The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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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.
Resita Arum, Sari; A, Suparmi; C, Cari
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 nr 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. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).
A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method
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H. T. Cho
2012-01-01
Full Text Available We discuss how to obtain black hole quasinormal modes (QNMs using the asymptotic iteration method (AIM, initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN, and Kerr black holes in a unified way. We discuss some advantages of the AIM over the continued fractions method (CFM. This paper presents for the first time the spin 0, 1/2 and 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM and confirms results previously obtained using the CFM. We also present some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher-dimensional generalizations and we give an example of doubly rotating black holes.
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, ...... Asymptotic 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.......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......, 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...
International Nuclear Information System (INIS)
This paper presents a non-linear analysis of elastically restrained imperfect shallow spherical shells on pasternak foundation. By adopting the asymptotic iteration method (AIM), an analytical expression concerning the external load and the central deflection of the shell is derived in a non-dimensional form. The solution incorporates the effects of involved parameters, such as geometrical imperfection, extensional and shear moduli of foundation and edge-restraint coefficients as well as structural geometry, and it can be used effectively to perform buckling analysis of such structures. For some classical boundary conditions, the resulting solution has been compared with data available resulting from various approximate methods including Alpha, Berger's method, modified Berger's method, Sinharay and Banerjee's approach and Galerkin's method. The evaluation of the effects of these parameters on critical buckling loads is made numerically. The results show that the present solution can be considered as a more exact solution for determination of non-linear behaviour of such structures
Pramono, Subur; Cari, Cari
2016-01-01
In this work, we study the exact solution of Dirac equation in the hyper-spherical coordinate under influence of separable q-Deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed non-central trigonometric Scarf potentials, where whole 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 lD-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 Mat Lab, the increase of radial quantum number n causes the increase of bound state relativistic energy level both in dimension D = 5 and D = 3. The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number nl.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Hageman, Louis A
2004-01-01
This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Assuming minimal mathematical background, it profiles the relative merits of several general iterative procedures. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a "red/black" block form, adaptive computational algorithms for the successive overrelaxation (SOR) method, and comp
ASYMPTOTIC METHODS OF STATISTICAL CONTROL
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Orlov A. I.
2014-10-01
Full Text Available Statistical control is a sampling control based on the probability theory and mathematical statistics. The article presents the development of the methods of statistical control in our country. It discussed the basics of the theory of statistical control – the plans of statistical control and their operational characteristics, the risks of the supplier and the consumer, the acceptance level of defectiveness and the rejection level of defectiveness. We have obtained the asymptotic method of synthesis of control plans based on the limit average output level of defectiveness. We have also developed the asymptotic theory of single sampling plans and formulated some unsolved mathematical problems of the theory of statistical control
Energy Technology Data Exchange (ETDEWEB)
Saadd, Y.
1994-12-31
In spite of the tremendous progress achieved in recent years in the general area of iterative solution techniques, there are still a few obstacles to the acceptance of iterative methods in a number of applications. These applications give rise to very indefinite or highly ill-conditioned non Hermitian matrices. Trying to solve these systems with the simple-minded standard preconditioned Krylov subspace methods can be a frustrating experience. With the mathematical and physical models becoming more sophisticated, the typical linear systems which we encounter today are far more difficult to solve than those of just a few years ago. This trend is likely to accentuate. This workshop will discuss (1) these applications and the types of problems that they give rise to; and (2) recent progress in solving these problems with iterative methods. The workshop will end with a hopefully stimulating panel discussion with the speakers.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe
1. Berlin, Heidelberg: Springer-Verlag, 2013 - (Björm, E.), s. 205-224 ISBN 978-3-540-70528-4 Institutional support: RVO:68145535 Keywords : classical iterative methods * applied computational mathematics * encyclopedia Subject RIV: BA - General Mathematics http://www.springerreference.com/docs/ navigation .do?m=Encyclopedia+of+Applied+and+Computational+Mathematics+%28Mathematics+and+Statistics%29-book224
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.
Asymptotic properties of solutions of some iterative functional inequalities
Dobiesław Brydak; Bogdan Choczewski; Marek Czerni
2008-01-01
Continuous solutions of iterative linear inequalities of the first and second order are considered, belonging to a class \\(\\mathcal{F}_T\\) of functions behaving at the origin as a prescribed function \\(T\\).
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Chang Shih-sen
2008-01-01
Full Text Available Abstract In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007, Liu (1996, Osilike (2004, Su and Li (2006, Gu (2007, Xu and Ori (2001.
Large Deviations and Asymptotic Methods in Finance
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...
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Jung Jong Soo
2007-01-01
Full Text Available Strong and weak convergence theorems for multistep iterative scheme with errors for finite family of asymptotically nonexpansive mappings are established in Banach spaces. Our results extend and improve the corresponding results of Chidume and Ali (2007, Cho et al. (2004, Khan and Fukhar-ud-din (2005, Plubtieng et al.(2006, Xu and Noor (2002, and many others.
Zhou, H. Y.; Cho, Y. J.; Kang, S. M.
2007-01-01
Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicomp...
Institute of Scientific and Technical Information of China (English)
Jian Feng WANG; Li Xin ZHANG
2007-01-01
Negatively associated sequences have been studied extensively in recent years. Asymp-totically negative association is a generalization of negative association. In this paper a Berry-Esseen theorem and a law of the iterated logarithm are obtained for asymptotically negatively associated sequences.
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
Quantum defect theory and asymptotic methods
International Nuclear Information System (INIS)
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.)
Asymptotic methods in mechanics of solids
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...
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
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.
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.
Iterative Runge–Kutta-type methods for nonlinear ill-posed problems
International Nuclear Information System (INIS)
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
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
ASYMPTOTICALLY OPTIMAL SUCCESSIVE OVERRELAXATION METHODS FOR SYSTEMS OF LINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhong-zhi Bai; Xue-bin Chi
2003-01-01
We present a class of asymptotically optimal successive overrelaxation methods forsolving the large sparse system of linear equations. Numerical computations show thatthese new methods are more efficient and robust than the classical successive overrelaxationmethod.
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.
Robust methods and asymptotic theory in nonlinear econometrics
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 ...
Asymptotics for maximum score method under general conditions
Taisuke Otsu; Myung Hwan Seo
2014-01-01
Abstract. Since Manski's (1975) seminal work, the maximum score method for discrete choice models has been applied to various econometric problems. Kim and Pollard (1990) established the cube root asymptotics for the maximum score estimator. Since then, however, econometricians posed several open questions and conjectures in the course of generalizing the maximum score approach, such as (a) asymptotic distribution of the conditional maximum score estimator for a panel data dynamic discrete ch...
Iterative Method for Generating Correlated Binary Sequences
Usatenko, O V; Apostolov, S S; Makarov, N M; Krokhin, A A
2014-01-01
We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated one. Each step of modulation increases the correlations until the desired level has been reached. Robustness and efficiency for the proposed algorithm are tested by generating sequences with inverse power-law correlations. The substantial increase in the strength of correlation in the iterative method with respect to the single-step filtering generation is shown for all studied correlation functions. Our results can be used for design of disordered superlattices, waveguides, and surfaces with selective transport properties.
Iterative Regularization with Minimum-Residual Methods
DEFF Research Database (Denmark)
Jensen, Toke Koldborg; Hansen, Per Christian
2007-01-01
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...
Iterative regularization with minimum-residual methods
DEFF Research Database (Denmark)
Jensen, Toke Koldborg; Hansen, Per Christian
2006-01-01
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...
An Iterative Method for Problems with Multiscale Conductivity
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Hyea Hyun Kim
2012-01-01
Full Text Available A model with its conductivity varying highly across a very thin layer will be considered. It is related to a stable phantom model, which is invented to generate a certain apparent conductivity inside a region surrounded by a thin cylinder with holes. The thin cylinder is an insulator and both inside and outside the thin cylinderare filled with the same saline. The injected current can enter only through the holes adopted to the thin cylinder. The model has a high contrast of conductivity discontinuity across the thin cylinder and the thickness of the layer and the size of holes are very small compared to the domain of the model problem. Numerical methods for such a model require a very fine mesh near the thin layer to resolve the conductivity discontinuity. In this work, an efficient numerical method for such a model problem is proposed by employing a uniform mesh, which need not resolve the conductivity discontinuity. The discrete problem is then solved by an iterative method, where the solution is improved by solving a simple discrete problem with a uniform conductivity. At each iteration, the right-hand side is updated by integrating the previous iterate over the thin cylinder. This process results in a certain smoothing effect on microscopic structures and our discrete model can provide a more practical tool for simulating the apparent conductivity. The convergence of the iterative method is analyzed regarding the contrast in the conductivity and the relative thickness of the layer. In numerical experiments, solutions of our method are compared to reference solutions obtained from COMSOL, where very fine meshes are used to resolve the conductivity discontinuity in the model. Errors of the voltage in L2 norm follow O(h asymptotically and the current density matches quitewell those from the reference solution for a sufficiently small mesh size h. The experimental results present a promising feature of our approach for simulating the apparent
Non-iterative method for camera calibration.
Hong, Yuzhen; Ren, Guoqiang; Liu, Enhai
2015-09-01
This paper presents a new and effective technique to calibrate a camera without nonlinear iteration optimization. To this end, the centre-of-distortion is accurately estimated firstly. Based on the radial distortion division model, point correspondences between model plane and its image were used to compute the homography and distortion coefficients afterwards. Once the homographies of calibration images are obtained, the camera intrinsic parameters are solved analytically. All the solution techniques applied in this calibration process are non-iterative that do not need any initial guess, with no risk of local minima. Moreover, estimation of the distortion coefficients and intrinsic parameters could be successfully decoupled, yielding the more stable and reliable result. Both simulative and real experiments have been carried out to show that the proposed method is reliable and effective. Without nonlinear iteration optimization, the proposed method is computationally efficient and can be applied to real-time online calibration. PMID:26368490
Preconditioned iterative methods for partial differential equations
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Leaf, G.K.; Minkoff, M.; Diaz, J.C.
1987-01-01
In this paper we consider several preconditioners and iterative methods for solving the linear algebraic system associated with a partial differential equation. Our interest stems from earlier work in Method of Lines (MOL) software for solving kinetics-diffusion equations and a recognition that the solution of the underlying linear system at each timestep is crucial in terms of computational storage and time. We are interested in developing an approach to handle nonsymmetric matrices so that we can deal with convective terms in the partial differential equation (PDE). To examine our methods we consider a model problem which has been used in related work. With regard to the approach there are two aspects: the preconditioner and the iterative method. Among the preconditioners considered are normal form LU factorization and variations related to approximate inverses. The iterative methods include normal form conjugate gradients and related nonsymmetric methods (ORTHOMIN and ORTHODIR). We have found that the use of either an approximate LU factorization or an approximate inverse in combination with normal form conjugate gradient iteration provides an effective approach for solving our model problem. This result suggests potential use of approximate inverses for parallel computation. 5 refs., 4 figs.
Selected asymptotic methods with applications to electromagnetics and antennas
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
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: 1.322, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/nla.2016/epdf
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...... steps, than what is customary in the Brinkman penalization, thus reducing its computational cost while maintaining the capability of the method to handle complex geometries. We demonstrate the accuracy of our method by considering challenging benchmark problems such as flow past an impulsively started...... cylinder and normal to an impulsively started and accelerated flat plate. We find that the present method enhances significantly the accuracy of the Brinkman penalization technique for the simulations of highly unsteady flows past complex geometries....
Coherent anomaly and asymptotic method in cooperative phenomena
International Nuclear Information System (INIS)
A new general method is proposed to study asymptotic behaviors of cooperative systems. This is based on the appearance of ''coherent anomaly'' in mean-field-type approximations of cooperative systems. This is powerful in evaluating non-classical scaling exponents of cooperative phenomena. (author)
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.
Asymptotic-Preserving methods and multiscale models for plasma physics
Degond, Pierre
2016-01-01
The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.
Asymptotic-Preserving methods and multiscale models for plasma physics
Degond, Pierre; Deluzet, Fabrice
2016-01-01
The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or dif...
Conformal symmetries of gravity from asymptotic methods: further developments
Lambert, Pierre-Henry
2014-01-01
In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in $d$ dimensions with and without a cosmological constant. The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions. The second part of this thesis contains the original contributions. Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure...
Iterative Methods for MPC on Graphical Processing Units
DEFF Research Database (Denmark)
Gade-Nielsen, Nicolai Fog; Jørgensen, John Bagterp; Dammann, Bernd
2012-01-01
applicability for GPUs. We examine published techniques for iterative methods in interior points methods (IPMs) by applying them to simple test cases, such as a system of masses connected by springs. Iterative methods allows us deal with the ill-conditioning occurring in the later iterations of the IPM as well...
A short remark on fractional variational iteration method
Energy Technology Data Exchange (ETDEWEB)
He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China)
2011-09-05
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed. -- Highlights: → The variational iteration method and its fractional modification are compared. → The demerits arising are overcome by the fractional complex transform. → The Letter provides a powerful tool to solving fractional differential equations.
A short remark on fractional variational iteration method
International Nuclear Information System (INIS)
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed. -- Highlights: → The variational iteration method and its fractional modification are compared. → The demerits arising are overcome by the fractional complex transform. → The Letter provides a powerful tool to solving fractional differential equations.
AIR Tools - A MATLAB package of algebraic iterative reconstruction methods
DEFF Research Database (Denmark)
Hansen, Per Christian; Saxild-Hansen, Maria
2012-01-01
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...
Nonlinear vibrations of buckled plates by an asymptotic numerical method
Benchouaf, Lahcen; Boutyour, El Hassan
2016-03-01
This work deals with nonlinear vibrations of a buckled von Karman plate by an asymptotic numerical method and harmonic balance approach. The coupled nonlinear static and dynamic problems are transformed into a sequence of linear ones solved by a finite-element method. The static behavior of the plate is first computed. The fundamental frequency of nonlinear vibrations of the plate, about any equilibrium state, is obtained. To improve the validity range of the power series, Padé approximants are incorporated. A continuation technique is used to get the whole solution. To show the effectiveness of the proposed methodology, numerical tests are presented.
Asymptotic stability properties of θ-methods for delay differential equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
Extension to the integral transport equation of an iterative method
Energy Technology Data Exchange (ETDEWEB)
Jehouani, A. [EPRA, Department of Physics, Faculty of Sciences, Semlalia, PO Box 2390, 40000 Marrakech (Morocco)]. E-mail: jehouani@ucam.ac.ma; Elmorabiti, A. [Centre d' Etudes Nucleaires de Maamoura, CNESTEN (Morocco); Ghassoun, J. [EPRA, Department of Physics, Faculty of Sciences, Semlalia, PO Box 2390, 40000 Marrakech (Morocco)
2006-09-15
In this paper we describe an extension to the neutron integral transport equation of an iterative method. Indeed an iterative scheme is used for both energy and space including external iteration for the multiplication factor and internal iteration for flux calculations. The Monte Carlo method is used to evaluate the spatial transfer integrals. The results were compared with those obtained by using the APOLLO2 code for a cylindrical cell.
Extension to the integral transport equation of an iterative method
International Nuclear Information System (INIS)
In this paper we describe an extension to the neutron integral transport equation of an iterative method. Indeed an iterative scheme is used for both energy and space including external iteration for the multiplication factor and internal iteration for flux calculations. The Monte Carlo method is used to evaluate the spatial transfer integrals. The results were compared with those obtained by using the APOLLO2 code for a cylindrical cell
An Iterative Tikhonov Method for Large Scale Computations
Loli Piccolomini, Elena; Zama, Fabiana
2009-01-01
In this paper we present an iterative method for the minimization of the Tikhonov regularization functional in the absence of information about noise. Each algorithm iteration updates both the estimate of the regularization parameter and the Tikhonov solution. In order to reduce the number of iterations, an inexact version of the algorithm is also proposed. In this case the inner Conjugate Gradient (CG) iterations are truncated before convergence. In the numerical experi...
Iterative Method for Intrinsic Viscosity Measurements on Perpendicular Recording Media
Kim, Phan Le; Lodder, Cock
2002-01-01
We introduce a new method that allows one to directly measure the intrinsic viscosity (S/sub i/) for perpendicular media using a vibrating sample magnetometer. The measurement is carried out in a number of iterations. In each iteration, the behavior of applied field (H/sub a/) with time is gradually adjusted according to the change in the internal field (H/sub i/) calculated from the relaxation behavior measured in the previous iteration. Eventually, during the last iteration, from which the ...
Iterative methods for Toeplitz-like matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Universitaet Wurzburg (Germany)
1994-12-31
In this paper the author will give a survey on iterative methods for solving linear equations with Toeplitz matrices, Block Toeplitz matrices, Toeplitz plus Hankel matrices, and matrices with low displacement rank. He will treat the following subjects: (1) optimal (w)-circulant preconditioners is a generalization of circulant preconditioners; (2) Optimal implementation of circulant-like preconditioners in the complex and real case; (3) preconditioning of near-singular matrices; what kind of preconditioners can be used in this case; (4) circulant preconditioning for more general classes of Toeplitz matrices; what can be said about matrices with coefficients that are not l{sub 1}-sequences; (5) preconditioners for Toeplitz least squares problems, for block Toeplitz matrices, and for Toeplitz plus Hankel matrices.
An Efficient Bayesian Iterative Method for Solving Linear Systems
Institute of Scientific and Technical Information of China (English)
Deng DING; Kin Sio FONG; Ka Hou CHAN
2012-01-01
This paper concerns with the statistical methods for solving general linear systems.After a brief review of Bayesian perspective for inverse problems,a new and efficient iterative method for general linear systems from a Bayesian perspective is proposed.The convergence of this iterative method is proved,and the corresponding error analysis is studied.Finally,numerical experiments are given to support the efficiency of this iterative method,and some conclusions are obtained.
Solving the Kuramoto-Sivashinsky equation via Variational Iteration Method
Directory of Open Access Journals (Sweden)
majeed Ahmed Yousif
2014-06-01
Full Text Available In this study, the approximate solutions for the Kuramoto-Sivashinsky equation by using the Variational Iteration Method (VIM are obtained. Comparisons with the exact solutions and the solutions obtained by the Homotopy Perturbation Method (HPM, the numerical example show that the Variational Iteration Method (VIM is accurate and effective and suitable for this kind of problem. Keywords: Kuramoto-Sivashinsky equation, Variational Iteration Method.
Asymptotic solution for EI Nino-southern oscillation of nonlinear model
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; LIN Wan-tao
2008-01-01
A class of nonlinear coupled system for E1 Nino-Southern Oscillation (ENSO) model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.
Fields Institute International Symposium on Asymptotic Methods in Stochastics
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.
A Parallel Iterative Method for Computing Molecular Absorption Spectra
Koval, Peter; Foerster, Dietrich; Coulaud, Olivier
2010-01-01
We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting cod...
Regularization and Iterative Methods for Monotone Variational Inequalities
Directory of Open Access Journals (Sweden)
Xiubin Xu
2010-01-01
Full Text Available We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an iterative method as discretization of the regularization method. We prove that both regularization and iterative methods converge in norm.
On the asymptotic methods for nuclear collective models
Gheorghe, A. C.; Raduta, A. A.
2009-01-01
Contractions of orthogonal groups to Euclidean groups are applied to analytic descriptions of nuclear quantum phase transitions. The semiclassical asymptotic of multipole collective Hamiltonians are also investigated.
An iterative method for indefinite systems of linear equations
Ito, K.
1984-01-01
An iterative method for solving nonsymmetric indefinite linear systems is proposed. The method involves the successive use of a modified version of the conjugate residual method. A numerical example is given to illustrate the method.
THE CONVERGENCE BEHAVIOR OF ITERATIVE METHODS ON SEVERELY STRETCHED GRIDS
BOTTA, EFF; WUBS, FW
1993-01-01
In this paper we examine the dramatic influence that a severe stretching of finite difference grids can have on the convergence behaviour of iterative methods. For the most important classes of iterative methods this phenomenon is considered for a simple model problem with various boundary condition
Asymptotic Method for Cladding Stress Evaluation in PCMI
International Nuclear Information System (INIS)
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
New Parallel Three-level Iterative Method for Diffusion Equation
Directory of Open Access Journals (Sweden)
Tinghuai Ma
2010-01-01
Full Text Available To solve the diffusion equation on parallel computers, we first derived an o(τ2+h6 order implicit finite difference method based on a class of alternating group explicit iterative method. Based on this method, we devised a new alternating group explicit iterative method. Moreover, the absolute stability and convergence of the New Alternating Group Explicit Iterative (N-AGEI method was proved. Finally, the numerical experiments were conducted to verify our method. Both the theoretical analysis and simulation results showed that our proposed difference format had satisfied stability error estimate and convergence.
Leapfrog variants of iterative methods for linear algebra equations
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.
Parallel iterative methods for sparse linear and nonlinear equations
Saad, Youcef
1989-01-01
As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.
Reducing the latency of the Fractal Iterative Method to half an iteration
Béchet, Clémentine; Tallon, Michel
2013-12-01
The fractal iterative method for atmospheric tomography (FRiM-3D) has been introduced to solve the wavefront reconstruction at the dimensions of an ELT with a low-computational cost. Previous studies reported the requirement of only 3 iterations of the algorithm in order to provide the best adaptive optics (AO) performance. Nevertheless, any iterative method in adaptive optics suffer from the intrinsic latency induced by the fact that one iteration can start only once the previous one is completed. Iterations hardly match the low-latency requirement of the AO real-time computer. We present here a new approach to avoid iterations in the computation of the commands with FRiM-3D, thus allowing low-latency AO response even at the scale of the European ELT (E-ELT). The method highlights the importance of "warm-start" strategy in adaptive optics. To our knowledge, this particular way to use the "warm-start" has not been reported before. Futhermore, removing the requirement of iterating to compute the commands, the computational cost of the reconstruction with FRiM-3D can be simplified and at least reduced to half the computational cost of a classical iteration. Thanks to simulations of both single-conjugate and multi-conjugate AO for the E-ELT,with FRiM-3D on Octopus ESO simulator, we demonstrate the benefit of this approach. We finally enhance the robustness of this new implementation with respect to increasing measurement noise, wind speed and even modeling errors.
Iteration of Runge-Kutta methods with block triangular Jacobians
Houwen, P.J. van der; Sommeijer, B.P.
1995-01-01
We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Jacobian. For IVPs
Iterative Method for Intrinsic Viscosity Measurements on Perpendicular Recording Media
Kim, Phan Le; Lodder, Cock
2002-01-01
We introduce a new method that allows one to directly measure the intrinsic viscosity (S/sub i/) for perpendicular media using a vibrating sample magnetometer. The measurement is carried out in a number of iterations. In each iteration, the behavior of applied field (H/sub a/) with time is gradually
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.
Multi-Level iterative methods in computational plasma physics
International Nuclear Information System (INIS)
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
MULTILEVEL ITERATION METHODS FOR SOLVING LINEAR ILL-POSED PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper we develop multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for ill-posed problems. The algorithm and its convergence analysis are presented in an abstract framework.
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.
A WEIGHTED ITERATIVE METHOD FOR ROBUST SELF-CALIBRATION
Institute of Scientific and Technical Information of China (English)
Liu Shigang; Wu Chengke; Tang Li; Jia Jing
2006-01-01
A robust self-calibration method is presented, which can efficiently discard the outliers based on a Weighted Iteration Method (WIM). The method is an iterative process in which the projective reconstruction is obtained based on the weights of all the points, whereas the weights are defined in inverse proportion to the reciprocal of the re-projective errors. The weights of outliers trend to zero after several iterations, and the accurate projective reconstruction is determined. The location of the absolute conic and the camera intrinsic parameters are obtained after the projective reconstruction. The theory and experiments with both simulate and real data demonstrate that the proposed method is very efficient and robust.
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Arablouei, Reza; Doğançay, Kutluyıl; Werner, Stefan
2014-01-01
We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously-proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being ...
BOUNDEDNESS AND ASYMPTOTIC STABILITY OF MULTISTEP METHODS FOR GENERALIZED PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang; Geng Sun
2004-01-01
In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained.
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
Conference on iterative methods for large linear systems
Energy Technology Data Exchange (ETDEWEB)
Kincaid, D.R. [comp.
