of a negative cosmological constant have been introduced using Penrose's conformal techniques. The subsequent analysis has led to expressions of conserved quantities (associated with asymptotic symmetries) involving asymptotic Weyl curvature. On the other hand, if the underlying space-time is equipped with isometries, a generalization of the Komar integral which incorporates the cosmological constant is also available. Thus, in the presence of an isometry, one is faced with two apparently unrelated definitions. It is shown that these definitions agree. This coherence supports the choice of boundary conditions for asymptotically anti-de Sitter space-times and reinforces the definitions of conserved quantities

  20. Electromagnetic scattering using the iterative multi-region technique

    CERN Document Server

    Al Sharkawy, Mohamed H

    2007-01-01

    In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique.Different enhan