1988-12-01
This conference is dedicated to providing an overview of the state of the art in the use of iterative methods for solving sparse linear systems with an eye to contributions of the past, present and future. The emphasis is on identifying current and future research directions in the mainstream of modern scientific computing. Recently, the use of iterative methods for solving linear systems has experienced a resurgence of activity as scientists attach extremely complicated three-dimensional problems using vector and parallel supercomputers. Many research advances in the development of iterative methods for high-speed computers over the past forty years are reviewed, as well as focusing on current research.
Energy Technology Data Exchange (ETDEWEB)
Corcelli, S.A.; Kress, J.D.; Pratt, L.R.
1995-08-07
This paper develops and characterizes mixed direct-iterative methods for boundary integral formulations of continuum dielectric solvation models. We give an example, the Ca{sup ++}{hor_ellipsis}Cl{sup {minus}} pair potential of mean force in aqueous solution, for which a direct solution at thermal accuracy is difficult and, thus for which mixed direct-iterative methods seem necessary to obtain the required high resolution. For the simplest such formulations, Gauss-Seidel iteration diverges in rare cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the non-symmetric iteration matrix. This establishes that those divergences are due to inaccuracies of the asymptotic approximations used in evaluation of the matrix elements corresponding to accidental close encounters of boundary elements on different atomic spheres. The spectral radii are then greater than one for those diverging cases. This problem is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those cases performing an ``in-line`` Monte Carlo integration to evaluate the required matrix elements. These difficulties are not expected and have not been observed for the thoroughly coarsened equations obtained when only a direct solution is sought. Finally, we give an example application of hybrid quantum-classical methods to deprotonation of orthosilicic acid in water.
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guang-wei Yuan; Xu-deng Hang
2006-01-01
This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.
Multicore Performance of Block Algebraic Iterative Reconstruction Methods
DEFF Research Database (Denmark)
Sørensen, Hans Henrik B.; Hansen, Per Christian
2014-01-01
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......, and those that compute a result for each block in parallel and then combine these results before the next iteration. The goal of this work is to demonstrate which block methods are best suited for implementation on modern multicore computers. To compare the performance of the different block methods......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...
An Iterative Brinkman penalization for particle vortex methods
DEFF Research Database (Denmark)
Walther, Jens Honore; Hejlesen, Mads Mølholm; Leonard, A.; Koumoutsakos, P.
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...
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the...
Iotti, Robert
2015-04-01
ITER is an international experimental facility being built by seven Parties to demonstrate the long term potential of fusion energy. The ITER Joint Implementation Agreement (JIA) defines the structure and governance model of such cooperation. There are a number of necessary conditions for such international projects to be successful: a complete design, strong systems engineering working with an agreed set of requirements, an experienced organization with systems and plans in place to manage the project, a cost estimate backed by industry, and someone in charge. Unfortunately for ITER many of these conditions were not present. The paper discusses the priorities in the JIA which led to setting up the project with a Central Integrating Organization (IO) in Cadarache, France as the ITER HQ, and seven Domestic Agencies (DAs) located in the countries of the Parties, responsible for delivering 90%+ of the project hardware as Contributions-in-Kind and also financial contributions to the IO, as ``Contributions-in-Cash.'' Theoretically the Director General (DG) is responsible for everything. In practice the DG does not have the power to control the work of the DAs, and there is not an effective management structure enabling the IO and the DAs to arbitrate disputes, so the project is not really managed, but is a loose collaboration of competing interests. Any DA can effectively block a decision reached by the DG. Inefficiencies in completing design while setting up a competent organization from scratch contributed to the delays and cost increases during the initial few years. So did the fact that the original estimate was not developed from industry input. Unforeseen inflation and market demand on certain commodities/materials further exacerbated the cost increases. Since then, improvements are debatable. Does this mean that the governance model of ITER is a wrong model for international scientific cooperation? I do not believe so. Had the necessary conditions for success
An Iterative Method for Extracting Chinese Unknown Words
Institute of Scientific and Technical Information of China (English)
HE Shan; ZHU Jie
2001-01-01
An iterative method for extractingunknown words from a Chinese text corpus is pro-posed in this paper. Unlike traditional non-iterativesegmentation-detection approaches, which use onlyknown words for segmentation, the proposed methoditeratively extracts new words and adds them into thelexicon. Then the augmented dictionary, which in-cludes known words and potential unknown words, isused in the next iteration to re-segment the input cor-pus. Experiments show that both the precision andrecall rates of segmentation are improved.
Iteration of Runge-Kutta methods with block triangular Jacobians
Houwen, van der, P.J.; Sommeijer, Ben
1995-01-01
We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Jacobian. For IVPs of large dimension, this approach is not attractive because of the high costs involved in the LU-decomposition of the Jacobian of the RK equations. Several proposals have been made to reduce these...
Mathematical justification of Kelvin-Voigt beam models by asymptotic methods
Rodríguez-Arós, Á. D.; Viaño, J. M.
2012-06-01
The authors derive and justify two models for the bending-stretching of a viscoelastic rod by using the asymptotic expansion method. The material behaviour is modelled by using a general Kelvin-Voigt constitutive law.
MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-Zhi Bai; Yong-Hua Gao
2007-01-01
We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX2+BX+C=0,where A,B and C are square matrices.This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices.Under suitable conditions, we prove the local linear convergence of the Dew method.An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm.In addition,we also describe and analyze the block version of the modified Bernoulli iteration method.
Preconditioning methods for improved convergence rates in iterative reconstructions
International Nuclear Information System (INIS)
Because of the characteristics of the tomographic inversion problem, iterative reconstruction techniques often suffer from poor convergence rates--especially at high spatial frequencies. By using preconditioning methods, the convergence properties of most iterative methods can be greatly enhanced without changing their ultimate solution. To increase reconstruction speed, the authors have applied spatially-invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques. In a sample application, the authors performed reconstructions from noiseless, simulated projection data, using preconditioned and conventional steepest-descent algorithms. The preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the unassisted algorithms at the same iteration. Applications of these methods to regularized reconstructions from projection data containing Poisson noise showed similar, although not as dramatic, behavior
Energy Technology Data Exchange (ETDEWEB)
Yarmukhamedov, R. [Institute of Nuclear Physics, Academy of Sciences of Uzbekistan, 100214 Tashkent (Uzbekistan)
2014-05-09
The basic methods of the determination of asymptotic normalization coefficient for A+a→B of astrophysical interest are briefly presented. The results of the application of the specific asymptotic normalization coefficients derived within these methods for the extrapolation of the astrophysical S factors to experimentally inaccessible energy regions (E ≤ 25 keV) for the some specific radiative capture A(a,γ)B reactions of the pp-chain and the CNO cycle are presented.
Asymptotic solving method for a sea—air oscillator model of atmospheric physics
International Nuclear Information System (INIS)
In this paper, a class of coupled system for the El Niño/La Niña southern oscillation (ENSO) atmospheric physics oscillation model is considered. We propose an ENSO atmospheric physics model using a method from the asymptotic theory. It is indicated from the results that the asymptotic method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly of the atmosphere—ocean oscillation for the ENSO model in the equatorial Pacific. (general)
Shadow boundary effects in hybrid numerical-asymptotic methods for high frequency scattering
Hewett, David P.
2014-01-01
The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high frequency solution asymptotics. In this paper we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction ...
Natural Preconditioning and Iterative Methods for Saddle Point Systems
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.
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
Analysis of the electrical conduction using an iterative method
Dziuba, Z.; Górska, M.
1992-01-01
An iterative method for transforming the electrical conduction versus magnetic field $\\hat{\\sigma}\\,(H)$ into the mobility spectrum of the electrical conduction density s (μ) is presented. The mobility spectrum is a new form of presentation of carrier parameters. The method is especially useful in the analysis of a mixed conduction in semiconductors like HgCdTe or in quantum well systems.
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...
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.
Approximate iterative operator method for potential-field downward continuation
Tai, Zhenhua; Zhang, Fengxu; Zhang, Fengqin; Hao, Mengcheng
2016-05-01
An approximate iterative operator method in wavenumber domain was proposed to improve the stability and accuracy of downward continuation of potential fields measured from the ground surface, marine or airborne. Firstly, the generalized iterative formula of downward continuation is derived in wavenumber domain; then, the transformational relationship between horizontal second-order partial derivatives and continuation is derived based on the Taylor series and Laplace equation, to obtain an approximate operator. By introducing this operator to the generalized iterative formula, a rapid algorithm is developed for downward continuation. The filtering and convergence characteristics of this method are analyzed for the purpose of estimating the optimal interval of number of iterations. We demonstrate the proposed method on synthetic data, and the results validate the flexibility of the proposed method. At last, we apply the proposed method to real data, and the results show the proposed method can enhance gravity anomalies generated by concealed orebodies. And in the contour obtained by making our proposed method results continue upward to measured level, the numerical results have approximate distribution and amplitude with original anomalies.
APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS
Institute of Scientific and Technical Information of China (English)
SHAO Xin-hui; SHEN Hai-long; LI Chang-jun
2006-01-01
Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.
Variational iteration method for solving compressible Euler equations
International Nuclear Information System (INIS)
This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient. (general)
A New Iterative Method to Calculate [pi
Dion, Peter; Ho, Anthony
2012-01-01
For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…
Scattering from a multilayered chiral sphere using an iterative method
Shang, Qing-Chao; Wu, Zhen-Sen; Qu, Tan; Li, Zheng-Jun; Bai, Lu
2016-04-01
An iterative method for electromagnetic scattering from a multilayered chiral sphere is presented based on Lorenz-Mie regime. Electromagnetic fields in each region are expanded in terms of spherical vector wave functions. To calculate the scattering coefficients of the fields in outer space, an iterative form is constructed according to the coefficients equations obtained by the boundary condition on each layer. The iterative relations are expressed in forms of ratios and logarithmic derivatives of Riccati-Bessel functions, which can be calculated conveniently by their recurrence relations. The theory and codes are verified by comparing the scattered fields with those of a multilayered isotropic achiral sphere, and those of a single layered chiral sphere. Scattered fields of multilayered chiral spheres are presented and discussed, including a large sized case and a Gaussian beam incidence case.
Energy Technology Data Exchange (ETDEWEB)
de Almeida, V.F.
2004-01-28
A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicularly to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiative intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiative intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.
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
A Picard-S hybrid type iteration method for solving a differential equation with retarded argument
Gürsoy, Faik; Karakaya, Vatan
2014-01-01
We introduce a new iteration method called Picard-S iteration. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and converges faster than CR iteration method for the aforementioned class of mappings. Furthermore, by providing an example, it is shown that the Picard-S iteration method converges faster than all Picard, Mann, Ishikawa, Noor, SP, CR, S and some other iteration metho...
Institute of Scientific and Technical Information of China (English)
Shi Sheng ZHANG; Chi Kin CHAN; H.W. JOSEPH LEE
2012-01-01
The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-φ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality.Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces.As applications we utilize the results presented in the paper to solving the convex feasibility problem (CFP) and zero point problem of maximal monotone mappings in Banach spaces.The results presented in the paper improve and extend the corresponding results announced by many authors.
Soft Error Vulnerability of Iterative Linear Algebra Methods
Energy Technology Data Exchange (ETDEWEB)
Bronevetsky, G; de Supinski, B
2008-01-19
Devices are increasingly vulnerable to soft errors as their feature sizes shrink. Previously, soft error rates were significant primarily in space and high-atmospheric computing. Modern architectures now use features so small at sufficiently low voltages that soft errors are becoming important even at terrestrial altitudes. Due to their large number of components, supercomputers are particularly susceptible to soft errors. Since many large scale parallel scientific applications use iterative linear algebra methods, the soft error vulnerability of these methods constitutes a large fraction of the applications overall vulnerability. Many users consider these methods invulnerable to most soft errors since they converge from an imprecise solution to a precise one. However, we show in this paper that iterative methods are vulnerable to soft errors, exhibiting both silent data corruptions and poor ability to detect errors. Further, we evaluate a variety of soft error detection and tolerance techniques, including checkpointing, linear matrix encodings, and residual tracking techniques.
Variational Iteration Method for a Fractional-Order Brusselator System
Directory of Open Access Journals (Sweden)
H. Jafari
2014-01-01
Full Text Available This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.
Iteration Complexity Analysis of Block Coordinate Descent Methods
Hong, Mingyi; Wang, Xiangfeng; Razaviyayn, Meisam; Luo, Zhi-Quan
2013-01-01
In this paper, we provide a unified iteration complexity analysis for a family of general block coordinate descent (BCD) methods, covering popular methods such as the block coordinate gradient descent (BCGD) and the block coordinate proximal gradient (BCPG), under various different coordinate update rules. We unify these algorithms under the so-called Block Successive Upper-bound Minimization (BSUM) framework, and show that for a broad class of multi-block nonsmooth convex problems, all algor...
Object-oriented design of preconditioned iterative methods
Energy Technology Data Exchange (ETDEWEB)
Bruaset, A.M. [SINTEF, Oslo (Norway)
1994-12-31
In this talk the author discusses how object-oriented programming techniques can be used to develop a flexible software package for preconditioned iterative methods. The ideas described have been used to implement the linear algebra part of Diffpack, which is a collection of C++ class libraries that provides high-level tools for the solution of partial differential equations. In particular, this software package is aimed at rapid development of PDE-based numerical simulators, primarily using finite element methods.
Gao, Hao
2015-01-01
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. Specifically, 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 convergenc...
A Parallel Iterative Method for Computing Molecular Absorption Spectra.
Koval, Peter; Foerster, Dietrich; Coulaud, Olivier
2010-09-14
We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamic polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about 1 order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general, and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics. PMID:26616067
Iterative methods for stationary convection-dominated transport problems
Energy Technology Data Exchange (ETDEWEB)
Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)
1994-12-31
It is well known that many iterative methods fail when applied to nonlinear systems of convection-dominated transport equations. Most successful methods for obtaining steady-state solutions to such systems rely on time-stepping through an artificial transient, combined with careful construction of artificial dissipation operators. These operators provide control over spurious oscillations which pollute the steady state solutions, and, in the nonlinear case, may become amplified and lead to instability. In the present study, we investigate Taylor Galerkin and SUPG-type methods and compare results for steady-state solutions to the Euler equations of gas dynamics. In particular, we consider the efficiency of different iterative strategies and present results for representative two-dimensional calculations.
Iterative methods for simultaneous inclusion of polynomial zeros
Petković, Miodrag
1989-01-01
The simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous ...
Improved criticality convergence via a modified Monte Carlo iteration method
Energy Technology Data Exchange (ETDEWEB)
Booth, Thomas E [Los Alamos National Laboratory; Gubernatis, James E [Los Alamos National Laboratory
2009-01-01
Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights that must sum somehow to maintain the second eigenfunction. Summing negative and positive weights can be done using point detector mechanics, but this sometimes can be quite slow. We show that an approximate cancellation scheme is sufficient to accelerate the convergence to the dominant eigenfunction. A second difficulty is that for some problems the Monte Carlo implementation of the modified power method has some stability problems. We also show that a simple method deals with this in an effective, but ad hoc manner.
Iterative reconstruction methods in X-ray CT.
Beister, Marcel; Kolditz, Daniel; Kalender, Willi A
2012-04-01
Iterative reconstruction (IR) methods have recently re-emerged in transmission x-ray computed tomography (CT). They were successfully used in the early years of CT, but given up when the amount of measured data increased because of the higher computational demands of IR compared to analytical methods. The availability of large computational capacities in normal workstations and the ongoing efforts towards lower doses in CT have changed the situation; IR has become a hot topic for all major vendors of clinical CT systems in the past 5 years. This review strives to provide information on IR methods and aims at interested physicists and physicians already active in the field of CT. We give an overview on the terminology used and an introduction to the most important algorithmic concepts including references for further reading. As a practical example, details on a model-based iterative reconstruction algorithm implemented on a modern graphics adapter (GPU) are presented, followed by application examples for several dedicated CT scanners in order to demonstrate the performance and potential of iterative reconstruction methods. Finally, some general thoughts regarding the advantages and disadvantages of IR methods as well as open points for research in this field are discussed. PMID:22316498
Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
Degond, Pierre; Lozinski, Alexei; Narski, Jacek; Negulescu, Claudia
2010-01-01
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic preserving reformulation of the original system, permitting an accurate resolution independently of the anisotropy strength and without the need of a mesh adapted to this anisotropy. The counterpart of this original procedure is the larger system size, enlarged by adding auxiliary variables and Lagrange multipliers. This Asymptotic-Preserving method generalizes the method investigated in a previous paper [arXiv:0903.4984v2] to the case of an arbitrary anisotropy direction field.
Non-asymptotic fractional order differentiators via an algebraic parametric method
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.
Computation of saddle-type slow manifolds using iterative methods
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
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...... 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...
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...
Energy Technology Data Exchange (ETDEWEB)
Belov, P. A., E-mail: pavelbelov@gmail.com; Yakovlev, S. L., E-mail: yakovlev@cph10.phys.spbu.ru [St. Petersburg State University, Department of Computational Physics (Russian Federation)
2013-02-15
The process of neutron-deuteron scattering at energies above the deuteron-breakup threshold is described within the three-body formalism of Faddeev equations. Use is made of the method of solving Faddeev equations in configuration space on the basis of expanding wave-function components in the asymptotic region in bases of eigenfunctions of specially chosen operators. Asymptotically, wave-function components are represented in the form of an expansion in an orthonormalized basis of functions depending on the hyperangle. This basis makes it possible to orthogonalize the contributions of elastic-scattering and breakup channels. The proposed method permits determining scattering and breakup parameters from the asymptotic representation of the wave function without reconstructing it over the entire configuration space. The scattering and breakup amplitudes for states of total spin S = 1/2 and 3/2 were obtained for the s-wave Faddeev equation.
ASYMPTOTIC STABILITY OF RUNGE-KUTTA METHODS FOR THE PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jing-jun Zhao; Wan-rong Cao; Ming-zhu Liu
2004-01-01
This paper considers the asymptotic stability analysis of both exact and numericalsolutions of the following neutral delay differential equation with pantograph delay.{x′(t)+Bx(t)+Cx′(qt)+Dx(qt)=0, t>0,x(0)=x0,where B, C, D ∈ Cd×d, q ∈ (0, 1), and B is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a Lstable Runge-Kutta method can preserve the above-mentioned stability properties.
An Alternating Iterative Method and Its Application in Statistical Inference
Institute of Scientific and Technical Information of China (English)
Ning Zhong SHI; Guo Rong HU; Qing CUI
2008-01-01
This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. (Biometrika, 72, 465–472 (1983)), Shi N. Z. (J. Multivariate Anal.,50, 282–293 (1994)) and El Barmi H. and Dykstra R. (Ann. Statist., 26, 1878–1893 (1998)).
International Nuclear Information System (INIS)
In this article, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM) are presented. Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like Fisher type. The approximate solutions of the fractional Fisher type equation are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than Haar wavelet method
On the interplay between inner and outer iterations for a class of iterative methods
Energy Technology Data Exchange (ETDEWEB)
Giladi, E. [Stanford Univ., CA (United States)
1994-12-31
Iterative algorithms for solving linear systems of equations often involve the solution of a subproblem at each step. This subproblem is usually another linear system of equations. For example, a preconditioned iteration involves the solution of a preconditioner at each step. In this paper, the author considers algorithms for which the subproblem is also solved iteratively. The subproblem is then said to be solved by {open_quotes}inner iterations{close_quotes} while the term {open_quotes}outer iteration{close_quotes} refers to a step of the basic algorithm. The cost of performing an outer iteration is dominated by the solution of the subproblem, and can be measured by the number of inner iterations. A good measure of the total amount of work needed to solve the original problem to some accuracy c is then, the total number of inner iterations. To lower the amount of work, one can consider solving the subproblems {open_quotes}inexactly{close_quotes} i.e. not to full accuracy. Although this diminishes the cost of solving each subproblem, it usually slows down the convergence of the outer iteration. It is therefore interesting to study the effect of solving each subproblem inexactly on the total amount of work. Specifically, the author considers strategies in which the accuracy to which the inner problem is solved, changes from one outer iteration to the other. The author seeks the `optimal strategy`, that is, the one that yields the lowest possible cost. Here, the author develops a methodology to find the optimal strategy, from the set of slowly varying strategies, for some iterative algorithms. This methodology is applied to the Chebychev iteration and it is shown that for Chebychev iteration, a strategy in which the inner-tolerance remains constant is optimal. The author also estimates this optimal constant. Then generalizations to other iterative procedures are discussed.
Thermal diffusivity identification based on an iterative regularization method
Attar, Lamia; Perez, Laetitia; Nouailletas, Rémy; Moulay, Emmanuel; Autrique, Laurent
2015-01-01
International audience This article deals with the identification of a space and time dependent material thermal diffusivity. Such parameter is involved in heat transfers described by partial differential equations. An iterative regularization method based on a conjugate gradient algorithm is implemented. Such approach is attractive in order to efficiently deal with measurement noises and model errors. Numerical results are illustrated according to severa...
Computation of electron energy loss spectra by an iterative method
Energy Technology Data Exchange (ETDEWEB)
Koval, Peter [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián (Spain); Ljungberg, Mathias Per [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Foerster, Dietrich [LOMA, Université de Bordeaux 1, 351 Cours de la Liberation, 33405 Talence (France); Sánchez-Portal, Daniel [Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastián (Spain); Centro de Física de Materiales CFM-MPC, Centro Mixto CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, E-20018 San Sebastián (Spain)
2015-07-01
A method is presented to compute the dielectric function for extended systems using linear response time-dependent density functional theory. Localized basis functions with finite support are used to expand both eigenstates and response functions. The electron-energy loss function is directly obtained by an iterative Krylov-subspace method. We apply our method to graphene and silicon and compare it to plane-wave based approaches. Finally, we compute electron-energy loss spectrum of C{sub 60} crystal to demonstrate the merits of the method for molecular crystals, where it will be most competitive.
Computation of electron energy loss spectra by an iterative method
International Nuclear Information System (INIS)
A method is presented to compute the dielectric function for extended systems using linear response time-dependent density functional theory. Localized basis functions with finite support are used to expand both eigenstates and response functions. The electron-energy loss function is directly obtained by an iterative Krylov-subspace method. We apply our method to graphene and silicon and compare it to plane-wave based approaches. Finally, we compute electron-energy loss spectrum of C60 crystal to demonstrate the merits of the method for molecular crystals, where it will be most competitive
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo
2015-01-01
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...... 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 an...
Application of Non-Iterative Method in Image Deblurring
Directory of Open Access Journals (Sweden)
MILADINOVIC Marko
2012-05-01
Full Text Available This paper presents a non-iterative method thatfinds application in a broad scientific field such as imagedeblurring. A method for image deblurring, based on thepseudo-inverse matrix is apply for removal of blurr inan image caused by linear motion. This methodassumes that linear motion corresponds to an integralnumber of pixels. Compared to other classicalmethods, this method attains higher values of theImprovement in Signal to Noise Ratio (ISNRparameter and of the Peak Signal-to-Noise Ratio(PSNR. We give an implementation in the MATLABprogramming package.
Zoom synchrosqueezing transform and iterative demodulation: Methods with application
Cao, Hongrui; Xi, Songtao; Chen, Xuefeng; Wang, Shibin
2016-05-01
Synchrosqueezing is a powerful time-frequency analysis tool for signals with time-varying frequency. However, as it is based on the continuous wavelet transform, its time-frequency representation (TFR) has better time but worse frequency resolution in higher frequency region, while worse time but better frequency resolution in lower frequency region. It makes the synchrosqueezing difficult to accurately estimate IFs with highly oscillating rate but small fluctuation amplitude. To address this issue, a zoom synchrosqueezing transform (ZST) is proposed to generate both excellent time and frequency resolution in a specific frequency region and analyze the mono-component signal in the particular frequency region to obtain accurate IF estimation results. For multi-component signals with nonlinear and close IFs, a ZST based dual iterative demodulation method is proposed, with the inner iteration to gradually refine and accurately extract a concerned mono-component, and the outer iteration to extract all mono-components gradually to alleviate the interference between individual components. Then satisfactory energy concentrated TFRs and accurate IF estimation results of mono-components can be obtained by the proposed ZST. The TFR of the multi-component signal can be gained by superposing the TFRs of all mono-components. The effectiveness of the proposed methods was validated using both simulated signals and a rub-impact signal collected from an engineering machine unit.
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.
ASYMPTOTIC BEHAVIOR OF MULTISTEP RUNGE-KUTTA METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
张诚坚; 廖晓昕
2001-01-01
This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stability of onestep Runge-Kutta methods, we obtain that a multistep Runge-Kutta method for DDEs is stable iff the corresponding methods for ODEs is A-stable under suitable interpolation conditions.
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
2015-01-01
This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers. .
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: 1.590, year: 2014
AIR: fused Analytical and Iterative Reconstruction method for computed tomography
Yang, Liu; Qi, Sharon X; Gao, Hao
2013-01-01
Purpose: CT image reconstruction techniques have two major categories: analytical reconstruction (AR) method and iterative reconstruction (IR) method. AR reconstructs images through analytical formulas, such as filtered backprojection (FBP) in 2D and Feldkamp-Davis-Kress (FDK) method in 3D, which can be either mathematically exact or approximate. On the other hand, IR is often based on the discrete forward model of X-ray transform and formulated as a minimization problem with some appropriate image regularization method, so that the reconstructed image corresponds to the minimizer of the optimization problem. This work is to investigate the fused analytical and iterative reconstruction (AIR) method. Methods: Based on IR with L1-type image regularization, AIR is formulated with a AR-specific preconditioner in the data fidelity term, which results in the minimal change of the solution algorithm that replaces the adjoint X-ray transform by the filtered X-ray transform. As a proof-of-concept 2D example of AIR, FB...
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 th...
Parallel computation of multigroup reactivity coefficient using iterative method
International Nuclear Information System (INIS)
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
Iterative methods for dose reduction and image enhancement in tomography
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.
Energy Technology Data Exchange (ETDEWEB)
Griebel, M. [Technische Universitaet Muenchen (Germany)
1994-12-31
In recent years, it has turned out that many modern iterative algorithms (multigrid schemes, multilevel preconditioners, domain decomposition methods etc.) for solving problems resulting from the discretization of PDEs can be interpreted as additive (Jacobi-like) or multiplicative (Gauss-Seidel-like) subspace correction methods. The key to their analysis is the study of certain metric properties of the underlying splitting of the discretization space V into a sum of subspaces V{sub j}, j = 1{hor_ellipsis}, J resp. of the variational problem on V into auxiliary problems on these subspaces. Here, the author proposes a modified approach to the abstract convergence theory of these additive and multiplicative Schwarz iterative methods, that makes the relation to traditional iteration methods more explicit. To this end he introduces the enlarged Hilbert space V = V{sub 0} x {hor_ellipsis} x V{sub j} which is nothing else but the usual construction of the Cartesian product of the Hilbert spaces V{sub j} and use it now in the discretization process. This results in an enlarged, semidefinite linear system to be solved instead of the usual definite system. Then, modern multilevel methods as well as domain decomposition methods simplify to just traditional (block-) iteration methods. Now, the convergence analysis can be carried out directly for these traditional iterations on the enlarged system, making convergence proofs of multilevel and domain decomposition methods more clear, or, at least, more classical. The terms that enter the convergence proofs are exactly the ones of the classical iterative methods. It remains to estimate them properly. The convergence proof itself follow basically line by line the old proofs of the respective traditional iterative methods. Additionally, new multilevel/domain decomposition methods are constructed straightforwardly by now applying just other old and well known traditional iterative methods to the enlarged system.
Non-stationary iterative methods for solving macroeconomic numeric models
Directory of Open Access Journals (Sweden)
Bogdan OANCEA
2006-01-01
Full Text Available Macroeconometric modeling was influenced by the development of new and efficient computational techniques. Rational Expectations models, a particular class of macroeconometric models, give raise to very large systems of equations, the solution of which requires heavy computations. Therefore, such models are an interesting testing ground for the numerical methods addressed in this research. The most difficult problem is to obtain the solution of the linear system that arises during the Newton step. As an alternative to the direct methods, we propose non-stationary iterative methods, also called Krylov methods, to solve these models. Numerical experiments conducted by authors confirm the interesting features of these methods: low computational complexity and storage requirements.
A Matrix Pencil Algorithm Based Multiband Iterative Fusion Imaging Method
Zou, Yong Qiang; Gao, Xun Zhang; Li, Xiang; Liu, Yong Xiang
2016-01-01
Multiband signal fusion technique is a practicable and efficient way to improve the range resolution of ISAR image. The classical fusion method estimates the poles of each subband signal by the root-MUSIC method, and some good results were get in several experiments. However, this method is fragile in noise for the proper poles could not easy to get in low signal to noise ratio (SNR). In order to eliminate the influence of noise, this paper propose a matrix pencil algorithm based method to estimate the multiband signal poles. And to deal with mutual incoherent between subband signals, the incoherent parameters (ICP) are predicted through the relation of corresponding poles of each subband. Then, an iterative algorithm which aimed to minimize the 2-norm of signal difference is introduced to reduce signal fusion error. Applications to simulate dada verify that the proposed method get better fusion results at low SNR.
Statistics of electron multiplication in a multiplier phototube; Iterative method
International Nuclear Information System (INIS)
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
Comment on “A New Second-Order Iteration Method for Solving Nonlinear Equations”
Directory of Open Access Journals (Sweden)
Haibin Li
2013-01-01
Full Text Available Kang et al. claimed that they obtained a new iteration formulation for nonlinear algebraic equations; however the “new” formulation was first derived in 2007 by the variational iteration method.
Guoping Xu; Harry Zheng
2010-01-01
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is...
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...
Computer methods for ITER-like materials LIBS diagnostics
Łepek, Michał; Gąsior, Paweł
2014-11-01
Recent development of Laser-Induced Breakdown Spectroscopy (LIBS) caused that this method is considered as the most promising for future diagnostic applications for characterization of the deposited materials in the International Thermonuclear Experimental Reactor (ITER), which is currently under construction. In this article the basics of LIBS are shortly discussed and the software for spectra analyzing is presented. The main software function is to analyze measured spectra with respect to the certain element lines presence. Some program operation results are presented. Correct results for graphite and aluminum are obtained although identification of tungsten lines is a problem. The reason for this is low tungsten lines intensity, and thus low signal to noise ratio of the measured signal. In the second part artificial neural networks (ANNs) as the next step for LIBS spectra analyzing are proposed. The idea is focused on multilayer perceptron network (MLP) with backpropagation learning method. The potential of ANNs for data processing was proved through application in several LIBS-related domains, e.g. differentiating ancient Greek ceramics (discussed). The idea is to apply an ANN for determination of W, Al, C presence on ITER-like plasma-facing materials.
FAST NAS-RIF ALGORITHM USING ITERATIVE CONJUGATE GRADIENT METHOD
Directory of Open Access Journals (Sweden)
A.M.Raid
2014-04-01
Full Text Available Many improvements on image enhancemen have been achieved by The Non-negativity And Support constraints Recursive Inverse Filtering (NAS-RIF algorithm. The Deterministic constraints such as non negativity, known finite support, and existence of blur invariant edges are given for the true image. NASRIF algorithms iterative and simultaneously estimate the pixels of the true image and the Point Spread Function (PSF based on conjugate gradients method. NAS-RIF algorithm doesn’t assume parametric models for either the image or the blur, so we update the parameters of conjugate gradient method and the objective function for improving the minimization of the cost function and the time for execution. We propose a different version of linear and nonlinear conjugate gradient methods to obtain the better results of image restoration with high PSNR.
On new methods of asymptotic formulas determination in waves diffraction problems
International Nuclear Information System (INIS)
A new approach to the determination of asymptotic formulas is demonstrated by solving the problem on shear plane wave diffraction in elastic plane at semi-infinite crack edge. As opposed to the well-known traditional methods, the solving of problems like these is deducted to Riemann-type boundary problem for real axis. In order to investigate the solution obtained in the form of Fourier integrals, the sections are drawn across the coordinate axis in complex plane and as a result the problem solution is represented in form of regular integrals in sections. The asymptotic formulas are determined by the integration by parts of integrals representing wave field in contrast to the steepest descend method
Asymptotically Optimal Algorithm for Short-Term Trading Based on the Method of Calibration
V'yugin, Vladimir
2012-01-01
A trading strategy based on a natural learning process, which asymptotically outperforms any trading strategy from RKHS (Reproduced Kernel Hilbert Space), is presented. In this process, the trader rationally chooses his gambles using predictions made by a randomized well calibrated algorithm. Our strategy is based on Dawid's notion of calibration with more general changing checking rules and on some modification of Kakade and Foster's randomized algorithm for computing calibrated forecasts. We use also Vovk's method of defensive forecasting in RKHS.
Solution of the Falkner-Skan wedge flow by a revised optimal homotopy asymptotic method.
Madaki, A G; Abdulhameed, M; Ali, M; Roslan, R
2016-01-01
In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner-Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge-Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique. PMID:27186477
The rate of convergence of some asymptotically chi-square distributed statistics by Stein's method
Gaunt, Robert E.; Reinert, Gesine
2016-01-01
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and establish some simple sufficient conditions for convergence rates of order $n^{-1}$ for smooth test functions. These general bounds are applied to Friedman's statistic for comparing $r$ treatments across $n$ trials and the family of power divergence statistics fo...
Iterated preconditioned LSQR method for inverse problems on unstructured grids
International Nuclear Information System (INIS)
This article presents a method for solving large-scale linear inverse imaging problems regularized with a nonlinear, edge-preserving penalty term such as total variation or the Perona–Malik technique. Our method is aimed at problems defined on unstructured meshes, where such regularizers naturally arise in unfactorized form as a stiffness matrix of an anisotropic diffusion operator and factorization is prohibitively expensive. In the proposed scheme, the nonlinearity is handled with lagged diffusivity fixed point iteration, which involves solving a large-scale linear least squares problem in each iteration. Because the convergence of Krylov methods for problems with discontinuities is notoriously slow, we propose to accelerate it by means of priorconditioning (Bayesian preconditioning). priorconditioning is a technique that, through transformation to the standard form, embeds the information contained in the prior (Bayesian interpretation of a regularizer) directly into the forward operator and thence into the solution space. We derive a factorization-free preconditioned LSQR algorithm (MLSQR), allowing implicit application of the preconditioner through efficient schemes such as multigrid. The resulting method is also matrix-free i.e. the forward map can be defined through its action on a vector. We illustrate the performance of the method on two numerical examples. Simple 1D-deblurring problem serves to visualize the discussion throughout the paper. The effectiveness of the proposed numerical scheme is demonstrated on a three-dimensional problem in fluorescence diffuse optical tomography with total variation regularization derived algebraic multigrid preconditioner, which is the type of large scale, unstructured mesh problem, requiring matrix-free and factorization-free approaches that motivated the work here. (paper)
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.
Iterative Methods for Scalable Uncertainty Quantification in Complex Networks
Surana, Amit; Banaszuk, Andrzej
2011-01-01
In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power, thermal and communication networks) are often composed of weakly interacting subnetworks. We propose intrusive and non-intrusive iterative schemes that exploit such weak interconnections to overcome dimensionality curse associated with traditional uncertainty quantification methods (e.g. generalized Polynomial Chaos, Probabilistic Collocation) and accelerate uncertainty propagation in systems with large number of uncertain parameters. This approach relies on integrating graph theoretic methods and waveform relaxation with generalized Polynomial Chaos, and Probabilistic Collocation, rendering these techniques scalable. We analyze convergence properties of this scheme and illustrate it on several examples.
PET iterative reconstruction incorporating an efficient positron range correction method.
Bertolli, Ottavia; Eleftheriou, Afroditi; Cecchetti, Matteo; Camarlinghi, Niccolò; Belcari, Nicola; Tsoumpas, Charalampos
2016-02-01
Positron range is one of the main physical effects limiting the spatial resolution of positron emission tomography (PET) images. If positrons travel inside a magnetic field, for instance inside a nuclear magnetic resonance (MR) tomograph, the mean range will be smaller but still significant. In this investigation we examined a method to correct for the positron range effect in iterative image reconstruction by including tissue-specific kernels in the forward projection operation. The correction method was implemented within STIR library (Software for Tomographic Image Reconstruction). In order to obtain the positron annihilation distribution of various radioactive isotopes in water and lung tissue, simulations were performed with the Monte Carlo package GATE [Jan et al. 2004 [1
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution, the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick...
Direct determination of asymptotic structural postbuckling behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1997-01-01
Application of the Finite Element Method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of nonlinear terms of different orders. A general method is given here that explains the reason for the numerical...... problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick...
Krylov iterative methods and synthetic acceleration for transport in binary statistical media
International Nuclear Information System (INIS)
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 S2 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.
Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality
Degond, Pierre; Deluzet, Fabrice; Navoret, Laurent; Sun, An-Bang; Vignal, Marie-Hélène
2009-01-01
This paper deals with the numerical resolution of the Vlasov-Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an ``Asymptotic-Preserving" PIC scheme which is not subject to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and s...
On the solution of two-dimensional coupled Burgers' equations by variational iteration method
International Nuclear Information System (INIS)
By means of variational iteration method the solutions of two-dimensional Burgers' and inhomogeneous coupled Burgers' equations are exactly obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He's variational iteration method is given approximate solutions that can converge to its exact solutions faster than those of Adomain's method.
The Renormalization-Group Method Applied to Asymptotic Analysis of Vector Fields
Kunihiro, T
1996-01-01
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifurcation leads to the Landau-Stuart and the (time-dependent) Ginzburg-Landau equations. It is confirmed that this method is actually a powerful theory for the reduction of the dynamics as the reductive perturbation method is. Some examples for ordinary diferential equations, such as the forced Duffing, the Lotka-Volterra and the Lorenz equations, are worked out in this method: The time evolution of the solution of the Lotka-Volterra equation is explicitly given, while the center manifolds of the Lorenz equation are constructed in a simple way in the RG 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.
Loli Piccolomini, Elena; Zama, Fabiana
2009-01-01
Ill posed problems constitute the mathematical model of a large variety of applications. Aim of this paper is to define an iterative algorithm finding the solution of a regularization problem. The method minimizes a function constituted by a least squares term and a generally nonlinear regularization term, weighted by a regularization parameter. The proposed method computes a sequence of iterates approximating the regularization parameter and a sequence of iterates appro...
The A-Forest Iteration Method for the Stochastic Generalized Transportation Problem
Qi, L.
1984-01-01
The stochastic generalized transportation problem (SGTP) has an optimal solution: each of the connected subgraphs of its graph is either a tree or a one-loop tree. We call such a graph an A-forest. We propose here a finitely convergent method, the A-forest iteration method, to solve the SGTP. It iterates from one base A-forest triple to another base A-Forest triple. The iteration techniques constitute some modifications of those for the first iteration method for solving the stochastic transp...
Iterative Method and Dithering with Averaging used for Correction of ADC Error
Kamenský, M.; Kováč, K.
2009-01-01
Additive iterative method in combination with averaging of dithered samples is designed for self-correction of ADC linearity error in the paper. Iterative method is one of the automated error correction techniques. Dithering is a special tool for quantizer performance enhancement. Dither theory for Gaussian noise and averaging has been used for exhibition of method abilities in ADC characteristic improvement.
Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method
Energy Technology Data Exchange (ETDEWEB)
Ameen, Maqsood M.; Harursampath, Dineshkumar, E-mail: m.ameen@tue.nl, E-mail: dinesh@aero.iisc.ernet.in [Department of Aerospace Engineering, Indian Institute of Science, Bangalore-560012 (India)
2015-03-10
The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam ref-erence curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.
Analysis of transverse shear strains in pre-twisted thick beams using variational asymptotic method
International Nuclear Information System (INIS)
The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam ref-erence curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Iterative methods for symmetric ill-conditioned Toeplitz matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Institut fuer Informatik, Muenchen (Germany)
1996-12-31
We consider ill-conditioned symmetric positive definite, Toeplitz systems T{sub n}x = b. If we want to solve such a system iteratively with the conjugate gradient method, we can use band-Toeplitz-preconditioners or Sine-Transform-peconditioners M = S{sub n}{Lambda}S{sub n}, S{sub n} the Sine-Transform-matrix and {Lambda} a diagonal matrix. A Toeplitz matrix T{sub n} = (t{sub i-j)}{sub i}{sup n},{sub j=1} is often related to an underlying function f defined by the coefficients t{sub j}, j = -{infinity},..,-1,0, 1,.., {infinity}. There are four cases, for which we want to determine a preconditioner M: - T{sub n} is related to an underlying function which is given explicitly; - T{sub n} is related to an underlying function that is given by its Fourier coefficients; - T{sub n} is related to an underlying function that is unknown; - T{sub n} is not related to an underlying function. Especially for the first three cases we show how positive definite and effective preconditioners based on the Sine-Transform can be defined for general nonnegative underlying function f. To define M, we evaluate or estimate the values of f at certain positions, and build a Sine-transform matrix with these values as eigenvalues. Then, the spectrum of the preconditioned system is bounded from above and away from zero.
Towards advanced welding methods for the ITER vacuum vessel sectors
International Nuclear Information System (INIS)
The problem of joining the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) sectors, considering the tolerance requirements of the blanket attachments, and the time required for TIG welding, continues to stimulate EU R and D into power beam welding techniques which can yield fewer passes, less welding time and lower distortion. The previous work on reduced pressure e-beam welding showed that penetration varied with position, fit-up, distance and pressure and single-pass weld control was deemed to be not reliable enough so the work direction changed to an all-e-beam welding procedure where the root weld is carried out with rest-current-control and the fill passes by wire-fill. In addition, a novel method of increasing the possible single-pass weld thickness for overhead positions is investigated demonstrated and now patented. Another solution may be offered with wire-fill NdYAG laser welding, which has demonstrated useable and stable results and proved improved performance over TIG. Preliminary work has shown even further advantages with the introduction of hybrid MIG/Laser welding
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.
Directory of Open Access Journals (Sweden)
HongYu Li
2009-01-01
Full Text Available We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for the minimization problem.
Research on the iterative method for model updating based on the frequency response function
Institute of Scientific and Technical Information of China (English)
Wei-Ming Li; Jia-Zhen Hong
2012-01-01
Model reduction technique is usually employed in model updating process,In this paper,a new model updating method named as cross-model cross-frequency response function (CMCF) method is proposed and a new iterative method associating the model updating method with the model reduction technique is investigated.The new model updating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency response function,which could greatly increase the number of the equations and the updating parameters.Based on the traditional iterative method,a correction term related to the errors resulting from the replacement of the reduction matrix of the experimental model with that of the finite element model is added in the new iterative method.Comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels,and both of these two iterative methods combine the CMCF method and the succession-level approximate reduction technique.Results show the effectiveness of the CMCF method and the proposed iterative method.
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....
Comparison of advanced iterative reconstruction methods for SPECT/CT
International Nuclear Information System (INIS)
Aim: Corrective image reconstruction methods which produce reconstructed images with improved spatial resolution and decreased noise level became recently commercially available. In this work, we tested the performance of three new software packages with reconstruction schemes recommended by the manufacturers using physical phantoms simulating realistic clinical settings. Methods: A specially designed resolution phantom containing three 99mTc lines sources and the NEMA NU-2 image quality phantom were acquired on three different SPECT/CT systems (General Electrics Infinia, Philips BrightView and Siemens Symbia T6). Measurement of both phantoms was done with the trunk filled with a 99mTc-water solution. The projection data were reconstructed using the GE's Evolution for Bone registered, Philips Astonish registered and Siemens Flash3D registered software. The reconstruction parameters employed (number of iterations and subsets, the choice of post-filtering) followed theses recommendations of each vendor. These results were compared with reference reconstructions using the ordered subset expectation maximization (OSEM) reconstruction scheme. Results: The best results (smallest value for resolution, highest percent contrast values) for all three packages were found for the scatter corrected data without applying any post-filtering. The advanced reconstruction methods improve the full width at half maximum (FWHM) of the line sources from 11.4 to 9.5 mm (GE), from 9.1 to 6.4 mm (Philips), and from 12.1 to 8.9 mm (Siemens) if no additional post filter was applied. The total image quality control index measured for a concentration ratio of 8:1 improves for GE from 147 to 189, from 179. to 325 for Philips and from 217 to 320 for Siemens using the reference method for comparison. The same trends can be observed for the 4:1 concentration ratio. The use of a post-filter reduces the background variability approximately by a factor of two, but deteriorates significantly the
An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
Chertock, Alina; Neusser, Jochen
2015-01-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
Monitoring 3D dose distributions in proton therapy by reconstruction using an iterative method.
Kim, Young-Hak; Yoon, Changyeon; Lee, Wonho
2016-08-01
The Bragg peak of protons can be determined by measuring prompt γ-rays. In this study, prompt γ-rays detected by single-photon emission computed tomography with a geometrically optimized collimation system were reconstructed by an iterative method. The falloff position by iterative method (52.48mm) was most similar to the Bragg peak (52mm) of an 80MeV proton compared with those of back-projection (54.11mm) and filtered back-projection (54.91mm) methods. Iterative method also showed better image performance than other methods. PMID:27179145
On the Convergence for an Iterative Method for Quasivariational Inclusions
Directory of Open Access Journals (Sweden)
Wu Changqun
2010-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of solutions of quasivariational inclusion problems and of the set of fixed points of strict pseudocontractions in the framework Hilbert spaces. The results presented in this paper improve and extend the corresponding results announced by many others.
Application of optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
Marinca, Vasile; Bereteu, Liviu
2015-01-01
Magnetorheological fluids (MR) are stable suspensions of magnetizable microparticles, characterized by the property to change the rheological characteristics when subjected to the action of magnetic field. Together with another class of materials that change their rheological characteristics in the presence of an electric field, called electrorheological materials are known in the literature as the smart materials or controlled materials. In the absence of a magnetic field the particles in MR fluid are dispersed in the base fluid and its flow through the apertures is behaves as a Newtonian fluid having a constant shear stress. When the magnetic field is applying a MR fluid behavior change, and behaves like a Bingham fluid with a variable shear stress. Dynamic response time is an important characteristic for determining the performance of MR dampers in practical civil engineering applications. The purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear d...
International Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
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...
Dilts, James
2016-01-01
For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar curvature problem, which provides a necessary condition on the seed data for the conformal constraint equations to (possibly) admit a solution. We then consider sets of asymptotically Euclidean (AE) seed data for which solutions of the conformal constraint equations exist, and examine the blowup properties of these solutions as the seed data sets approach sets for which no solutions exist. We also prove that there are AE seed data sets which include a Yamabe nonpositive metric and lead to solutions of the conformal constraints. These data sets allow the mean curvature function to have zeroes.
Non-iterative and exact method for constraining particles in a linear geometry
Tapia-McClung, Horacio; Grønbech-Jensen, Niels
2004-01-01
We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy only by the numerical methods for solving small systems of linear equations. As a result of the non-iterative and exact (within numerical accuracy) nature of the procedure there is no drift in the constrained geometry, and the method is therefore readily appli...
Energy Technology Data Exchange (ETDEWEB)
Kalaida, A.F. [Kiev Univ. (Ukraine)
1994-11-10
We construct and analyze for convergence a quadrature-iteration method for Volterra integral equations of the second kind and a quadrature-splitting method for linear equations. The iteration processes producing an approximate solution are accelerated, because the integral operator is approximated by a quadrature operator with an arbitrarily small residual operator.
On Two Iterative Methods for Mixed Monotone Variational Inequalities
Directory of Open Access Journals (Sweden)
Xiwen Lu
2010-01-01
Full Text Available A mixed monotone variational inequality (MMVI problem in a Hilbert space H is formulated to find a point u∗∈H such that 〈Tu∗,v−u∗〉+φ(v−φ(u∗≥0 for all v∈H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function on H. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the work of Wang et al., (2001 has in general weak convergence in an infinite-dimensional space, and the algorithm introduced in the paper of Noor (2001 fails in general to converge to a solution.
Fourier analysis of multigrid-type iterative methods
International Nuclear Information System (INIS)
Experiments indicate that a multigrid-type cycle can be used as an efficient preconditioner in the iterative solution of the discrete problem corresponding to a singularly perturbed elliptic boundary-value problem. Motivated by a report of Goldstein, the author explores the theoretical basis for the efficiency of such a preconditioner when applied to a model problem. The techniques developed are also used to analyze a multigrid V-cycle when used alone as a fast iterative solver. The solution of the one-dimensional indefinite Helmholtz problem using standard multigrid V-cycles is considered. By analyzing various choices of projection, interpolation, smoothers, and coarse-grid operators, a particular combination is found that preserves typical multigrid efficiency even in this indefinite case
ITERATIVE MULTICHANNEL BLIND DECONVOLUTION METHOD FOR TEMPORALLY COLORED SOURCES
Institute of Scientific and Technical Information of China (English)
Zhang Mingjian; Wei Gang
2004-01-01
An iterative separation approach, i.e. source signals are extracted and removed one by one, is proposed for multichannel blind deconvolution of colored signals. Each source signal is extracted in two stages: a filtered version of the source signal is first obtained by solving the generalized eigenvalue problem, which is then followed by a single channel blind deconvolution based on ensemble learning. Simulation demonstrates the capability of the approach to perform efficient mutichannel blind deconvolution.
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces
Wang Lin
2006-01-01
In real Hilbert space , from an arbitrary initial point , an explicit iteration scheme is defined as follows: , where , is a nonexpansive mapping such that is nonempty, is a -strongly monotone and -Lipschitzian mapping, , and . Under some suitable conditions, the sequence is shown to converge strongly to a fixed point of and the necessary and sufficient conditions that converges strongly to a fixed point of are obtained.
Drawing Dynamical and Parameters Planes of Iterative Families and Methods
Chicharro, Francisco I.
2013-01-01
The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones). PMID:24376386
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.
International Nuclear Information System (INIS)
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.)
Mullen, Marie
2010-01-01
The main focus of this work is to contribute to the development of iterative solvers applied to the method of moments solution of electromagnetic wave scattering problems. In recent years there has been much focus on current marching iterative methods, such as Gauss-Seidel and others. These methods attempt to march a solution for the unknown basis function amplitudes in a manner that mimics the physical processes which create the current. In particular the forward backwar...
Asymptotics and Borel summability
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
An iterative method for robust in-line phase contrast imaging
Carroll, Aidan J.; van Riessen, Grant A.; Balaur, Eugeniu; Dolbnya, Igor P.; Tran, Giang N.; Peele, Andrew G.
2016-04-01
We present an iterative near-field in-line phase contrast method that allows quantitative determination of the thickness of an object given the refractive index of the sample material. The iterative method allows for quantitative phase contrast imaging in regimes where the contrast transfer function (CTF) and transport of intensity equation (TIE) cannot be applied. Further, the nature of the iterative scheme offers more flexibility and potentially allows more high-resolution image reconstructions when compared to TIE method and less artefacts when compared to the CTF method. While, not addressed here, extension of our approach in future work to broadband illumination will also be straightforward as the wavelength dependence of the refractive index of an object can be readily incorporated into the iterative approach.
SOLUTION OF THE TWO-PHASE STEFAN PROBLEM BY USING THE PICARD'S ITERATIVE METHOD
Roman Witula; Edyta Hetmaniok; Damian Slota; Adam Zielonka
2011-01-01
In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of some base functions. Coefficients of this combination are determined by minimizing a properly construct...
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K.; Barba, Lorena A.
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. ...
Hanfeng Kuang; Jinbo Liu; Xi Chen; Jie Mao; Linjie He
2013-01-01
The asymptotic behavior of a class of switched stochastic cellular neural networks (CNNs) with mixed delays (discrete time-varying delays and distributed time-varying delays) is investigated in this paper. Employing the average dwell time approach (ADT), stochastic analysis technology, and linear matrix inequalities technique (LMI), some novel sufficient conditions on the issue of asymptotic behavior (the mean-square ultimate boundedness, the existence of an attractor, and the mean-square ...
Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method
International Nuclear Information System (INIS)
We prove results on exact asymptotics as n→∞ for the expectations Ea exp{-θΣk=0n-1g(Xk)} and probabilities Pa{(1/n Σk=0n-1g(Xk)k}k=1∞ is a sequence of independent identically Laplace-distributed random variables, Xn=X0+Σk=1nξk, n≥1, is the corresponding random walk on R, g(x) is a positive continuous function satisfying certain conditions, and d>0, θ>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|p, log (|x|p+1), p>0, |x| log (|x|+1), or eα|x|-1, 0<α<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.
Benvenuto, F.; La Camera, A.; Theys, C.; Ferrari, A.; Lantéri, H.; Bertero, M.
2008-06-01
In 1993, Snyder et al investigated the maximum-likelihood (ML) approach to the deconvolution of images acquired by a charge-coupled-device camera and proved that the iterative method proposed by Llacer and Nuñez in 1990 can be derived from the expectation-maximization method of Dempster et al for the solution of ML problems. The utility of the approach was shown on the reconstruction of images of the Hubble space Telescope. This problem deserves further investigation because it can be important in the deconvolution of images of faint objects provided by next-generation ground-based telescopes that will be characterized by large collecting areas and advanced adaptive optics. In this paper, we first prove the existence of solutions of the ML problem by investigating the properties of the negative log of the likelihood function. Next, we show that the iterative method proposed by the above-mentioned authors is a scaled gradient method for the constrained minimization of this function in the closed and convex cone of the non-negative vectors and that, if it is convergent, the limit is a solution of the constrained ML problem. Moreover, by looking for the asymptotic behavior in the regime of high numbers of photons, we find an approximation that, as proved by numerical experiments, works well for any number of photons, thus providing an efficient implementation of the algorithm. In the case of image deconvolution, we also extend the method to take into account boundary effects and multiple images of the same object. The approximation proposed in this paper is tested on a few numerical examples.
A fast iterative method to compute the flow around a submerged body
Energy Technology Data Exchange (ETDEWEB)
Malmliden, J.F.; Petersson, N.A.
1996-07-01
The authors develop an efficient iterative method for computing steady linearized potential flow around a submerged body moving in a liquid of finite constant depth. In this paper they restrict the presentation to the two-dimensional problem, but the method is readily generalizable to the three-dimensional case, i.e., the flow in a canal. The problem is indefinite, which makes the convergence of most iterative methods unstable. To circumvent this difficulty, the authors decompose the problem into two more easily solvable subproblems and form a Schwarz-type iteration to solve the original problem. The first subproblem is definite and can therefore be solved by standard iterative methods. The second subproblem is indefinite but has no body. It is therefore easily and efficiently solvable by separation of variables. The authors prove that the iteration converges for sufficiently small Froude numbers. In addition, they present numerical results for a second-order accurate discretization of the problem. They demonstrate that the iterative method converges rapidly, and that the convergences rate improves when the Froude number decreases. They also verify numerically that the convergence rate is essentially independent of the grid size. 20 refs., 6 figs., 10 tabs.
Iterative methods for distributed parameter estimation in parabolic PDE
Energy Technology Data Exchange (ETDEWEB)
Vogel, C.R. [Montana State Univ., Bozeman, MT (United States); Wade, J.G. [Bowling Green State Univ., OH (United States)
1994-12-31
The goal of the work presented is the development of effective iterative techniques for large-scale inverse or parameter estimation problems. In this extended abstract, a detailed description of the mathematical framework in which the authors view these problem is presented, followed by an outline of the ideas and algorithms developed. Distributed parameter estimation problems often arise in mathematical modeling with partial differential equations. They can be viewed as inverse problems; the `forward problem` is that of using the fully specified model to predict the behavior of the system. The inverse or parameter estimation problem is: given the form of the model and some observed data from the system being modeled, determine the unknown parameters of the model. These problems are of great practical and mathematical interest, and the development of efficient computational algorithms is an active area of study.
Evaluating user reputation in online rating systems via an iterative group-based ranking method
Gao, Jian
2015-01-01
Reputation is a valuable asset in online social lives and it has drawn increased attention. How to evaluate user reputation in online rating systems is especially significant due to the existence of spamming attacks. To address this issue, so far, a variety of methods have been proposed, including network-based methods, quality-based methods and group-based ranking method. In this paper, we propose an iterative group-based ranking (IGR) method by introducing an iterative reputation-allocation process into the original group-based ranking (GR) method. More specifically, users with higher reputation have higher weights in dominating the corresponding group sizes. The reputation of users and the corresponding group sizes are iteratively updated until they become stable. Results on two real data sets suggest that the proposed IGR method has better performance and its robustness is considerably improved comparing with the original GR method. Our work highlights the positive role of users' grouping behavior towards...
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.
Application of SSOR-PCG method with improved iteration format in FEM simulation of massive concrete
Directory of Open Access Journals (Sweden)
Lin HAN
2011-09-01
Full Text Available In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method (SSOR-PCGM with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete (RCC gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.
Intelligent Iterated Local Search Methods for Solving Vehicle Routing Problem with Different Fleets
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.
Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods
DEFF Research Database (Denmark)
Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.; Mirgolbabaei, H.
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 to...... solve the diffusion equations herein have been applied to a variety of problems in the recent past, and have proved to yield highly accurate solutions. Comparison is made between the exact solutions and the results of the variational iteration method (VIM) and homotopy perturbation method (HPM) in order...... to verify the accuracy of the results, revealing the fact that these methods are very effective and simple....
CONVERGENCE OF PARALLEL DIAGONAL ITERATION OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Xiao-hua Ding; Mingzhu Liu
2004-01-01
Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob-lem. But the iteration technique used to solve implicit Runge-Kutta method requires lots of computational efforts. In this paper, we extend the Parallel Diagonal Iterated Runge-Kutta(PDIRK) methods to delay differential equations(DDEs). We give the convergence region of PDIRK methods, and analyze the speed of convergence in three parts for the P-stability region of the Runge-Kutta corrector method. Finally, we analysis the speed-up factor through a numerical experiment. The results show that the PDIRK methods to DDEs are efficient.
A Direct Iteration Method using Resonance Integral Table for the Self-Shielding Calculations
International Nuclear Information System (INIS)
In this paper, a direct iteration method using the resonance integral table is introduced for the self-shielding calculations. The basic purpose of this paper is to show the possibility that the HELIOS subgroup method can be replaced with this method. This method doesn't use the subgroup data but only the resonance integral tables given in library. The basic idea of this method is to use the Bondarenko's iteration in order to obtain the self-shielded effective cross sections with the background cross sections which are calculated by the heterogeneous transport calculation. This method is implemented in the KARMA lattice calculation code and tested
A Direct Iteration Method using Resonance Integral Table for the Self-Shielding Calculations
Energy Technology Data Exchange (ETDEWEB)
Hong, Ser Gi; Kim, Kang Seog; Song, Jae Seung [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-10-15
In this paper, a direct iteration method using the resonance integral table is introduced for the self-shielding calculations. The basic purpose of this paper is to show the possibility that the HELIOS subgroup method can be replaced with this method. This method doesn't use the subgroup data but only the resonance integral tables given in library. The basic idea of this method is to use the Bondarenko's iteration in order to obtain the self-shielded effective cross sections with the background cross sections which are calculated by the heterogeneous transport calculation. This method is implemented in the KARMA lattice calculation code and tested.
Institute of Scientific and Technical Information of China (English)
Zhu Hanqing; Wu Zhengde; K. M. Luk
2003-01-01
In this paper, an absorbing Fictitious Boundary Condition (FBC) is presented to generate an iterative Domain Decomposition Method (DDM) for analyzing waveguide problems.The relaxed algorithm is introduced to improve the iterative convergence. And the matrix equations are solved using the multifrontal algorithm. The resulting CPU time is greatly reduced.Finally, a number of numerical examples are given to illustrate its accuracy and efficiency.
Iterative and FEM methods to solve the 2-D Radiative Transfer Equation with specular reflexion
Le Hardy, David; Favennec, Yann; Rousseau, Benoît
2016-01-01
The present paper deals with iterative algorithms coupled with finite element methods (FEM) to solve the Radiative Transfer Equation (RTE) within semi-transparent heterogenous materials where specular reflexions occur on their boundaries. As our intention is to use such solution for inversion, the forward model should be solved as fastly as possible. This communication compares, in terms of both accuracy and CPU, the Discontinuous Galerkin (DG) method with the Streamline Upwind Petrov-Galerkin (SUPG) method, both being coupled with the Discrete Ordinate Method. Next, several iteratives methods used to accelerate the convergence are compared. These methods are the Gauss-Siedel (GS), the Source-Iteration (SI) and the Successive Over-Relaxation (SOR) methods.
International Nuclear Information System (INIS)
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
STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES
Institute of Scientific and Technical Information of China (English)
Yongfu SU; Xiaolong QIN
2008-01-01
K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonexpansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial's condition.
Energy Technology Data Exchange (ETDEWEB)
Poole, G.; Heroux, M. [Engineering Applications Group, Eagan, MN (United States)
1994-12-31
This paper will focus on recent work in two widely used industrial applications codes with iterative methods. The ANSYS program, a general purpose finite element code widely used in structural analysis applications, has now added an iterative solver option. Some results are given from real applications comparing performance with the tradition parallel/vector frontal solver used in ANSYS. Discussion of the applicability of iterative solvers as a general purpose solver will include the topics of robustness, as well as memory requirements and CPU performance. The FIDAP program is a widely used CFD code which uses iterative solvers routinely. A brief description of preconditioners used and some performance enhancements for CRAY parallel/vector systems is given. The solution of large-scale applications in structures and CFD includes examples from industry problems solved on CRAY systems.
Improving Convergence of Iterative Feedback Tuning using Optimal External Perturbations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Hjalmarsson, Håkon; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
Iterative feedback tuning constitutes an attractive control loop tuning method for processes in the absence of sufficient process insight. It is a purely data driven approach to optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost...... introducing an optimal perturbation signal in the tuning algorithm. For minimum variance control design the optimal design of an external perturbation signal is derived in terms of the asymptotic accuracy of the iterative feedback tuning method....
Frequency-space domain acoustic wave simulation with the BiCGstab (ℓ) iterative method
Du, Zengli; Liu, Jianjun; Liu, Wenge; Li, Chunhong
2016-02-01
The vast computational cost and memory requirements of LU decomposition are major obstacles to 3D seismic modelling in the frequency-space domain. BiCGstab (ℓ) is an effective bi-conjugate gradient method to solve the giant sparse linear equations, but the convergence rate is extremely low when the threshold value is set small enough. The BiCGstab (ℓ) iterative method was introduced into 3D numerical simulation to overcome these problems in this paper. Numerical examples have shown that the precision of the BiCGstab (ℓ) iterative method meets the demand of seismic modelling and the result is equivalent to that of LU decomposition. The computational cost and memory resource demands of the BiCGstab (ℓ) iterative method are superior to that of LU decomposition. It is an effective method of 3D seismic modelling in the frequency-space domain.
Dilts, James
2014-01-01
We prove that in a certain class of conformal data on an asymptotically cylindrical manifold, if the conformally decomposed Einstein constraint equations do not admit a solution, then one can always find a nontrivial solution to the limit equation first explored by Dahl, Gicquaud, and Humbert in [DGH11]. We also give an example of a Ricci curvature condition on the manifold which precludes the existence of a solution to this limit equation, showing that such a limit criterion can be a useful tool for studying the Einstein constraint equations on manifolds with asymptotically cylindrical ends.
International Nuclear Information System (INIS)
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
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...
Institute of Scientific and Technical Information of China (English)
Gou Fu-Yan; Liu Cai; Liu Yang; Feng Xuan; Cui Fang-Zi
2014-01-01
In seismic prospecting,fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent high-precision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model andfi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.
International Nuclear Information System (INIS)
Precise knowledge of cold-atom collision properties is essential for the studies of Bose-Einstein condensation or cold molecule formation. In such experiments, the interaction mainly occurs at rather large interatomic distance, in the so-called asymptotic region. We have developed a purely asymptotic method which allows us to fully describe the collision properties of cold alkali atoms without using the inner part of the molecular potentials, which is often known with a poor precision. The key point of the method is the setting of nodal lines, which are the lines connecting the nodes of successive radial wavefunctions near the ground state threshold. Within the framework of Born-Oppenheimer approximation, computing such nodal lines, by numerical integration of the radial Schroedinger equation in the asymptotic region only, provides a very simple way to derive scattering lengths from observed bound level positions. The method has been extended to the multichannel case and appears now as a genuine parametric method, in which a few parameters (some chosen nodal lines) replace the inner part of the potentials. These nodal lines are used as fitting parameters, which are adjusted on experimental results. Once these parameters have been determined, any collision property such as scattering lengths, clock shifts or magnetic field induced Feshbach resonances can be deduced in principle. This method has been applied to obtain the collision properties of ultracold sodium and cesium atoms. (author)
Directory of Open Access Journals (Sweden)
Baojian Hong
2014-01-01
Full Text Available Based on He’s variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS. The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
Hong, Baojian; Lu, Dianchen
2014-01-01
Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations. PMID:25276865
Second degree generalized Jacobi iteration method for solving system of linear equations
Directory of Open Access Journals (Sweden)
Tesfaye Kebede Enyew
2016-05-01
Full Text Available In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1}=b_{1}[D_{m}^{-1}(L_{m}+U_{m}x^{(n}+k_{1m}]-a_{1}x^{(n-1}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ in comparison with FDJ, FDGJ, SDJ.
A CLASS OF LDPC CODE'S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD
Institute of Scientific and Technical Information of China (English)
Huang Zhonghu; Shen Lianfeng
2006-01-01
This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.
Accumulated approximation: A new method for structural optimization by iterative improvement
Rasmussen, John
1990-01-01
A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.
Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality
Degond, Pierre; Doyen, David
2015-01-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly we...
The use of He's variational iteration method for solving a Fokker-Planck equation
International Nuclear Information System (INIS)
This paper applies the variational iteration method to an initial value problem of parabolic type. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. This method is a powerful tool for solving various kinds of problems. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. Using the variational iteration method of He, a rapid convergent sequence is produced which tends to the exact solution of the problem. The results of this method are the same as with the results obtained by the Adomian decomposition method. The fact that this technique solves nonlinear equations without using Adomian polynomials can be considered as an advantage of this method over the Adomian decomposition procedure. The linear and nonlinear cases of the Fokker-Planck equation are considered and solved using the variational iteration method. To show the efficiency of the variational iteration method, several examples are presented
Bousquet-Mélou, Mireille; Soria, Michèle
2014-01-01
The present volume collects the proceedings of Aofa’14, the 25th International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms held at Université Pierre et Marie Curie, Paris, France, during June 16-20, 2014. The conference builds on the communities of the former series of conferences “Mathematics and Computer Science” and “Analysis of Algorithms”, and aims at studying rigorously the combinatorial objects which appear in the analysis of data stru...
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
International Nuclear Information System (INIS)
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Energy Technology Data Exchange (ETDEWEB)
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Highly Nonlinear Temperature-Dependent Fin Analysis by Variational Iteration Method
DEFF Research Database (Denmark)
Fouladi, F.; Hosseinzadeh, E.; Barari, Amin;
2010-01-01
In this research, the variational iteration method as an approximate analytical method is utilized to overcome some inherent limitations arising as uncontrollability to the nonzero endpoint boundary conditions and is used to solve some examples in the field of heat transfer. The available exact s...
Modified variational iteration method for an El Ni(n)o Southern Oscillation delayed oscillator
Institute of Scientific and Technical Information of China (English)
Cao Xiao-Qun; Song Jun-Qiang; Zhu Xiao-Qian; Zhang Li-Lun; Zhang Wei-Min; ZhaoJun
2012-01-01
This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Ni(n)o 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.
DIRECT ITERATIVE METHODS FOR RANK DEFICIENT GENERALIZED LEAST SQUARES PROBLEMS
Institute of Scientific and Technical Information of China (English)
Jin-yun Yuan; Xiao-qing Jin
2000-01-01
The generalized least squares (LS) problem appears in many application areas. Here W is an m × m symmetric positive definite matrix and A is an m × n matrix with m≥n. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well.
Directory of Open Access Journals (Sweden)
Qiang Wu
2013-01-01
Full Text Available Bioluminescence tomography (BLT has a great potential to provide a powerful tool for tumor detection, monitoring tumor therapy progress, and drug development; developing new reconstruction algorithms will advance the technique to practical applications. In the paper, we propose a BLT reconstruction algorithm by combining SP3 equations and Bregman iteration method to improve the quality of reconstructed sources. The numerical results for homogeneous and heterogeneous phantoms are very encouraging and give significant improvement over the algorithms without the use of SP3 equations and Bregman iteration method.
Iterative Methods for the Force-based Quasicontinuum Approximation
Dobson, Matthew; Luskin, Mitchell; Ortner, Christoph
2009-01-01
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation,...
Three-Step Iterative Methods with Sixth-Order Convergence for Solving Nonlinear Equations
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Behzad GHANBARI
2012-09-01
Full Text Available In this paper, we develop new families of sixth-order methods for solving simple zeros of non-linear equations. These methods are constructed such that the convergence is of order six. Each member of the families requires two evaluations of the given function and two of its derivative per iteration. These methods have more advantages than Newton’s method and other methods with the same convergence order, as shown in the illustration examples.
Chatter suppression methods of a robot machine for ITER vacuum vessel assembly and maintenance
International Nuclear Information System (INIS)
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
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.
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
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.
A concise iterative method using the Bezier technique for baseline construction.
Liu, Yuanjie; Zhou, Xiaoguang; Yu, Yude
2015-12-01
A novel approach, coined the Corner-Cutting method (CC, for short), is presented in this paper which affords the efficient construction of the baseline for analytical data streams. It was derived from techniques used in computer aided geometric design, a field established to produce curves and surfaces for the aviation and automobile industries. This corner-cutting technique provided a very efficient baseline calculation through an iterative process. Furthermore, a terminal condition was developed to make the process fully automated and truly non-parametric. Finally, we employed a Bezier curve to convert the iterating result into a smooth baseline solution. Compared to other iterative schemes used for baseline detection, our method was significantly efficient, easier to implement, and had a broader range of applications. PMID:26517702
The Projected GSURE for Automatic Parameter Tuning in Iterative Shrinkage Methods
Giryes, Raja; Eldar, Yonina C
2010-01-01
Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value lambda and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.
Generation of Shaped beam Radiation patterns from a Line source using Iterative sampling method
Directory of Open Access Journals (Sweden)
G.R.L.V.N.Srinivasa Raju
2013-08-01
Full Text Available For the generation of cosecant and trapezoidal radiation patterns an iterative sampling method is introduced by Stutzman. In this paper, an original radiation pattern which is some approximation to the desired radiation pattern is generated by a standard synthesis method and a series of correction patterns are applied to it by addinga correction pattern. This process is continued until the desired performance is achieved. In the present work, ramp, sector, cosecant, trapezoidal and stair stepped radiation patterns are generated using iterative procedure. The current distribution is found after corrections are applied. Studies are made with good number of examples, which showed that patterns with low side lobe level or low main beam ripple or sharp cut off from the main beam can be obtained. An iterative procedure is simple and converges rapidly.
The asymptotic convergence factor for a polygon under a perturbation
Energy Technology Data Exchange (ETDEWEB)
Li, X. [Georgia Southern Univ., Statesboro, GA (United States)
1994-12-31
Let Ax = b be a large system of linear equations, where A {element_of} C{sup NxN}, nonsingular and b {element_of} C{sup N}. A few iterative methods for solving have recently been presented in the case where A is nonsymmetric. Many of their algorithms consist of two phases: Phase I: estimate the extreme eigenvalues of A; Phase II: construct and apply an iterative method based on the estimates. For convenience, it is rewritten as an equivalent fixed-point form, x = Tx + c. Let {Omega} be a compact set excluding 1 in the complex plane, and let its complement in the extended complex plane be simply connected. The asymptotic convergence factor (ACF) for {Omega}, denoted by {kappa}({Omega}), measures the rate of convergence for the asymptotically optimal semiiterative methods for solving, where {sigma}(T) {contained_in} {Omega}.
Iterative method of finding hydraulic conductivity characteristics of soil moisture
Rysbaiuly, Bolatbek; Adamov, Abilmazhin
2016-08-01
The work considers an initial boundary value problem for a nonlinear equation of hydraulic conductivity. A method of finding a nonlinear diffusion coefficient is developed and hydraulic conductivity of soil moisture is found. Numerical calculations are conducted.
Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
Degond, Pierre; Deluzet, Fabrice; Lozinski, Alexei; Narski, Jacek; Negulescu, Claudia
2010-01-01
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic preserving reformulation of the original system, permitting an accurate resolution independently of the anisotropy strength and without the need of a mesh adapted to this anisotropy. The counterpart of this original procedure is the larger system size, enlarged ...
On the preconditioned AOR iterative method for Z-matrices
Salkuyeh, Davod Khojasteh
2011-01-01
Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \\in \\mathbb{R}^{n \\times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners $P$, where $P\\in \\mathbb{R}^{n\\times n}$ is nonsingular, nonnegative and has unit diagonal entries. Numerical results for corresponding preconditioned GMRES methods are given to illustrate the theoretical results.
Iterative methods for compressible Navier-Stokes and Euler equations
Energy Technology Data Exchange (ETDEWEB)
Tang, W.P.; Forsyth, P.A.
1996-12-31
This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.
An iterative method to invert the LTSn matrix
Energy Technology Data Exchange (ETDEWEB)
Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)
1996-12-31
Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.
International Nuclear Information System (INIS)
Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. We present a Kronecker-structured representation for calcium release site models and perform benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. In particular, multi-level methods provide excellent convergence with modest additional memory requirements for the Kronecker representation of calcium release site models. When an exact solution is not feasible, iterative approximate methods based on the power method may be used, with performance similar to Monte Carlo estimates. This suggests approximate methods with multi-level iterative engines as a promising avenue of future research for large-scale calcium release site models
A robust iterative unfolding method for signal processing
International Nuclear Information System (INIS)
It is a common problem in signal processing to remove a non-ideal detector resolution from a measured probability density function of some physical quantity. This process is called unfolding (a special case is the deconvolution), and it would involve the inversion of the integral operator describing the folding (i.e. the smearing of the detector). Currently, there is no unbiased method known in the literature for this issue (here, by unbiased we mean those approaches which do not assume an ansatz for the unknown probability density function). There is a well-known series expansion (Neumann series) in functional analysis for perturbative inversion of specific operators on Banach spaces. However, operators that appear in signal processing (e.g. folding and convolution of probability density functions), in general, do not satisfy the usual convergence condition of that series expansion. This paper provides some theorems on the convergence criteria of a similar series expansion for this more general case, which is not yet covered by the literature. The main result is that a series expansion provides a robust unbiased unfolding and deconvolution method. For the case of the deconvolution, such a series expansion can always be applied, and the method always recovers the maximum possible information about the initial probability density function, thus the method is optimal in this sense. A very significant advantage of the presented method is that one does not have to introduce ad hoc frequency regulations etc, as in the case of usual naive deconvolution methods. For the case of general unfolding problems, we present a computer-testable sufficient condition for the convergence of the series expansion in question. Some test examples and physics applications are also given. The most important physics example shall be (which originally motivated our survey on this topic) the case of π0 → γ + γ particle decay: we show that one can recover the initial π0 momentum density
Numerical radiative transfer with state-of-the-art iterative methods made easy
Lambert, Julien; Paletou, Frédéric; Josselin, Eric; Glorian, Jean-Michel
2016-01-01
This article presents an on-line tool and its accompanying software resources for the numerical solution of basic radiation transfer out of local thermodynamic equilibrium (LTE). State-of-the-art stationary iterative methods such as Accelerated Λ-iteration and Gauss-Seidel schemes, using a short characteristics-based formal solver are used. We also comment on typical numerical experiments associated to the basic non-LTE radiation problem. These resources are intended for the largest use and benefit, in support to more classical radiation transfer lectures usually given at the Master level.
International Nuclear Information System (INIS)
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
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
Basic Iterative Methods for Solving Elliptic Partial Differential Equation
Qahraman, Yousif Ahmed
2014-01-01
ABSTRACT: In this thesis, we studied the numerical techniques for the solution of two dimensional Elliptic partial differential equations such as Laplace's and Poisson's equations. These types of differential equations have specific applications in physical and engineering models. The discrete approximation of both equations is based on finite difference method. In this research, five points finite difference approximation is used for Laplace's and Poisson's equations. To solve the resulting ...
Method and apparatus for iterative lysis and extraction of algae
Chew, Geoffrey; Boggs, Tabitha; Dykes, Jr., H. Waite H.; Doherty, Stephen J.
2015-12-01
A method and system for processing algae involves the use of an ionic liquid-containing clarified cell lysate to lyse algae cells. The resulting crude cell lysate may be clarified and subsequently used to lyse algae cells. The process may be repeated a number of times before a clarified lysate is separated into lipid and aqueous phases for further processing and/or purification of desired products.
On iteration method of the partial wave analysis of the 3π-systems
International Nuclear Information System (INIS)
Iteration method has been used to define more precisely the experimental setup acceptance in the effective mass range 700-800 MeV. It has led to better accuracy of the 0-S-wave intensity and 0-S-0-P phase shift. 6 refs., 5 figs
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: 1.788, year: 2014
2014-01-01
The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Energy Technology Data Exchange (ETDEWEB)
Vengerskii, P.S.; Kardash, A.I.; Sen`o, P.S. [L`vov State Univ. (Russian Federation)
1994-06-05
We consider the problem of finding real solutions of a system of nonlinear algebraic equations using interval analysis. Several versions of Newton and Runge interval iteration methods are presented. The computational aspects of their application are explained. 6 refs., 2 tabs.
Numerical Iterative Methods Solving three-phase Multilevel Voltage Converter
Czech Academy of Sciences Publication Activity Database
Kujan, Petr
Vol. IEEE CACSC CFP10CAC-CDR. Yokohama: IEEE, 2010, s. 1801-1806. ISBN 978-1-4244-5355-9. [The 10th IEEE International Symposium on Computer - Aided Control System Design . Yokohama, Kanagawa (JP), 08.09.2010-10.09.2010] R&D Projects: GA MŠk(CZ) 1M0567 Grant ostatní: GA ČR(CZ) GPP103/10/P323 Institutional research plan: CEZ:AV0Z10750506 Keywords : multilevel converter * numerical methods * optimal PWM * selective harmonic elimination Subject RIV: BC - Control Systems Theory
GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
Terui, Akira
2010-01-01
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.
Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality
Degond, Pierre; Deluzet, Fabrice; Doyen, David
2015-01-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm l...
Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management
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.
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.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
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.
Variational iteration solving method for El Nino phenomenon atmospheric physics of nonlinear model
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A class of El Nino atmospheric physics oscillation model is considered. The El Nino atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and westem Pacific anomaly patterns. An El Nino atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the seaair oscillation for El Nino atmospheric physics model can be analyzed. El Nino is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.
A block-iterative nodal integral method for forced convection problems
International Nuclear Information System (INIS)
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
Solution of problems in calculus of variations via He's variational iteration method
International Nuclear Information System (INIS)
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
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
Zhang, Z.; Chen, J.; Chao, B. F.; Lu, Y.
2013-12-01
The dual-satellite mission of GRACE (Gravity Recovery And Climate Experiment) launched in 2002 has been making precise measurement of the Earth's (tiny) time-variable gravity (TVG), providing new and important information about mass transport on or in the Earth. Given the nature of the measurement technique, the GRACE TVG solutions, in the standard form of monthly spherical harmonic (SH) Stokes coefficients, are plagued with short-wavelength noises on regional to local scales, preventing proper interpretation of the TVG signals. Spatial low-pass filtering, or 'smoothing', is necessary. However, all kinds of filters remove noises and useful signal synchronously. In case of processing GRACE TVG solutions, when we use the Gaussian filter to remove short-wavelength noises, it also causes a reduction on spatial resolution. Here we devise an approach to recover the filtered GRACE TVG signal by iterative method. We deduce a formula to do iteration as a function of filter weight in spherical harmonic domain, so its implementation is straightforward and its iteration error is convergence. The simulation tests based on land hydrological monthly model solutions show that this method is able to recover the reduced amplitude caused by low-pass filter and improve spatial resolution. Without removing the glacial isostatic adjustment (GIA) effect, the slopes of mass change rates are -4.46Gt/yr and -28.73Gt/yr before and after recovering by iteration.
Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography
International Nuclear Information System (INIS)
We investigate fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography for applications in small animal imaging. Our forward model uses a diffusion approximation for optically inhomogeneous tissue, which we solve using a finite element method (FEM). We examine two approaches to incorporating the forward model into the solution of the inverse problem. In a conventional direct calculation approach one computes the full forward model by repeated solution of the FEM problem, once for each potential source location. We describe an alternative on-the-fly approach where one does not explicitly solve for the full forward model. Instead, the solution to the forward problem is included implicitly in the formulation of the inverse problem, and the FEM problem is solved at each iteration for the current image estimate. We evaluate the convergence speeds of several representative iterative algorithms. We compare the computation cost of those two approaches, concluding that the on-the-fly approach can lead to substantial reductions in total cost when combined with a rapidly converging iterative algorithm
Institute of Scientific and Technical Information of China (English)
Dao-qi Yang; Jennifer Zhao
2003-01-01
An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems withstrongly discontinuous solutions, conormal derivatives, and coefficients. This algorithmiteratively solves small problems for each single phase with good accuracy and exchangeinformation at the interface to advance the iteration until convergence, following the ideaof Schwarz Alternating Methods. Error estimates are derived to show that this algorithmalways converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases areperformed to show the accuracy of the method for capturing discontinuities in the solutionsand coefficients. In contrast to standard numerical methods, the accuracy of our methoddoes not seem to deteriorate as the coefficient discontinuity increases.
An iterative analytic—numerical method for scattering from a target buried beneath a rough surface
International Nuclear Information System (INIS)
An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Wei Shi-long; Guo Wei-ping
2015-01-01
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
Solution of the solidification problem by using the variational iteration method
E. Hetmaniok; D. Słota; A. Zielonka
2009-01-01
The paper presents the approximated solution of the solidification problem, modelled with the aid of the one-phase Stefan problem with the boundary condition of the second kind, by using the variational iteration method. For solving this problem one needs to determine the distribution of temperature in the given domain and the position of the moving interface. The proposed method of solution consists of describing the considered problem with a system of differential equations in a domain with...
Improvement of the image quality of random phase--free holography using an iterative method
Shimobaba, Tomoyoshi; Endo, Yutaka; Hirayama, Ryuji; Hiyama, Daisuke; Hasegawa, Satoki; Nagahama, Yuki; Sano, Marie; Oikawa, Minoru; Sugie, Takashige; Ito, Tomoyoshi
2015-01-01
Our proposed method of random phase-free holography using virtual convergence light can obtain large reconstructed images exceeding the size of the hologram, without the assistance of random phase. The reconstructed images have low-speckle noise in the amplitude and phase-only holograms (kinoforms); however, in low-resolution holograms, we obtain a degraded image quality compared to the original image. We propose an iterative random phase-free method with virtual convergence light to address this problem.
Asymptotic Behavior of a Competition-Diffusion System with Variable Coefficients and Time Delays
Miguel Uh Zapata; Eric Avila Vales; Angel G. Estrella
2008-01-01
A class of time-delay reaction-diffusion systems with variable coefficients which arise from the model of two competing ecological species is discussed. An asymptotic global attractor is established in terms of the variable coefficients, independent of the time delays and the effect of diffusion by the upper-lower solutions and iteration method.
Bernstein, Ally Leigh; Dhanantwari, Amar; Jurcova, Martina; Cheheltani, Rabee; Naha, Pratap Chandra; Ivanc, Thomas; Shefer, Efrat; Cormode, David Peter
2016-05-01
Computed tomography is a widely used medical imaging technique that has high spatial and temporal resolution. Its weakness is its low sensitivity towards contrast media. Iterative reconstruction techniques (ITER) have recently become available, which provide reduced image noise compared with traditional filtered back-projection methods (FBP), which may allow the sensitivity of CT to be improved, however this effect has not been studied in detail. We scanned phantoms containing either an iodine contrast agent or gold nanoparticles. We used a range of tube voltages and currents. We performed reconstruction with FBP, ITER and a novel, iterative, modal-based reconstruction (IMR) algorithm. We found that noise decreased in an algorithm dependent manner (FBP > ITER > IMR) for every scan and that no differences were observed in attenuation rates of the agents. The contrast to noise ratio (CNR) of iodine was highest at 80 kV, whilst the CNR for gold was highest at 140 kV. The CNR of IMR images was almost tenfold higher than that of FBP images. Similar trends were found in dual energy images formed using these algorithms. In conclusion, IMR-based reconstruction techniques will allow contrast agents to be detected with greater sensitivity, and may allow lower contrast agent doses to be used.
A fully nonlinear iterative solution method for self-similar potential flows with a free boundary
Iafrati, Alessandro
2013-01-01
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied under the assumptions of an ideal and incompressible fluid with negligible gravity and surface tension effects. The approach is based on a pseudo time stepping procedure, which uses a boundary integral equation method for the solution of the Laplace problem governing the velocity potential at each iteration. In order to demonstrate the flexibility and the capabilities of the approach, several applications are presented: the classical wedge entry problem, which is also used for a validation of the approach, the block sliding along an inclined sea bed, the vertical water entry of a flat plate and the ditching of an inclined plate. The solution procedure is also applied to cases in which the body surface is either porous or perforated. Comparisons with numerical or experimental d...
Kandel, Yudhishthir; Denbeaux, Gregory
2016-08-01
We develop a novel iterative method to accurately measure electron beam shape (current density distribution) and monotonic material response as a function of position. A common method is to scan an electron beam across a knife edge along many angles to give an approximate measure of the beam profile, however such scans are not easy to obtain in all systems. The present work uses only an electron beam and multiple exposed regions of a thin film of photoresist to measure the complete beam profile for any beam shape, where the material response is characterized externally. This simplifies the setup of new experimental tools. We solve for self-consistent photoresist thickness loss response to dose and the electron beam profile simultaneously by optimizing a novel functional iteratively. We also show the successful implementation of the method in a real world data set corrupted by noise and other experimental variabilities.
International Nuclear Information System (INIS)
In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes
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)
An Iterative Method for the Approximation of Fibers in Slow-Fast Systems
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Brøns, Morten; Starke, Jens
2014-01-01
In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite-dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers....... The method is demonstrated on the Michaelis--Menten--Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in nonstandard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers....
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.
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.
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
Wang, Jinguo; Zhao, Zhiqin, E-mail: zqzhao@uestc.edu.cn; Song, Jian; Chen, Guoping; Nie, Zaiping [School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731 (China); Liu, Qing-Huo [Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708 (United States)
2015-05-15
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.
Ramlau, R.; Saxenhuber, D.; Yudytskiy, M.
2014-07-01
The problem of atmospheric tomography arises in ground-based telescope imaging with adaptive optics (AO), where one aims to compensate in real-time for the rapidly changing optical distortions in the atmosphere. Many of these systems depend on a sufficient reconstruction of the turbulence profiles in order to obtain a good correction. Due to steadily growing telescope sizes, there is a strong increase in the computational load for atmospheric reconstruction with current methods, first and foremost the MVM. In this paper we present and compare three novel iterative reconstruction methods. The first iterative approach is the Finite Element- Wavelet Hybrid Algorithm (FEWHA), which combines wavelet-based techniques and conjugate gradient schemes to efficiently and accurately tackle the problem of atmospheric reconstruction. The method is extremely fast, highly flexible and yields superior quality. Another novel iterative reconstruction algorithm is the three step approach which decouples the problem in the reconstruction of the incoming wavefronts, the reconstruction of the turbulent layers (atmospheric tomography) and the computation of the best mirror correction (fitting step). For the atmospheric tomography problem within the three step approach, the Kaczmarz algorithm and the Gradient-based method have been developed. We present a detailed comparison of our reconstructors both in terms of quality and speed performance in the context of a Multi-Object Adaptive Optics (MOAO) system for the E-ELT setting on OCTOPUS, the ESO end-to-end simulation tool.
Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right-hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data. (paper)
International Nuclear Information System (INIS)
Highlights: • We present a Monte Carlo method for computing the adjoint-weighted kinetics parameters via the IFP algorithm. • Extensive verification tests are performed on simple models. • Several validation tests are performed on the measured values of effective delayed neutron fraction and Rossi alpha. - Abstract: The analysis of neutron kinetics relies on the knowledge of adjoint-weighted kinetics parameters, which are key to safety issues in the context of transient or accidental reactor behavior. The Iterated Fission Probability (IFP) method allows the adjoint-weighted mean generation time and delayed neutron fraction to be computed within a Monte Carlo power iteration calculation. In this work we describe the specific features of the implementation of the IFP algorithm in the reference Monte Carlo code TRIPOLI-4® developed at CEA. Several verification and validation tests are discussed, and the impact of nuclear data libraries, IFP cycle length and inter-cycle correlations are analyzed in detail
Least Squares Ranking on Graphs, Hodge Laplacians, Time Optimality, and Iterative Methods
Hirani, Anil N; Watts, Seth
2010-01-01
Given a set of alternatives to be ranked and some pairwise comparison values, ranking can be posed as a least squares computation on a graph. This was first used by Leake for ranking football teams. The residual can be further analyzed to find inconsistencies in the given data, and this leads to a second least squares problem. This whole process was formulated recently by Jiang et al. as a Hodge decomposition of the edge values. Recently, Koutis et al., showed that linear systems involving symmetric diagonally dominant (SDD) matrices can be solved in time approaching optimality. By using Hodge 0-Laplacian and 2-Laplacian, we give various results on when the normal equations for ranking are SDD and when iterative Krylov methods should be used. We also give iteration bounds for conjugate gradient method for these problems.
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2007-01-01
) transformations in the originally measured variables at the two points in time such as 1) changes in gain and offset in the measuring device used to acquire the data; 2) data normalization or calibration schemes that are linear (affine) in the gray values of the original variables; or 3) orthogonal or other...... affine transformations such as principal component (PC) or maximum autocorrelation factor (MAF) transformations. The IR-MAD method first calculates ordinary canonical and original MAD variates. In the following iterations we apply different weights to the observations, large weights are assigned 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...
A Non-Iterative Transformation Method for Newton's Free Boundary Problem
Fazio, Riccardo
2013-01-01
In book II of Newton's "Principia Mathematica" of 1687 several applicative problems are introduced and solved. There, we can find the formulation of the first calculus of variations problem that leads to the first free boundary problem of history. The general calculus of variations problem is concerned with the optimal shape design for the motion of projectiles subject to air resistance. Here, for Newton's optimal nose cone free boundary problem, we define a non-iterative initial value method...
Application of SSOR-PCG method with improved iteration format in FEM simulation of massive concrete
Han, Lin; Zi-ming ZHANG; Zhi-qiang N
2011-01-01
In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method (SSOR-PCGM) with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM w...
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.
Directory of Open Access Journals (Sweden)
Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Detailed Design and Fabrication Method of the ITER Vacuum Vessel Ports
International Nuclear Information System (INIS)
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
An Iterative Method for Constructing Equilibrium Phase Models of Stellar Systems
Rodionov, S A; Sotnikova, N Ya
2008-01-01
We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters and/or constraints. This method is very powerful, to a large extent due to its simplicity. It can be used for mass distributions with an arbitrary geometry and a large variety of kinematical constraints. We present several examples illustrating it. Applications of this method include the creation of initial conditions for N-body simulations and the modelling of galaxies from their photometric and kinematic observations.
Iterative Method for Constructing Complete Complementary Sequences with Lengths of 2mN
Institute of Scientific and Technical Information of China (English)
ZHANG Chao; HAN Chenggao; LIAO Yiting; LIN Xiaokang; HATORI Mitsutoshi
2005-01-01
Complete complementary sequences are widely used in spectrum spread communications because of their ideal correlation functions. A previous method generates complete complementary sequences with lengths of NnN (n,N∈Z+). This paper presents a new iterative method to construct complete complementary sequences with lengths of 2mN (m,N∈Z+). The analysis proves that this method can produce many sequence sets that do not appear in sequence sets generated by the former method, especially shorter sequence sets. The result will certainly increase the application of complete complementary sequences in communication engineering and related fields.
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
Energy Technology Data Exchange (ETDEWEB)
Lin, Lin; Shao, Sihong; E, Weinan
2012-11-06
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.
Dettmann, Carl P.
2002-01-01
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...
Moschidis, Georgios
2015-01-01
In [M. Dafermos and I. Rodnianski, A new physical-space approach to decay for the wave equation with applications to black hole spacetimes, in XVIth International Congress on Mathematical Physics, Pavel Exner ed., Prague 2009 pp. 421-433, 2009, arXiv:0910.4957], Dafermos and Rodnianski presented a novel approach to establish uniform decay rates for solutions $\\phi$ to the scalar wave equation $\\square_{g}\\phi=0$ on Minkowski, Schwarzschild and other asymptotically flat backgrounds. This paper generalises the methods and results of the above paper to a broad class of asymptotically flat spacetimes $(\\mathcal{M},g)$, including Kerr spacetimes in the full subextremal range $|a|
Iteration methods and algorithms for dielectric-resonator integral equations of the field
Davidovich, M. V.; Stefyuk, Yu. V.
2010-10-01
Quasi-eigenmodes of open cylindrical and rectangular dielectric resonators (DRs) are determined by the method of iterative solution of the volume integral and integro-differential equations with corresponding functionals. New forms of equations and iteration algorithms for the nonlinear input of the desired complex parameter are proposed. Frequencies and Q-factors of the H01δ and H011 modes of a cylindrical DR and the H mode of a rectangular DR for the uniform and nonuniform cases are obtained numerically. The influence of a thin semiconductor layer located at the ends of the DR and irradiated by high-power laser pulses on the frequencies and Q-factors of the DR modes is examined. It is shown that an up to ten or more percent tuning of resonant frequencies can be reached by transformation of a low conducting state to a high conducting state.
Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models
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.
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.
Solution of the solidification problem by using the variational iteration method
Directory of Open Access Journals (Sweden)
E. Hetmaniok
2009-10-01
Full Text Available The paper presents the approximated solution of the solidification problem, modelled with the aid of the one-phase Stefan problem with the boundary condition of the second kind, by using the variational iteration method. For solving this problem one needs to determine the distribution of temperature in the given domain and the position of the moving interface. The proposed method of solution consists of describing the considered problem with a system of differential equations in a domain with known boundary, and solving the received system with the aid of VIM method. The accuracy of the obtained approximated solution is verified by comparing it with the analytical solution.
Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method
Layton, Simon K
2015-01-01
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy controlled by the order of the expansion, $p$. We take advantage of a unique property of Krylov iterations that allow lower accuracy of the matrix-vector products as convergence proceeds, and propose a relaxation strategy based on progressively decreasing $p$. Via extensive numerical tests, we show that the relaxed Krylov iterations converge with speed-ups of between 2x and 4x for Laplace problems and between 3.5x and 4.5x for Stokes problems. We include an application to Stokes flow around red blood cells, computing with up to 64 cells and problem size up to 131k boundary elements and nearly 400k unknowns. The study was done with an in-house multi-threaded C++ code, on a quad-core CPU.
Preconditioners for Krylov Iterative Method for Two-Dimensional MOC Problems
International Nuclear Information System (INIS)
An appropriate selection of preconditioner for Krylov subspace method improves convergence of the iterative solutions of transport equations. The recent work, e.g., indicate that the consistent discretization requirement can be relaxed in diffusion synthetic acceleration (DSA) if it is used as a preconditioner for the Krylov iterative method. Coarse mesh rebalance (CMR) acceleration method also has been tested as a preconditioner for Krylov method. It is known that the CMR method is unstable or ineffective with scattering ratio c close to unity for optically thin or thick cells. In 1-D problems, this deficiency, however, disappeared and even improved when the CMR is used as a preconditioner. But in 2-D problems, CMR preconditioner sometimes had worsening effect on Krylov method. In other words, the Krylov method without preconditoiner preformed better than the preconditioned Krylov method. This paper, as an extension of previous work for finding good preconditioners for Krylov method, tested several preconditioners such as coarse mesh finite difference (CMFD), partial current coarse mesh finite difference (p-CMFD), and Jacobi preconditioners. The results are presented with discussions
Dai, Hui-Hui
2011-01-01
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical solutions of the deformations by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, ma...
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
Lin, Lin; Weinan, E
2012-01-01
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$,...
Preliminary Orbit Determination of a Tethered Satellite Using the p-Iteration Method
Cicci, D. A.; Qualls, C.
2016-04-01
The possibility of the future deployment of tethered satellites has created a need for a preliminary orbit determination method capable of determining whether or not a satellite is tethered to another satellite. Classical preliminary orbit determination methods, which are used for untethered satellites, typically require two or more position vectors along with their respective observation times in order to determine a preliminary orbital element set. However, these conventional methods can't distinguish between an untethered satellite and a tethered one, whose motion is modified due to the presence of a tether force. The use of conventional methods on a satellite which is part of a tethered satellite system will result in the calculation of inaccurate orbital elements. Modifications have been made to the p-iteration preliminary orbit determination method in order to allow for the identification of these tethered satellites. The modifications allow for the calculation of a modified gravitational parameter, which can be used to distinguish between a tethered satellite and an untethered one. This paper applies this modified p-iteration method to the problem of the quick identification of a tethered satellite. The performance of this method is evaluated through scenarios of differing tether lengths, levels of observation error, and orbital eccentricities. Due to the need for the preliminary orbit determination to be achieved quickly, only short time intervals between observations were considered. The manner in which this preliminary orbit information can be used to obtain tether parameters for the subsequent differential correction process is also described.
Institute of Scientific and Technical Information of China (English)
WANG Limin; CHEN Xi; GAO Furong
2013-01-01
Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry,a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures.This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC).A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences.For the convenience of implementation,only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control,consisting of dynamic output feedback plus feed-forward control.The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞ performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures.Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs),and design procedures,which formulate a convex optimization problem with LMI constraints,are presented.An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.
Akihiko Takahashi; Nakahiro Yoshida
2005-01-01
We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method, but also show its effectiveness through numerical examples such as computing optimal portfolio and pricing an average option. Finally, we show mathematical validity of our method.
Institute of Scientific and Technical Information of China (English)
Tao Zong-Ming; Zhang Yin-Chao; Liu Xiao-Qin; Tan Kun; Shao Shi-Sheng; Hu Huan-Ling; Zhang Gai-Xia; Lü Yong-Hui
2004-01-01
A new method is proposed to derive the size distribution of aerosol from the simulated multiwavelength lidar extinction coefficients. The basis for this iteration is to consider the extinction efficiency factor of particles as a set of weighting function covering the entire radius region of a distribution. The weighting functions are calculated exactly from Mie theory. This method extends the inversion region by subtracting some extinction coefficient. The radius range of simulated size distribution is 0.1-10.0μm, the inversion radius range is 0.1-2.0μm, but the inverted size distributions are in good agreement with the simulated one.
Investigation on vibration of single-walled carbon nanotubes by variational iteration method
Ahmadi Asoor, A. A.; Valipour, P.; Ghasemi, S. E.
2016-02-01
In this paper, the variational iteration method (VIM) has been used to investigate the non-linear vibration of single-walled carbon nanotubes (SWCNTs) based on the nonlocal Timoshenko beam theory. The accuracy of results is examined by the fourth-order Runge-Kutta numerical method. Comparison between VIM solutions with numerical results leads to highly accurate solutions. Also, the behavior of deflection and frequency in vibrations of SWCNTs are studied. The results show that frequency of single walled carbon nanotube versus amplitude increases by increasing the values of B.
Land cover classification of remotely sensed image with hierarchical iterative method
Institute of Scientific and Technical Information of China (English)
LI Peijun; HUANG Yingduan
2005-01-01
Based on the analysis of the single-stage classification results obtained by the multitemporal SPOT 5 and Landsat 7 ETM + multispectral images separately and the derived variogram texture, the best data combinations for each land cover class are selected, and the hierarchical iterative classification is then applied for land cover mapping. The proposed classification method combines the multitemporal images of different resolutions with the image texture, which can greatly improve the classification accuracy. The method and strategies proposed in the study can be easily transferred to other similar applications.
Comparison of Iterative Methods for Computing the Pressure Field in a Dynamic Network Model
DEFF Research Database (Denmark)
Mogensen, Kristian; Stenby, Erling Halfdan; Banerjee, Srilekha; Barker, Vincent A.
1999-01-01
In dynamic network models, the pressure map (the pressure in the pores) must be evaluated at each time step. This calculation involves the solution of a large number of nonlinear algebraic systems of equations and accounts for more than 80 of the total CPU-time. Each nonlinear system requires at...... least the partial solution of a sequence of linear systems. We present a comparative study of iterative methods for solving these systems, where we apply both standard routines from the public domain package ITPACK 2C and our own routines tailored to the network problem. The conjugate gradient method...
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
Application of the Picard’s iterative method for the solution of one-phase Stefan problem
Directory of Open Access Journals (Sweden)
R. Wituła
2010-10-01
Full Text Available In this paper, application of the Picard's iterative method for solving the one-phase Stefan problem is presented. In the proposed method, an iterative relation is formulated, which allows to determine the temperature distribution in the considered domain. The unknown function, describing the position of the moving interface, is approximated with the aid of the linear combination of some assumed base functions. The coefficients of this combination are determined by minimizing a properly constructed functional. Some examples, thatillustrate the precision and speed of convergence of the considered iterative procedure, are also shown.
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)
International Nuclear Information System (INIS)
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
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
Application of the Picard’s iterative method for the solution of one-phase Stefan problem
R. Wituła; E. Hetmaniok; D. Słota; A. Zielonka
2010-01-01
In this paper, application of the Picard's iterative method for solving the one-phase Stefan problem is presented. In the proposed method, an iterative relation is formulated, which allows to determine the temperature distribution in the considered domain. The unknown function, describing the position of the moving interface, is approximated with the aid of the linear combination of some assumed base functions. The coefficients of this combination are determined by minimizing a properly const...
International Nuclear Information System (INIS)
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. (paper)
An iterative stochastic ensemble method for parameter estimation of subsurface flow models
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.
Pürrer, Michael; Hannam, Mark
2012-01-01
We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial parameters by comparing the inspiral with post-Newtonian calculations. Our method is the first to be applied directly to the gravitational-wave (GW) signal, rather than the orbital motion. The GW signal is in general less contaminated by gauge effects, which, in moving-puncture simulations, limit orbital-motion-based measurements of the eccentricity to an uncertainty of $\\Delta e \\sim 0.002$, making it difficult to reduce the eccentricity below this value. Our new method can reach eccentricities below $10^{-3}$ in one or two iteration steps; we find that this is well below the requirements for GW astronomy in the advanced detector era. Our method can be readily adapted to any compact-binary simulation with GW emission, including black-hole-binary simulations that use alternative ...
Development of an iterative lattice-core coupling method based on MICROX-2 cross section libraries
International Nuclear Information System (INIS)
This paper describes an innovative online cross section generation method, developed based on Iterative Diffusion-Transport (IDT) calculation to minimize the inconsistency and inaccuracy in determining physics parameters by feeding actual reactor core conditions into the cross section generation process. A 2-dimensional (2-D) pin-by-pin lattice program, NEMA, was also developed to generate assembly lattice parameters using the embedded MICROX-2 cross section libraries and Nodal Expansion Method (NEM). The proposed methods were validated against a 2-D miniature core benchmark problem for both NEMA itself and its coupling to a reactor code by the IDT method (NEMA-DIF3D). The computational benchmark calculations have shown that the IDT improves the eigenvalue and power distribution predictions when compared with the conventional offline method. (author)
One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation
Institute of Scientific and Technical Information of China (English)
ZHANG Li; YANG Yan; LI Yuan-yuan; TAN Jie-qing
2014-01-01
A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation (WPIA for short) and consists of following steps:finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structure of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
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
Convergence rates for the iteratively regularized Gauss–Newton method in Banach spaces
International Nuclear Information System (INIS)
In this paper we consider the iteratively regularized Gauss–Newton method (IRGNM) in a Banach space setting and prove optimal convergence rates under approximate source conditions. These are related to the classical concept of source conditions that is available only in Hilbert space. We provide results in the framework of general index functions, which include, e.g. Hölder and logarithmic rates. Concerning the regularization parameters in each Newton step as well as the stopping index, we provide both a priori and a posteriori strategies, the latter being based on the discrepancy principle
International Nuclear Information System (INIS)
The purpose of this paper is the formulation of a Wave Concept Iterative Process (WCIP) for the analysis of the microwave planar circuits printed between two dielectric mediums in a cylindrical metallic box. This method is based on the transverse wave formulation. It also uses the Hankel Transform to express the integral relation in a spectral domain. An example of annular ring and circular patch loaded by annular ring has been studied and the obtained results validate the new approach. The good agreement between the simulation results and the experimental published data justifies the design procedure and validates the present analysis approach.
Directory of Open Access Journals (Sweden)
Yang Zhiwei
2010-01-01
Full Text Available We propose a subspace-tracking-based space-time adaptive processing technique for airborne radar applications. By applying a modified approximated power iteration subspace tracing algorithm, the principal subspace in which the clutter-plus-interference reside is estimated. Therefore, the moving targets are detected by projecting the data on the minor subspace which is orthogonal to the principal subspace. The proposed approach overcomes the shortcomings of the existing methods and has satisfactory performance. Simulation results confirm that the performance improvement is achieved at very small secondary sample support, a feature that is particularly attractive for applications in heterogeneous environments.
Modelling CH$_3$OH masers: Sobolev approximation and accelerated lambda iteration method
Nesterenok, Aleksandr
2015-01-01
A simple one-dimensional model of CH$_3$OH maser is considered. Two techniques are used for the calculation of molecule level populations: the accelerated lambda iteration (ALI) method and the large velocity gradient (LVG), or Sobolev, approximation. The LVG approximation gives accurate results provided that the characteristic dimensions of the medium are larger than 5-10 lengths of the resonance region. We presume that this condition can be satisfied only for the largest observed maser spot distributions. Factors controlling the pumping of class I and class II methanol masers are considered.
Directory of Open Access Journals (Sweden)
Qing-you Liu
2009-01-01
Full Text Available We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems, the set of common fixed points of infinitely many nonexpansive mappings, and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in Hilbert spaces. We give some strong-convergence theorems under mild assumptions on parameters. The results presented in this paper improve and generalize the main result of Yao et al. (2007.
Directory of Open Access Journals (Sweden)
Zeng Wei-you
2009-01-01
Full Text Available We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems, the set of common fixed points of infinitely many nonexpansive mappings, and the set of solutions of the variational inequality for -inverse-strongly monotone mappings in Hilbert spaces. We give some strong-convergence theorems under mild assumptions on parameters. The results presented in this paper improve and generalize the main result of Yao et al. (2007.
A comparison of multiprocessor scheduling methods for iterative data flow architectures
Storch, Matthew
1993-01-01
A comparative study is made between the Algorithm to Architecture Mapping Model (ATAMM) and three other related multiprocessing models from the published literature. The primary focus of all four models is the non-preemptive scheduling of large-grain iterative data flow graphs as required in real-time systems, control applications, signal processing, and pipelined computations. Important characteristics of the models such as injection control, dynamic assignment, multiple node instantiations, static optimum unfolding, range-chart guided scheduling, and mathematical optimization are identified. The models from the literature are compared with the ATAMM for performance, scheduling methods, memory requirements, and complexity of scheduling and design procedures.
Directory of Open Access Journals (Sweden)
Vladimir G. Danilov
2003-09-01
Full Text Available We present a new method for studying the interaction of solitons for non-integrable Korteweg-de Vries (KdV type equations with small dispersion and test this method for the KdV equation.
Directory of Open Access Journals (Sweden)
Ahmed K. Hassan
2008-01-01
Full Text Available One of the serious problems in any wireless communication system using multi carrier modulation technique like Orthogonal Frequency Division Multiplexing (OFDM is its Peak to Average Power Ratio (PAPR.It limits the transmission power due to the limitation of dynamic range of Analog to Digital Converter and Digital to Analog Converter (ADC/DAC and power amplifiers at the transmitter, which in turn sets the limit over maximum achievable rate.This issue is especially important for mobile terminals to sustain longer battery life time. Therefore reducing PAPR can be regarded as an important issue to realize efficient and affordable mobile communication services.This paper presents an efficient PAPR reduction method for OFDM signal. This method is based on clipping and iterative processing. Iterative processing is performed to limit PAPR in time domain but the subtraction process of the peak that over PAPR threshold with the original signal is done in frequency domain, not in time like usual clipping technique. The results of this method is capable of reducing the PAPR significantly with minimum bit error rate (BER degradation.
On Asymptotically Efficient Estimation in Semiparametric Models
Schick, Anton
1986-01-01
A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.
Development of an iterative diffusion-transport method based on MICROX-2 cross section libraries
International Nuclear Information System (INIS)
Highlights: • Innovative Iterative Diffusion Transport (IDT) method is developed. • A 2-dimensional (2-D) pin-by-pin lattice program, NEMA, is also developed. • The developed methods and codes are verified on benchmark problems. • Results show that the IDT method improves the global and local predictions. - Abstract: This paper introduces an innovative online cross section generation method, developed based on Iterative Diffusion-Transport (IDT) calculation to minimize the inconsistency and inaccuracy in determining physics parameters by feeding actual reactor core conditions into the cross section generation process. A two-dimensional (2-D) pin-by-pin lattice program, NEMA, was developed to generate assembly lattice parameters using the refined MICROX-2 cross section libraries and Nodal Expansion Method (NEM). The proposed method was verified against a 2-D miniature core (mini-core) benchmark problem. First, the few-group cross sections generated by NEMA were compared with those calculated by a Monte Carlo method code Serpent. Next, the analysis of a 2-D Light Water Reactor (LWR) mini-core benchmark problem was carried out by the nodal transport code DIF3D using few-group cross sections generated by NEMA, and the results were compared with those obtained from the Serpent full core calculation. Finally, the same benchmark problem was solved by the NEMA-DIF3D approach using the IDT coupling method. The computational benchmark calculations have shown that the homogenization technique implemented in NEMA is reliable when producing the few-group cross sections for the reactor core calculation. The IDT method also improves the eigenvalue and power distribution predictions
Application of Homotopy Perturbation and Variational Iteration Methods to SIR Epidemic Model
DEFF Research Database (Denmark)
Ghotbi, Abdoul R.; Barari, Amin; Omidvar, M.;
2011-01-01
Children born are susceptible to various diseases such as mumps, chicken pox etc. These diseases are the most common form of infectious diseases. In recent years, scientists have been trying to devise strategies to fight against these diseases. Since vaccination is considered to be the most....... In this article two methods namely Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are employed to compute an approximation to the solution of non-linear system of differential equations governing the problem. The obtained results are compared with those obtained by Adomian Decomposition...... Method (ADM). This research reveals that although the obtained results are the same, HPM and VIM are much more robust, more convenient and efficient in comparison to ADM....
International Nuclear Information System (INIS)
In this work the well known variational iteration method is used for finding the solution of a semi-linear inverse parabolic equation. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method a rapid convergent sequence is produced which tends to the exact solution of the problem. Thus the variational iteration method is suitable for finding the approximation of the solution without discretization of the problem. We will change the main problem to a direct problem which is easy to handle the variational iteration method. To show the efficiency of the present method, several examples are presented. Also it is shown that this method coincides with Adomian decomposition method for the studied problem
A non-iterative method for the electrical impedance tomography based on joint sparse recovery
Lee, Ok Kyun; Kang, Hyeonbae; Ye, Jong Chul; Lim, Mikyoung
2015-07-01
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric potential values inside the object can be expressed by integrals of densities with a common sparse support on the location of anomalies. Based on this integral expression, we formulate the reconstruction problem of small anomalies as a joint sparse recovery and present an efficient non-iterative recovery algorithm of small anomalies. Furthermore, we also provide a slightly modified algorithm to reconstruct an extended anomaly. We validate the effectiveness of the proposed algorithm over the linearized method and the multiple signal classification algorithm by numerical simulations. This work is supported by the Korean Ministry of Education, Sciences and Technology through NRF grant No. NRF-2010-0017532 (to H K), the Korean Ministry of Science, ICT & Future Planning; through NRF grant No. NRF-2013R1A1A3012931 (to M L), the R&D Convergence Program of NST (National Research Council of Science & Technology) of Republic of Korea (Grant CAP-13-3-KERI) (to O K L and J C Y).
Directory of Open Access Journals (Sweden)
Ibrahim Karahan
2016-04-01
Full Text Available Let C be a nonempty closed convex subset of a real Hilbert space H. Let {T_{n}}:C›H be a sequence of nearly nonexpansive mappings such that F:=?_{i=1}^{?}F(T_{i}?Ø. Let V:C›H be a ?-Lipschitzian mapping and F:C›H be a L-Lipschitzian and ?-strongly monotone operator. This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem. It is shown that under certain approximate assumptions on the operators and parameters, the modified iterative sequence {x_{n}} converges strongly to x^{*}?F which is also the unique solution of the following variational inequality: ?0, ?x?F. As a special case, this projection method can be used to find the minimum norm solution of above variational inequality; namely, the unique solution x^{*} to the quadratic minimization problem: x^{*}=argmin_{x?F}?x?². The results here improve and extend some recent corresponding results of other authors.
Decoherence suppression for three-qubit W-like state using weak measurement and iteration method
Yang, Guang; Lian, Bao-Wang; Nie, Min
2016-08-01
Multi-qubit entanglement states are the key resources for various multipartite quantum communication tasks. For a class of generalized three-qubit quantum entanglement, W-like state, we demonstrate that the weak measurement and the reversal measurement are capable of suppressing the amplitude damping decoherence by reducing the initial damping factor into a smaller equivalent damping factor. Furthermore, we propose an iteration method in the weak measurement and the reversal measurement to enhance the success probability of the total measurements. Finally, we discuss how the number of the iterations influences the overall effect of decoherence suppression, and find that the “half iteration” method is a better option that has more practical value. Project supported by the National Natural Science Foundation of China (Grant No. 61172071), the International Scientific Cooperation Program of Shaanxi Province, China (Grant No. 2015KW-013), and the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 16JK1711).
Use of the iterative solution method for coupled finite element and boundary element modeling
International Nuclear Information System (INIS)
Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver
Modified Step Variational Iteration Method for Solving Fractional Biochemical Reaction Model
Directory of Open Access Journals (Sweden)
R. Yulita Molliq
2011-01-01
Full Text Available A new method called the modification of step variational iteration method (MoSVIM is introduced and used to solve the fractional biochemical reaction model. The MoSVIM uses general Lagrange multipliers for construction of the correction functional for the problems, and it runs by step approach, which is to divide the interval into subintervals with time step, and the solutions are obtained at each subinterval as well adopting a nonzero auxiliary parameter ℏ to control the convergence region of series' solutions. The MoSVIM yields an analytical solution of a rapidly convergent infinite power series with easily computable terms and produces a good approximate solution on enlarged intervals for solving the fractional biochemical reaction model. The accuracy of the results obtained is in a excellent agreement with the Adam Bashforth Moulton method (ABMM.
Radiation pattern synthesis of planar antennas using the iterative sampling method
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.
ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
Mo Jiaqi; Zhang Weijiang; He Ming
2007-01-01
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
Abbasbandy, Saeid; Shivanian, Elyas
2009-01-01
In this paper, the variational iteration method is proposed to solve system of nonlinear Volterra's integro-differential equations. Four numerical examples are illustrated by this method. The results reveal that this method is very effective and highly promising in comparison with other numerical methods.
Directory of Open Access Journals (Sweden)
Elise Cormie-Bowins
2012-10-01
Full Text Available We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the initial state? This problem can be reduced to solving a linear equation Ax = b for x, where A is a matrix and b is a vector. We consider two iterative methods to solve the linear equation: the Jacobi method and the biconjugate gradient stabilized (BiCGStab method. For both methods, a sequential and a parallel version have been implemented. The parallel versions have been implemented on the compute unified device architecture (CUDA so that they can be run on a NVIDIA graphics processing unit (GPU. From our experiments we conclude that as the size of the matrix increases, the CUDA implementations outperform the sequential implementations. Furthermore, the BiCGStab method performs better than the Jacobi method for dense matrices, whereas the Jacobi method does better for sparse ones. Since the reachability probabilities problem plays a key role in probabilistic model checking, we also compared the implementations for matrices obtained from a probabilistic model checker. Our experiments support the conjecture by Bosnacki et al. that the Jacobi method is superior to Krylov subspace methods, a class to which the BiCGStab method belongs, for probabilistic model checking.
A guidance law for UAV autonomous aerial refueling based on the iterative computation method
Directory of Open Access Journals (Sweden)
Luo Delin
2014-08-01
Full Text Available The rendezvous and formation problem is a significant part for the unmanned aerial vehicle (UAV autonomous aerial refueling (AAR technique. It can be divided into two major phases: the long-range guidance phase and the formation phase. In this paper, an iterative computation guidance law (ICGL is proposed to compute a series of state variables to get the solution of a control variable for a UAV conducting rendezvous with a tanker in AAR. The proposed method can make the control variable converge to zero when the tanker and the UAV receiver come to a formation flight eventually. For the long-range guidance phase, the ICGL divides it into two sub-phases: the correction sub-phase and the guidance sub-phase. The two sub-phases share the same iterative process. As for the formation phase, a velocity coordinate system is created by which control accelerations are designed to make the speed of the UAV consistent with that of the tanker. The simulation results demonstrate that the proposed ICGL is effective and robust against wind disturbance.
mtDNA analysis of 174 Eurasian populations using a new iterative rank correlation method.
Juhász, Zoltán; Fehér, Tibor; Németh, Endre; Pamjav, Horolma
2016-02-01
In this study, we analyse 27-dimensional mtDNA haplogroup distributions of 174 Eurasian, North-African and American populations, including numerous ancient data as well. The main contribution of this work was the description of the haplogroup distribution of recent and ancient populations as compounds of certain hypothetic ancient core populations immediately or indirectly determining the migration processes in Eurasia for a long time. To identify these core populations, we developed a new iterative algorithm determining clusters of the 27 mtDNA haplogroups studied having strong rank correlation among each other within a definite subset of the populations. Based on this study, the current Eurasian populations can be considered as compounds of three early core populations regarding to maternal lineages. We wanted to show that a simultaneous analysis of ancient and recent data using a new iterative rank correlation algorithm and the weighted SOC learning technique may reveal the most important and deterministic migration processes in the past. This technique allowed us to determine geographically, historically and linguistically well-interpretable clusters of our dataset having a very specific, hardly classifiable structure. The method was validated using a 2-dimensional stepping stone model. PMID:26142878
An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
Chertock, Alina; Degond, Pierre; Neusser, Jochen
2015-01-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To ove...
A fast-converging iterative method for X-ray in-line phase contrast tomography
Vo, Nghia T.; Atwood, Robert C.; Moser, Herbert O.; Lee, Peter D.; Breese, Mark B. H.; Drakopoulos, Michael
2012-11-01
X-ray in-line phase contrast tomography holds great promise for the quantitative analysis of soft materials. However, its applications have been limited, so far, by the fact that direct methods based on the transport-of-intensity equation and the contrast transfer function are sensitive to noise and applicable only to limited types of samples. Here, we propose an iterative method based on the Gerchberg-Saxton algorithm (R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972)), but overcoming its slow convergence by an acceleration technique, named random signed feedback, which shows an excellent performance, both in numerical simulation and tomographic experiment, of discriminating various polymers even when using 53 keV synchrotron X-rays.
Dyka, Zoya
2011-01-01
Securing communication channels is especially needed in wireless environments. But applying cipher mechanisms in software is limited by the calculation and energy resources of the mobile devices. If hardware is applied to realize cryptographic operations cost becomes an issue. In this paper we describe an approach which tackles all these three points. We implemented a hardware accelerator for polynomial multiplication in extended Galois fields (GF) applying Karatsuba's method iteratively. With this approach the area consumption is reduced to 2.1 mm^2 in comparison to. 6.2 mm^2 for the standard application of Karatsuba's method i.e. for recursive application. Our approach also reduces the energy consumption to 60 per cent of the original approach. The price we have to pay for these achievement is the increased execution time. In our implementation a polynomial multiplication takes 3 clock cycles whereas the recurisve Karatsuba approach needs only one clock cycle. But considering area, energy and calculation sp...
Complex Mode Frequency Iteration Method for Flutter Analysis of 2-DOF Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For a vibration system with 2-DOF of bend and torsion, itscritical flutter wind speed can be calculated by using complex mode frequency iteration (CMFI) method based on MatLab 5.2, the results of which are in agree with those acquired by wind tunnel test. Not only critical flutter wind speed, but also vibration characteristic of a system under different wind speeds can be determined. CMFI method is suitable for both of separated-flow torsional flutter and classic coupling flutter analysis, which is presented by flutter analysis of an ideal thin plate and a bluff bridge deck. Furthermore, it is proved through the investigation of the relationship between flutter derivatives and its critical flutter wind speed that coupling aerodynamic derivatives are necessary for classic coupling flutter to occur.
Masmoudi, Nabil
2014-05-01
Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the
Accuracy improvement of a hybrid robot for ITER application using POE modeling method
International Nuclear Information System (INIS)
Highlights: ► The product of exponential (POE) formula for error modeling of hybrid robot. ► Differential Evolution (DE) algorithm for parameter identification. ► Simulation results are given to verify the effectiveness of the method. -- Abstract: This paper focuses on the kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial–parallel hybrid robot to improve its accuracy. The robot was designed to perform the assembling and repairing tasks of the vacuum vessel (VV) of the international thermonuclear experimental reactor (ITER). By employing the product of exponentials (POEs) formula, we extended the POE-based calibration method from serial robot to redundant serial–parallel hybrid robot. The proposed method combines the forward and inverse kinematics together to formulate a hybrid calibration method for serial–parallel hybrid robot. Because of the high nonlinear characteristics of the error model and too many error parameters need to be identified, the traditional iterative linear least-square algorithms cannot be used to identify the parameter errors. This paper employs a global optimization algorithm, Differential Evolution (DE), to identify parameter errors by solving the inverse kinematics of the hybrid robot. Furthermore, after the parameter errors were identified, the DE algorithm was adopted to numerically solve the forward kinematics of the hybrid robot to demonstrate the accuracy improvement of the end-effector. Numerical simulations were carried out by generating random parameter errors at the allowed tolerance limit and generating a number of configuration poses in the robot workspace. Simulation of the real experimental conditions shows that the accuracy of the end-effector can be improved to the same precision level of the given external measurement device
Accuracy improvement of a hybrid robot for ITER application using POE modeling method
Energy Technology Data Exchange (ETDEWEB)
Wang, Yongbo, E-mail: yongbo.wang@hotmail.com [Laboratory of Intelligent Machines, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland); Wu, Huapeng; Handroos, Heikki [Laboratory of Intelligent Machines, Lappeenranta University of Technology, FIN-53851 Lappeenranta (Finland)
2013-10-15
Highlights: ► The product of exponential (POE) formula for error modeling of hybrid robot. ► Differential Evolution (DE) algorithm for parameter identification. ► Simulation results are given to verify the effectiveness of the method. -- Abstract: This paper focuses on the kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial–parallel hybrid robot to improve its accuracy. The robot was designed to perform the assembling and repairing tasks of the vacuum vessel (VV) of the international thermonuclear experimental reactor (ITER). By employing the product of exponentials (POEs) formula, we extended the POE-based calibration method from serial robot to redundant serial–parallel hybrid robot. The proposed method combines the forward and inverse kinematics together to formulate a hybrid calibration method for serial–parallel hybrid robot. Because of the high nonlinear characteristics of the error model and too many error parameters need to be identified, the traditional iterative linear least-square algorithms cannot be used to identify the parameter errors. This paper employs a global optimization algorithm, Differential Evolution (DE), to identify parameter errors by solving the inverse kinematics of the hybrid robot. Furthermore, after the parameter errors were identified, the DE algorithm was adopted to numerically solve the forward kinematics of the hybrid robot to demonstrate the accuracy improvement of the end-effector. Numerical simulations were carried out by generating random parameter errors at the allowed tolerance limit and generating a number of configuration poses in the robot workspace. Simulation of the real experimental conditions shows that the accuracy of the end-effector can be improved to the same precision level of the given external measurement device.
Six-Party Qualification Program of FW Fabrication Methods for ITER Blanket Module Procurement
International Nuclear Information System (INIS)
In December 2005, the new procurement allocation plan of the ITER components among the seven Parties was prepared. The need to qualify for procurement of the specific components was especially introduced in the document. The main features and milestones of the qualification program are described in '' Procurement Plan '' for each specific component. The management rules for cases of failure in the qualification are also documented in the Procurement Plan. Due to the complicated features of FW procurement (by 6 Parties: CN, EU, JA, KO, RF and US), the procurement document has to be developed precisely. To guarantee high quality of 1700 FW panels produced by 6 different Parties, a qualification program is essential. The qualification mock-up is 80 mm wide, 240 mm long and 81 mm thick with 3 beryllium tiles 10 mm thick. Three identical mock-ups will be fabricated by each of the 6 Parties in 2006-2007 with the same method as for the ITER first wall panels. Heat load tests will be performed on the qualification mock-ups in 2007 in EU and USA facilities. During the testing, the coolant velocity is reduced to 1-2 m/s instead of 4.5 m/s to simulate the nuclear heating. The cycle time of the test will be ∼ 4 minutes. When the heat flux is increased by ∼ 40 %, the cycle time can be ∼90 sec according to thermal and stress analysis. The maximum design heat load on the ITER FW is 0.5 MW/m2 (steady state) x 30,000 shots. The heat load due to NB shine-through to achieve H-mode plasma during the hydrogen phase will be 1 MW/m2 in a certain area of the outboard equatorial region (total 1,000 shots for 2.5 years). The maximum heat flux due to MARFE: 0.5-1.4 MW/m2 (up to 10 sec duration) also needs to be taken into account in the heat load test conditions. Mechanical tests of joints are also required using standardized methods. Only Parties which have satisfied the acceptance criteria of the qualification tests can proceed to the procurement stage of the ITER FW. Semi
Clinical correlative evaluation of an iterative method for reconstruction of brain SPECT images
Energy Technology Data Exchange (ETDEWEB)
Nobili, Flavio E-mail: fnobili@smartino.ge.it; Vitali, Paolo; Calvini, Piero; Bollati, Francesca; Girtler, Nicola; Delmonte, Marta; Mariani, Giuliano; Rodriguez, Guido
2001-08-01
Background: Brain SPECT and PET investigations have showed discrepancies in Alzheimer's disease (AD) when considering data deriving from deeply located structures, such as the mesial temporal lobe. These discrepancies could be due to a variety of factors, including substantial differences in gamma-cameras and underlying technology. Mesial temporal structures are deeply located within the brain and the commonly used Filtered Back-Projection (FBP) technique does not fully take into account either the physical parameters of gamma-cameras or geometry of collimators. In order to overcome these limitations, alternative reconstruction methods have been proposed, such as the iterative method of the Conjugate Gradients with modified matrix (CG). However, the clinical applications of these methods have so far been only anecdotal. The present study was planned to compare perfusional SPECT data as derived from the conventional FBP method and from the iterative CG method, which takes into account the geometrical and physical characteristics of the gamma-camera, by a correlative approach with neuropsychology. Methods: Correlations were compared between perfusion of the hippocampal region, as achieved by both the FBP and the CG reconstruction methods, and a short-memory test (Selective Reminding Test, SRT), specifically addressing one of its function. A brain-dedicated camera (CERASPECT) was used for SPECT studies with {sup 99m}Tc-hexamethylpropylene-amine-oxime in 23 consecutive patients (mean age: 74.2{+-}6.5) with mild (Mini-Mental Status Examination score {>=}15, mean 20.3{+-}3), probable AD. Counts from a hippocampal region in each hemisphere were referred to the average thalamic counts. Results: Hippocampal perfusion significantly correlated with the MMSE score with similar statistical significance (p<0.01) between the two reconstruction methods. Correlation between hippocampal perfusion and the SRT score was better with the CG method (r=0.50 for both hemispheres, p<0
Clinical correlative evaluation of an iterative method for reconstruction of brain SPECT images
International Nuclear Information System (INIS)
Background: Brain SPECT and PET investigations have showed discrepancies in Alzheimer's disease (AD) when considering data deriving from deeply located structures, such as the mesial temporal lobe. These discrepancies could be due to a variety of factors, including substantial differences in gamma-cameras and underlying technology. Mesial temporal structures are deeply located within the brain and the commonly used Filtered Back-Projection (FBP) technique does not fully take into account either the physical parameters of gamma-cameras or geometry of collimators. In order to overcome these limitations, alternative reconstruction methods have been proposed, such as the iterative method of the Conjugate Gradients with modified matrix (CG). However, the clinical applications of these methods have so far been only anecdotal. The present study was planned to compare perfusional SPECT data as derived from the conventional FBP method and from the iterative CG method, which takes into account the geometrical and physical characteristics of the gamma-camera, by a correlative approach with neuropsychology. Methods: Correlations were compared between perfusion of the hippocampal region, as achieved by both the FBP and the CG reconstruction methods, and a short-memory test (Selective Reminding Test, SRT), specifically addressing one of its function. A brain-dedicated camera (CERASPECT) was used for SPECT studies with 99mTc-hexamethylpropylene-amine-oxime in 23 consecutive patients (mean age: 74.2±6.5) with mild (Mini-Mental Status Examination score ≥15, mean 20.3±3), probable AD. Counts from a hippocampal region in each hemisphere were referred to the average thalamic counts. Results: Hippocampal perfusion significantly correlated with the MMSE score with similar statistical significance (p<0.01) between the two reconstruction methods. Correlation between hippocampal perfusion and the SRT score was better with the CG method (r=0.50 for both hemispheres, p<0.01) than with
An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids
Kokonkov, N. I.; Nikolaeva, O. V.
2015-10-01
A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.
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.
Energy Technology Data Exchange (ETDEWEB)
Clemens, M.; Weiland, T. [Technische Hochschule Darmstadt (Germany)
1996-12-31
In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.
Amano, Ken-ich
2013-01-01
We propose iterative methods for obtaining solvation structures on a solid plate which use force distributions measured by surface force apparatus (SFA) and atomic force microscopy (AFM) as input data. Two model systems are considered here. In the model system for SFA, the same two solid plates are immersed in a solvent, and a probe tip and a solid plate are immersed in a solvent in the model system for AFM. Advantages of the iterative methods are as follows: The iterative method for SFA can obtain the solvation structure, for example, in a Lennard-Jones liquid; The iterative method for AFM can obtain the solvation structure without an input datum of solvation structure around the probe tip.
Green`s function of Maxwell`s equations and corresponding implications for iterative methods
Energy Technology Data Exchange (ETDEWEB)
Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)
1996-12-31
Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.
International Nuclear Information System (INIS)
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)
The development of in-situ calibration method for divertor IR thermography in ITER
International Nuclear Information System (INIS)
For the development of the calibration method of the emissivity in IR light on the divertor plate in ITER divertor IR thermography system, the laboratory experiments have been performed by using IR instruments. The calibration of the IR camera was performed by the plane black body in the temperature of 100–600 degC. The radiances of the tungsten heated by 280 degC were measured by the IR camera without filter (2.5–5.1 μm) and with filter (2.95 μm, 4.67 μm). The preliminary data of the scattered light of the laser of 3.34 μm that injected into the tungsten were acquired
Iterative methods for solving the non-sparse equations of quantum mechanical reactive scattering
International Nuclear Information System (INIS)
Several iterative techniques are applied to solve the non-sparse, indefinite algebraic variational equations of the L2 quantum mechanical description of three-dimensional atom-diatom scattering. We do not assume a symmetric matrix although we employ a symmetric test problem that allows comparison to the standard conjugate gradient algorithm. Convergence of general minimal residual and Lanczos algorithms is shown to be rapid, enabling large savings of computer time as compared to direct methods for large-scale calculations of selected elements or columns of the reactance matrix. As the number M of basis functions varies from 100 to 504, minimal residual calculations based on the Arnoldi basis show very smooth and stable convergence, with computer time scaling as M1.8, and a Lanczos recursive algorithm is found to scale as M1.5 (for off-diagonal matrix elements). (orig.)
Dynamic linear calibration method for a wide range neutron flux monitor system in ITER
International Nuclear Information System (INIS)
As a key part of the diagnosis system in the International Thermonuclear Experimental Reactor (ITER), the neutron flux monitor (NFM), which measures the neutron intensity of the fusion reaction, is a Counting-Campbelling system with a large dynamic counting range. A dynamic linear calibration method is proposed in this paper to solve the problem of cross-over between the different counting and Campbelling channels, and improve the accuracy of the cross-calibration for long-term operation. The experimental results show that the NFM system with the dynamic linear calibration system can obtain the neutron flux of the fusion reactor in real time and realize the seamless measurement area connection between the two channels. (authors)
Fourier transform based iterative method for x-ray differential phase-contrast computed tomography
Cong, Wenxiang; Wang, Ge
2011-01-01
Biological soft tissues encountered in clinical and pre-clinical imaging mainly consist of light element atoms, and their composition is nearly uniform with little density variation. Thus, x-ray attenuation imaging suffers from low image contrast resolution. By contrast, x-ray phase shift of soft tissues is about a thousand times greater than x-ray absorption over the diagnostic energy range, thereby a significantly higher sensitivity can be achieved in terms of phase shift. In this paper, we propose a novel Fourier transform based iterative method to perform x-ray tomographic imaging of the refractive index directly from differential phase shift data. This approach offers distinct advantages in cases of incomplete and noisy data than analytic reconstruction, and especially suitable for phase-contrast interior tomography by incorporating prior knowledge in a region of interest (ROI). Biological experiments demonstrate the merits of the proposed approach.
Fully Implicit Iterative Solving Method for the Fokker-Planck Equation in Tokamak Plasmas
Institute of Scientific and Technical Information of China (English)
ZHENG Pingwei; GONG Xueyu; YU Jun; DU Dan
2014-01-01
A three dimensional bounce-averaged Fokker-Planck (FP) numerical code has been newly developed based on fully implicit iterative solving method,and relativistic effect is also included in the code.The code has been tested against various benchmark cases:Ohmic conductivity in the presence of weak Ohmic electric field,runaway losses of electrons in the presence of strong Ohmic electric field,lower hybrid current drive and electron cyclotron current drive via two-or three-dimensional simulation.All the test cases run fast and correctly during calculations.As a result,the code provides a set of powerful tools for studying radio frequency wave heating and current drive in tokamak plasmas.
Abedin, Kazi Monowar; Mujibur Rahman, S. M.
2012-06-01
We applied the iterative Fresnel integrals method for the numerical computation of Fresnel diffraction patterns from rectangular apertures tilted at an arbitrary angle to the optical axis. Detailed theoretical formalism is developed and discussed, and then is applied for the numerical computation and simulation of the actual diffraction patterns for an arbitrary optical configuration. The generated intensity distributions (images) show distortion and stretching in the direction of the tilt, but not in the other orthogonal direction. Significant decrease of the intensity is also predicted and observed, the decrease being proportionate with the tilt angle. The simulated images qualitatively resemble those published in the literature. In addition to single-axis tilts, simultaneous rotations (tilts) of the aperture in two orthogonal coordinate axes were also briefly considered and simulated.
Adaptive and Iterative Methods for Simulations of Nanopores with the PNP-Stokes Equations
Mitscha-Baude, Gregor; Tulzer, Gerhard; Heitzinger, Clemens
2016-01-01
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equ...
Fully Implicit Iterative Solving Method for the Fokker-Planck Equation in Tokamak Plasmas
International Nuclear Information System (INIS)
A three dimensional bounce-averaged Fokker-Planck (FP) numerical code has been newly developed based on fully implicit iterative solving method, and relativistic effect is also included in the code. The code has been tested against various benchmark cases: Ohmic conductivity in the presence of weak Ohmic electric field, runaway losses of electrons in the presence of strong Ohmic electric field, lower hybrid current drive and electron cyclotron current drive via two- or three-dimensional simulation. All the test cases run fast and correctly during calculations. As a result, the code provides a set of powerful tools for studying radio frequency wave heating and current drive in tokamak plasmas. (magnetically confined plasma)
Numerical Asymptotic Solutions Of Differential Equations
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.
Fuzzy based method for project planning of the infrastructure design for the diagnostic in ITER
Energy Technology Data Exchange (ETDEWEB)
Piros, Attila, E-mail: attila.piros@gt3.bme.hu [Department of Machine and Product Design, Budapest University of Technology and Economics, Budapest (Hungary); Veres, Gábor [Department of Plasma Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest (Hungary)
2013-10-15
The long-term design projects need special preparation before the start of the execution. This preparation usually includes the drawing of the network diagram for the whole procedure. This diagram includes the time estimation of the individual subtasks and gives us information about the predicted dates of the milestones. The calculated critical path in this network characterizes a specific design project concerning to its duration very well. Several methods are available to support this step of preparation. This paper describes a new method to map the structure of the design process and clarify the milestones and predict the dates of these milestones. The method is based on the PERT (Project Evaluation and Review Technique) network but as a novelty it applies fuzzy logic to find out the concerning times in this graph. With the application of the fuzzy logic the handling of the different kinds of design uncertainties becomes feasible. Many kinds of design uncertainties exist from the possible electric blackout up to the illness of an engineer. In many cases these uncertainties are related with human errors and described with linguistic expressions. The fuzzy logic enables to transform these ambiguous expressions into numeric values for further mathematical evaluation. The method is introduced in the planning of the design project of the infrastructure for the diagnostic systems of ITER. The method not only helps the project in the planning phase, but it will be a powerful tool in mathematical modeling and monitoring of the project execution.
Fuzzy based method for project planning of the infrastructure design for the diagnostic in ITER
International Nuclear Information System (INIS)
The long-term design projects need special preparation before the start of the execution. This preparation usually includes the drawing of the network diagram for the whole procedure. This diagram includes the time estimation of the individual subtasks and gives us information about the predicted dates of the milestones. The calculated critical path in this network characterizes a specific design project concerning to its duration very well. Several methods are available to support this step of preparation. This paper describes a new method to map the structure of the design process and clarify the milestones and predict the dates of these milestones. The method is based on the PERT (Project Evaluation and Review Technique) network but as a novelty it applies fuzzy logic to find out the concerning times in this graph. With the application of the fuzzy logic the handling of the different kinds of design uncertainties becomes feasible. Many kinds of design uncertainties exist from the possible electric blackout up to the illness of an engineer. In many cases these uncertainties are related with human errors and described with linguistic expressions. The fuzzy logic enables to transform these ambiguous expressions into numeric values for further mathematical evaluation. The method is introduced in the planning of the design project of the infrastructure for the diagnostic systems of ITER. The method not only helps the project in the planning phase, but it will be a powerful tool in mathematical modeling and monitoring of the project execution
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 gradients * augmented lagrangian methods Subject RIV: BA - General Mathematics Impact factor: 1.475, year: 2007
Asymptotic methods in analysis
Bruijn, N G de
2010-01-01
An original, effective approach teaches by explaining worked examples in detail. ""Every step in the mathematical process is explained, its purpose and necessity made clear . . . the reader not only has no difficulty in following the rigorous proofs, but even turns to them with eager expectation."" - Nuclear Physics. 1981 edition.
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...... chosen with possible unknown constants which can be determined by imposing the boundary or initial conditions after few iterations. Comparison of the results with those obtained by Adomian’s decomposition method reveals that VIM is very effective, convenient and quite accurate to both linear and...
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...
Takata, Tadanori; Ichikawa, Katsuhiro; Hayashi, Hiroyuki; Mitsui, Wataru; Sakuta, Keita; Koshida, Haruka; Yokoi, Tomohiro; Matsubara, Kousuke; Horii, Jyunsei; Iida, Hiroji
2012-01-01
The purpose of this study was to evaluate the image quality of an iterative reconstruction method, the iterative reconstruction in image space (IRIS), which was implemented in a 128-slices multi-detector computed tomography system (MDCT), Siemens Somatom Definition Flash (Definition). We evaluated image noise by standard deviation (SD) as many researchers did before, and in addition, we measured modulation transfer function (MTF), noise power spectrum (NPS), and perceptual low-contrast detectability using a water phantom including a low-contrast object with a 10 Hounsfield unit (HU) contrast, to evaluate whether the noise reduction of IRIS was effective. The SD and NPS were measured from the images of a water phantom. The MTF was measured from images of a thin metal wire and a bar pattern phantom with the bar contrast of 125 HU. The NPS of IRIS was lower than that of filtered back projection (FBP) at middle and high frequency regions. The SD values were reduced by 21%. The MTF of IRIS and FBP measured by the wire phantom coincided precisely. However, for the bar pattern phantom, the MTF values of IRIS at 0.625 and 0.833 cycle/mm were lower than those of FBP. Despite the reduction of the SD and the NPS, the low-contrast detectability study indicated no significant difference between IRIS and FBP. From these results, it was demonstrated that IRIS had the noise reduction performance with exact preservation for high contrast resolution and slight degradation of middle contrast resolution, and could slightly improve the low contrast detectability but with no significance. PMID:22516592
Institute of Scientific and Technical Information of China (English)
Penggang SUN; Lin GAO
2009-01-01
Accumulating evidence suggests that biological systems are composed of interacting, separable, functional modules-groups of vertices within which connections are dense but between which they are sparse. Identifying these modules is likely through capturing the biologically mean-ingful interactions. In recent years, many algorithms have been developed for detecting such structures. These al-gorithms, however, are computationally demanding, which limits their applications. In this paper, we propose a fast iterative-clique percolation method (ICPM) for identifying overlapping functional modules in protein-protein interac-tion (PPI) networks. Our method is based on clique percola-tion method (CPM), and it not only considers the degree of nodes to minimize the search space (the vertices in k-cliques must have the degree of k - 1 at least), but also converts k-cliques to (k - 1)-cliques. It finds k-cliques by append-ing one node to (k - 1)-cliques. By testing our method on PPI networks, our analysis of the yeast PPI network suggeststhat most of these modules have well-supported biological significance.
On the effects of using the GTH method in the iterative-aggregation disaggregation technique
Energy Technology Data Exchange (ETDEWEB)
Dayar, T.; Stewart, W.J. [North Carolina State Univ., Raleigh, NC (United States)
1994-12-31
The iterative aggregation-disaggregation (IAD) technique is an effective method for solving finite nearly completely decomposable (NCD) Markov chains. Small perturbations in the transition probabilities of these chains lead to a considerable change in the stationary vector. Therefore, NCD Markov chains are referred to as being ill-conditioned. During an IAD step, this undesirable condition is inherited by the coupling matrix and one confronts the problem of finding the stationary vector of a stochastic matrix which has weighty diagonal elements close to one. In this paper, the authors investigate the effects of using the Grassmann-Taksar-Heyman (GTH) method to solve the coupling matrix formed in the aggregation step. Then, they extend the idea in such a way that this direct method can be incorporated into the disaggregation step. Finally, they discuss various implementation issues, demonstrate the effect of using the GTH method in the IAD algorithm on various examples, and elaborate on the conditions under which it should be applied.
Primal and dual-primal iterative substructuring methods of stochastic PDEs
International Nuclear Information System (INIS)
A novel non-overlapping domain decomposition method is proposed to solve the large-scale linear system arising from the finite element discretization of stochastic partial differential equations (SPDEs). The methodology is based on a Schur complement based geometric decomposition and an orthogonal decomposition and projection of the stochastic processes using Polynomial Chaos expansion. The algorithm offers a direct approach to formulate a two-level scalable preconditioner. The proposed preconditioner strictly enforces the continuity condition on the corner nodes of the interface boundary, while weakly satisfying the continuity condition over the remaining interface nodes. This approach relates to a primal version of an iterative substructuring method. Next, a Lagrange multiplier based dual-primal domain decomposition method is introduced in the context of SPDEs. In the dual-primal method the continuity condition on the corner nodes is strictly satisfied while Lagrange multipliers are used to enforce continuity on the remaining part of the interface boundary. For numerical illustrations, a two dimensional elliptic SPDE with non-Gaussian random coefficients is considered. The numerical results demonstrate the scalability of these algorithms with respect to the mesh size, subdomain size, fixed problem size per subdomain, order of Polynomial Chaos expansion and level of uncertainty in the input parameters. The numerical experiments are performed on a Linux cluster using MPI and PETSc libraries.
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.
An Improved Iterative Fitting Method to Estimate Nocturnal Residual Layer Height
Directory of Open Access Journals (Sweden)
Wei Wang
2016-08-01
Full Text Available The planetary boundary layer (PBL is an atmospheric region near the Earth’s surface. It is significant for weather forecasting and for the study of air quality and climate. In this study, the top of nocturnal residual layers—which are what remain of the daytime mixing layer—are estimated by an elastic backscatter Lidar in Wuhan (30.5°N, 114.4°E, a city in Central China. The ideal profile fitting method is widely applied to determine the nocturnal residual layer height (RLH from Lidar data. However, the method is seriously affected by an optical thick layer. Thus, we propose an improved iterative fitting method to eliminate the optical thick layer effect on RLH detection using Lidar. Two typical case studies observed by elastic Lidar are presented to demonstrate the theory and advantage of the proposed method. Results of case analysis indicate that the improved method is more practical and precise than profile-fitting, gradient, and wavelet covariance transform method in terms of nocturnal RLH evaluation under low cloud conditions. Long-term observations of RLH performed with ideal profile fitting and improved methods were carried out in Wuhan from 28 May 2011 to 17 June 2016. Comparisons of Lidar-derived RLHs with the two types of methods verify that the improved solution is practical. Statistical analysis of a six-year Lidar signal was conducted to reveal the monthly average values of nocturnal RLH in Wuhan. A clear RLH monthly cycle with a maximum mean height of about 1.8 km above ground level was observed in August, and a minimum height of about 0.7 km was observed in January. The variation in monthly mean RLH displays an obvious quarterly dependence, which coincides with the annual variation in local surface temperature.
Institute of Scientific and Technical Information of China (English)
柳华蔚; 郑树; 周怀春
2015-01-01
In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projec-tions, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection (VP) method. Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection (IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method, without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio (SNR) for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.
Lee, Heung-Rae
1997-01-01
A three-dimensional image reconstruction method comprises treating the object of interest as a group of elements with a size that is determined by the resolution of the projection data, e.g., as determined by the size of each pixel. One of the projections is used as a reference projection. A fictitious object is arbitrarily defined that is constrained by such reference projection. The method modifies the known structure of the fictitious object by comparing and optimizing its four projections to those of the unknown structure of the real object and continues to iterate until the optimization is limited by the residual sum of background noise. The method is composed of several sub-processes that acquire four projections from the real data and the fictitious object: generate an arbitrary distribution to define the fictitious object, optimize the four projections, generate a new distribution for the fictitious object, and enhance the reconstructed image. The sub-process for the acquisition of the four projections from the input real data is simply the function of acquiring the four projections from the data of the transmitted intensity. The transmitted intensity represents the density distribution, that is, the distribution of absorption coefficients through the object.
Directory of Open Access Journals (Sweden)
Vladimir V. Lyubimov
2007-01-01
Full Text Available The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT. The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a 27% gain in spatial resolution can be obtained.
Degond, Pierre; Lozinski, Alexei; Narski, Jacek; Negulescu, Claudia
2011-01-01
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0
Parallel iteration methods of Runge-Kutta methods for delay differential equations
Institute of Scientific and Technical Information of China (English)
丁效华; 刘明珠
2004-01-01
This paper deals with the parallel diagonal implicit Runge-Kutta methods for solving DDEs with a constant delay. It is shown that the suitable choice of the predictor matrix can guarantee the stability of the methods. It is proved that for the suitable selection of the diagonal matrix D, the method based on Radau IIA is δ-convergent, and the estimates for the non-stiff speed and the stiff speed of convergence are given.
Directory of Open Access Journals (Sweden)
Li-fang Dai
2013-01-01
Full Text Available An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation ∑i=1tMiZiNi=F, where Zi (i=1,2,…,t are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the least-squares solution can be derived by this method within finite iteration steps in the absence of roundoff errors. Meanwhile, the unique optimal approximation solution pair for given matrices Z~i can also be obtained by the least-norm least-squares solution of matrix equation ∑i=1tMiZ-iNi=F-, in which Z-i=Zi-Z~i, F-=F-∑i=1tMiZ~iNi. The given numerical examples illustrate the efficiency of this algorithm.
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.
Directory of Open Access Journals (Sweden)
Kim Jong
2011-01-01
Full Text Available Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
An iterative computation method for interpreting and extending an analytical battery model
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Battery models are of great importance to develop portable computing systems, for whether the design of low power hardware architecture or the design of battery-aware scheduling policies. In this paper, we present a physically justified iterative computing method to illustrate the discharge, recovery and charge process of Li/Li-ion batteries. The discharge and recovery processes correspond well to an existing accurate analytical battery model: R-V-W's analytical model, and thus interpret this model algorithmically. Our method can also extend R-V-W's model easily to accommodate the charge process. The work will help the system designers to grasp the characteristics of R-V-W's battery model and also, enable to predict the battery behavior in the charge process in a uniform way as the discharge process and the recovery process. Experiments are performed to show the accuracy of the extended model by comparing the predicted charge times with those derived from the DUALFOIL simulations.Various profiles with different combinations of battery modes were tested. The experimental results show that the extended battery model preserves high accuracy in predicting the charge behavior.
A convergence rates result for an iteratively regularized Gauss–Newton–Halley method in Banach space
International Nuclear Information System (INIS)
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss–Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings. (paper)
Mixed price and load forecasting of electricity markets by a new iterative prediction method
International Nuclear Information System (INIS)
Load and price forecasting are the two key issues for the participants of current electricity markets. However, load and price of electricity markets have complex characteristics such as nonlinearity, non-stationarity and multiple seasonality, to name a few (usually, more volatility is seen in the behavior of electricity price signal). For these reasons, much research has been devoted to load and price forecast, especially in the recent years. However, previous research works in the area separately predict load and price signals. In this paper, a mixed model for load and price forecasting is presented, which can consider interactions of these two forecast processes. The mixed model is based on an iterative neural network based prediction technique. It is shown that the proposed model can present lower forecast errors for both load and price compared with the previous separate frameworks. Another advantage of the mixed model is that all required forecast features (from load or price) are predicted within the model without assuming known values for these features. So, the proposed model can better be adapted to real conditions of an electricity market. The forecast accuracy of the proposed mixed method is evaluated by means of real data from the New York and Spanish electricity markets. The method is also compared with some of the most recent load and price forecast techniques. (author)
Pari, Sharareh Mehrabi; Shahri, Fatemeh Taghavi
2015-01-01
The "Iterative Laplace Transform Method" is used to solve the Fokker-Planck equation for finding the time evolution of the heavy quarks distribution functions such as charm and bottom in quark gluon plasma. These solutions will lead us to calculation of nuclear suppression factor RAA. The results have good agreement with available experiment data from the PHENIX collaboration.
Novel iterative reconstruction method for optimal dose usage in redundant CT - acquisitions
Bruder, H.; Raupach, R.; Allmendinger, T.; Kappler, S.; Sunnegardh, J.; Stierstorfer, K.; Flohr, T.
2014-03-01
In CT imaging, a variety of applications exist where reconstructions are SNR and/or resolution limited. However, if the measured data provide redundant information, composite image data with high SNR can be computed. Generally, these composite image volumes will compromise spectral information and/or spatial resolution and/or temporal resolution. This brings us to the idea of transferring the high SNR of the composite image data to low SNR (but high resolution) `source' image data. It was shown that the SNR of CT image data can be improved using iterative reconstruction [1] .We present a novel iterative reconstruction method enabling optimal dose usage of redundant CT measurements of the same body region. The generalized update equation is formulated in image space without further referring to raw data after initial reconstruction of source and composite image data. The update equation consists of a linear combination of the previous update, a correction term constrained by the source data, and a regularization prior initialized by the composite data. The efficiency of the method is demonstrated for different applications: (i) Spectral imaging: we have analysed material decomposition data from dual energy data of our photon counting prototype scanner: the material images can be significantly improved transferring the good noise statistics of the 20 keV threshold image data to each of the material images. (ii) Multi-phase liver imaging: Reconstructions of multi-phase liver data can be optimized by utilizing the noise statistics of combined data from all measured phases (iii) Helical reconstruction with optimized temporal resolution: splitting up reconstruction of redundant helical acquisition data into a short scan reconstruction with Tam window optimizes the temporal resolution The reconstruction of full helical data is then used to optimize the SNR. (iv) Cardiac imaging: the optimal phase image (`best phase') can be improved by transferring all applied over
Hand-eye LRF-based Iterative Plane Detection Method for Autonomous Robotic Welding
Directory of Open Access Journals (Sweden)
Sungmin Lee
2015-12-01
Full Text Available This paper proposes a hand-eye LRF-based (laser range finder welding plane-detection method for autonomous robotic welding in the field of shipbuilding. The hand-eye LRF system consists of a 6 DOF manipulator and an LRF attached to the wrist of the manipulator. The welding plane is detected by the LRF with only the wrist’s rotation to minimize a mechanical error caused by the manipulator’s motion. A position on the plane is determined as an average position of the detected points on the plane, and a normal vector to the plane is determined by applying PCA (principal component analysis to the detected points. In this case, the accuracy of the detected plane is analysed by simulations with respect to the wrist’s angle interval and the plane angle. As a result of the analysis, an iterative plane-detection method with the manipulator’s alignment motion is proposed to improve the performance of plane detection. For verifying the feasibility and effectiveness of the proposed plane-detection method, experiments are carried out with a prototype of the hand-eye LRF-based system, which consists of a 1 DOF wrist’s joint, an LRF system and a rotatable plane. In addition, the experimental results of the PCA-based plane detection method are compared with those of the two representative plane-detection methods, based on RANSAC (RANdom SAmple Consensus and the 3D Hough transform in both accuracy and computation time’s points of view.
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
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.)
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
Shihua Cao; Qihui Wang; Yaping Yuan; Junyang Yu
2014-01-01
Anomaly event detection is one of the research hotspots in wireless sensor networks. Aiming at the disadvantages of current detection solutions, a novel anomaly event detection algorithm based on compressed sensing and iteration is proposed. Firstly, a measured value can be sensed in each node, based on the compressed sensing. Then the problem of anomaly event detection is modeled as the minimization problem of weighted l1 norm, and OMP algorithm is adopted for solving the problem iteratively...
Environmental dose rate assessment of ITER using the Monte Carlo method
Karimian Alireza; Beheshti Amir; Abdi Mohammadreza; Jabbari Iraj
2014-01-01
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 th...
e-Learning Application for Machine Maintenance Process using Iterative Method in XYZ Company
Nurunisa, Suaidah; Kurniawati, Amelia; Pramuditya Soesanto, Rayinda; Yunan Kurnia Septo Hediyanto, Umar
2016-02-01
XYZ Company is a company based on manufacturing part for airplane, one of the machine that is categorized as key facility in the company is Millac 5H6P. As a key facility, the machines should be assured to work well and in peak condition, therefore, maintenance process is needed periodically. From the data gathering, it is known that there are lack of competency from the maintenance staff to maintain different type of machine which is not assigned by the supervisor, this indicate that knowledge which possessed by maintenance staff are uneven. The purpose of this research is to create knowledge-based e-learning application as a realization from externalization process in knowledge transfer process to maintain the machine. The application feature are adjusted for maintenance purpose using e-learning framework for maintenance process, the content of the application support multimedia for learning purpose. QFD is used in this research to understand the needs from user. The application is built using moodle with iterative method for software development cycle and UML Diagram. The result from this research is e-learning application as sharing knowledge media for maintenance staff in the company. From the test, it is known that the application make maintenance staff easy to understand the competencies.
International Nuclear Information System (INIS)
Among all Non-Destructive Examinations (NDE), active infrared thermography is becoming recognised as a technique available today for improving quality control of many materials and structures involved in heat transfer. The infrared thermography allows to characterise the bond between two materials having different thermal physical properties. In order to increase the defect detection limit of the SATIR test bed, several possibilities have been evaluated to improve the infrared thermography inspection. The implementation in 2003 of a micro-bolometer camera and the improving of the thermo-signal process allowed to increase considerably the detection sensitivity of the SATIR facility. The quality, the spatial stability of infrared image and the detection of edge defect have been also improved. The coupling on the same test bed of SATIR method with a lock-in thermography will be evaluated in this paper. An improvement of the global reliability is expected by data merging produced by the two thermal excitation sources. A new enhanced facility named SATIRPACA has been designed for the full Non Destructive Examination of the High Heat Flux ITER components taking into account these main improvements. These systematic acceptance tests obviously need tools for quality control of critical parts. (authors)
International Nuclear Information System (INIS)
Traditional numerical techniques for solving time-dependent partial differential equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and a certain number of their time derivatives at each time step. Although redundant in the dx → 0 limit, what if spatial derivatives were also stored? This paper presents an iterated, multipoint differential transform method (IMDTM) for numerically evolving PDE IVPs. Using this scheme, we demonstrate that stored spatial derivatives can be propagated in an efficient and self-consistent manner and can effectively contribute to the evolution procedure in a way that can confer several advantages, including aiding in solution verification. Lastly, in order to efficiently implement the IMDTM scheme, a generalized finite-difference stencil formula is derived that can take advantage of multiple higher-order spatial derivatives when computing even-higher-order derivatives. As demonstrated here, the performance of these techniques compares favorably to other explicit evolution schemes in terms of speed, memory footprint and accuracy.
Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models
Haddar, Houssem; Jiang, Zixian
2015-11-01
Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and it is therefore important that they are identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer’s small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. A standard iterative inversion algorithm is then applied to the asymptotic models to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and showing the benefits of the inversion procedure are provided.
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
Iglesias, Marco A.
2016-02-01
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The general aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box (e.g. with commercial software). The proposed regularizing ensemble Kalman method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme (Hanke 1997 Inverse Problems 13 79-95) in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad hoc fixes, such as covariance localization, are implemented. The aim of this paper is to provide a detailed numerical investigation of the regularizing and convergence properties of the proposed regularizing ensemble Kalman scheme; the proof of these properties is an open problem. By means of numerical experiments, we investigate the conditions under which the proposed method inherits the regularizing properties of the LM scheme of (Hanke 1997 Inverse Problems 13 79-95) and is thus stable and suitable for its application in problems where the computation of the Fréchet derivative is not computationally feasible. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method
International Nuclear Information System (INIS)
The reference process for the Tokamak Exhaust Processing (TEP) system of ITER is called CAPER and comprises three different, consecutive steps to recover hydrogen isotopes at highest purity for direct transfer to the cryogenic isotope separation system (ISS). The CAPER process was developed at the Tritium Laboratory Karlsruhe (TLK) and employs a palladium/silver permeator battery as the 1st step to separate more than 95% of the un-burnt deuterium/tritium fuel from impurities like helium, hydrocarbons and water. These so-called front-end permeators have a capacity of about 80 mol h-1/1 m2 effective surface area if operated under conditions currently specified for ITER. The front-end permeators of ITER should all the time be operated such that coking of the permeation membranes by hydrocarbon cracking is avoided, since this process lead to a reduction of the effective surface area and therefore to a reduction of the performance of the component. At TLK a method to measure the actual performance of a technical permeator has been developed. This method has been successfully tested with the experimental facility for the demonstration of the CAPER process at TLK and appears feasible for the TEP system of ITER
Directory of Open Access Journals (Sweden)
Mirela Kohr
2004-09-01
Full Text Available We study the low Reynolds number flow of an incompressible Newtonian fluid of infinite expanse past a cylinder of arbitrary cross section by using the method of matched asymptotic expansions. The analysis that will be made in this paper is equivalent to that developed by Power (1990 in order to solve the resulting inner (or Stokes problems with the completed double-layer boundary integral equation method (CDLBIEM due to Power and Miranda (1987. We will solve these problems by the boundary integral method developed by Hsiao and Kress (1985.
Probabilistic methods for physics
International Nuclear Information System (INIS)
We present an asymptotic method giving a probability of presence of the iterated spots of Rd 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.
Akira Maebatake; Ayaka Imamura; Yui Kodera; Yasuo Yamashita; Kazuhiko Himuro; Shingo Baba; Kenta Miwa; Masayuki Sasaki
2016-01-01
Objective(s): The aim of this study was to determine the optimal reconstruction parameters for iterative reconstruction in different devices and collimators for dopamine transporter (DaT) single-photon emission computed tomography (SPECT). The results were compared between filtered back projection (FBP) and different attenuation correction (AC) methods.Methods: An anthropomorphic striatal phantom was filled with 123I solutions at different striatum-to-background radioactivity ratios. Data wer...
Zhang, Cheng-Yi; Luo, Shuanghua; Xu, Zongben
2014-01-01
The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As special cases the convergence of the parallel block generalized AOR (BGAOR), the parallel block AOR (BAOR), the parallel block generalized SOR (BGSOR), the parallel block SOR (BSOR), the extrapolated parallel BAOR and the extrapolated parallel BSOR methods a...
Asymptotic analysis and boundary layers
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...
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....
Worst-case Analysis of Strategy Iteration and the Simplex Method
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm
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 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...
Low dose dynamic CT myocardial perfusion imaging using a statistical iterative reconstruction method
Energy Technology Data Exchange (ETDEWEB)
Tao, Yinghua [Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States); Chen, Guang-Hong [Department of Medical Physics and Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States); Hacker, Timothy A.; Raval, Amish N. [Department of Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53792 (United States); Van Lysel, Michael S.; Speidel, Michael A., E-mail: speidel@wisc.edu [Department of Medical Physics and Department of Medicine, University of Wisconsin-Madison, Madison, Wisconsin 53705 (United States)
2014-07-15
Purpose: Dynamic CT myocardial perfusion imaging has the potential to provide both functional and anatomical information regarding coronary artery stenosis. However, radiation dose can be potentially high due to repeated scanning of the same region. The purpose of this study is to investigate the use of statistical iterative reconstruction to improve parametric maps of myocardial perfusion derived from a low tube current dynamic CT acquisition. Methods: Four pigs underwent high (500 mA) and low (25 mA) dose dynamic CT myocardial perfusion scans with and without coronary occlusion. To delineate the affected myocardial territory, an N-13 ammonia PET perfusion scan was performed for each animal in each occlusion state. Filtered backprojection (FBP) reconstruction was first applied to all CT data sets. Then, a statistical iterative reconstruction (SIR) method was applied to data sets acquired at low dose. Image voxel noise was matched between the low dose SIR and high dose FBP reconstructions. CT perfusion maps were compared among the low dose FBP, low dose SIR and high dose FBP reconstructions. Numerical simulations of a dynamic CT scan at high and low dose (20:1 ratio) were performed to quantitatively evaluate SIR and FBP performance in terms of flow map accuracy, precision, dose efficiency, and spatial resolution. Results: Forin vivo studies, the 500 mA FBP maps gave −88.4%, −96.0%, −76.7%, and −65.8% flow change in the occluded anterior region compared to the open-coronary scans (four animals). The percent changes in the 25 mA SIR maps were in good agreement, measuring −94.7%, −81.6%, −84.0%, and −72.2%. The 25 mA FBP maps gave unreliable flow measurements due to streaks caused by photon starvation (percent changes of +137.4%, +71.0%, −11.8%, and −3.5%). Agreement between 25 mA SIR and 500 mA FBP global flow was −9.7%, 8.8%, −3.1%, and 26.4%. The average variability of flow measurements in a nonoccluded region was 16.3%, 24.1%, and 937
Iterative Otsu's method for OCT improved delineation in the aorta wall
Alonso, Daniel; Real, Eusebio; Val-Bernal, José F.; Revuelta, José M.; Pontón, Alejandro; Calvo Díez, Marta; Mayorga, Marta; López-Higuera, José M.; Conde, Olga M.
2015-07-01
Degradation of human ascending thoracic aorta has been visualized with Optical Coherence Tomography (OCT). OCT images of the vessel wall exhibit structural degradation in the media layer of the artery, being this disorder the final trigger of the pathology. The degeneration in the vessel wall appears as low-reflectivity areas due to different optical properties of acidic polysaccharides and mucopolysaccharides in contrast with typical ordered structure of smooth muscle cells, elastin and collagen fibers. An OCT dimension indicator of wall degradation can be generated upon the spatial quantification of the extension of degraded areas in a similar way as conventional histopathology. This proposed OCT marker can offer in the future a real-time clinical perception of the vessel status to help cardiovascular surgeons in vessel repair interventions. However, the delineation of degraded areas on the B-scan image from OCT is sometimes difficult due to presence of speckle noise, variable signal to noise ratio (SNR) conditions on the measurement process, etc. Degraded areas can be delimited by basic thresholding techniques taking advantage of disorders evidences in B-scan images, but this delineation is not optimum in the aorta samples and requires complex additional processing stages. This work proposes an optimized delineation of degraded areas within the aorta wall, robust to noisy environments, based on the iterative application of Otsu's thresholding method. Results improve the delineation of wall anomalies compared with the simple application of the algorithm. Achievements could be also transferred to other clinical scenarios: carotid arteries, aorto-iliac or ilio-femoral sections, intracranial, etc.
Asymptotic Study to the N-Dimensional Radial Schr(o)dinger Equation for the Quark-Antiquark System
Institute of Scientific and Technical Information of China (English)
Ramesh Kumar; Fakir Chand
2013-01-01
Here an asymptotic study to the N-dimensional radial Schr(o)dinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out.The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state,for large "r" and for small "r".From this analysis,the mass spectra of heavy quarkonia is derived in three dimensions.Our analytical and numerical results are in good correspondence with other experimental and theoretical studies.
Degond, Pierre; Narski, Jacek; Negulescu, Claudia
2011-01-01
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0<\\eps <<1$, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields $b$ and the simple extension to the case of a non-constant anisotropy intensity $1/\\eps$. The mathematical approach and the numerical scheme are different from those presented in the previous work [Degond et al. (2010), arXiv:1008.3405v1] and its considerable advantages are pointed out.
Büsing, Henrik
2013-04-01
Two-phase flow in porous media occurs in various settings, such as the sequestration of CO2 in the subsurface, radioactive waste management, the flow of oil or gas in hydrocarbon reservoirs, or groundwater remediation. To model the sequestration of CO2, we consider a fully coupled formulation of the system of nonlinear, partial differential equations. For the solution of this system, we employ the Box method after Huber & Helmig (2000) for the space discretization and the fully implicit Euler method for the time discretization. After linearization with Newton's method, it remains to solve a linear system in every Newton step. We compare different iterative methods (BiCGStab, GMRES, AGMG, c.f., [Notay (2012)]) combined with different preconditioners (ILU0, ASM, Jacobi, and AMG as preconditioner) for the solution of these systems. The required Jacobians can be obtained elegantly with automatic differentiation (AD) [Griewank & Walther (2008)], a source code transformation providing exact derivatives. We compare the performance of the different iterative methods with their respective preconditioners for these linear systems. Furthermore, we analyze linear systems obtained by approximating the Jacobian with finite differences in terms of Newton steps per time step, steps of the iterative solvers and the overall solution time. Finally, we study the influence of heterogeneities in permeability and porosity on the performance of the iterative solvers and their robustness in this respect. References [Griewank & Walther(2008)] Griewank, A. & Walther, A., 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA, 2nd edn. [Huber & Helmig(2000)] Huber, R. & Helmig, R., 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media, Computational Geosciences, 4, 141-164. [Notay(2012)] Notay, Y., 2012. Aggregation-based algebraic multigrid for convection
International Nuclear Information System (INIS)
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)
The iterative thermal emission method: A more implicit modification of IMC
Long, A. R.; Gentile, N. A.; Palmer, T. S.
2014-11-01
For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does
The iterative thermal emission method: A more implicit modification of IMC
Energy Technology Data Exchange (ETDEWEB)
Long, A.R., E-mail: arlong.ne@tamu.edu [Department of Nuclear Engineering, Texas A and M University, 3133 TAMU, College Station, TX 77843 (United States); Gentile, N.A. [Lawrence Livermore National Laboratory, L-38, P.O. Box 808, Livermore, CA 94550 (United States); Palmer, T.S. [Nuclear Engineering and Radiation Health Physics, Oregon State University, 100 Radiation Center, Corvallis, OR 97333 (United States)
2014-11-15
For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does
The iterative thermal emission method: A more implicit modification of IMC
International Nuclear Information System (INIS)
For over 40 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems typically contain regions that are optically thick and diffusive, as a consequence of the high degree of “pseudo-scattering” introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features that could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be nonphysical, in that they violate a maximum principle, where IMC-calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called iterative thermal emission IMC, which is designed to have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit version of IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time step material temperature during a time step. A better estimate of the end of time step material temperature allows for a more implicit estimate of other temperature-dependent quantities: opacity, heat capacity, Fleck factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. We have verified the ITE IMC method against 0-D and 1-D analytic solutions and problems from the literature. These results are compared with traditional IMC. We perform an infinite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. The ITE IMC method does
The iterative self-consistent reaction-field method: The refractive index of pure water
DEFF Research Database (Denmark)
Sylvester-Hvid, Kristian O.; Mikkelsen, K. V.; Ratner, M.A.
2011-01-01
We present different microscopic models for describing electromagnetic properties of condensed phases and the models involve iterative self-consistent procedures for calculating the properties. We report calculations of the frequency-dependent refractive index of pure water. We investigate the...
Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Institute of Scientific and Technical Information of China (English)
Hai Yun ZHOU
2004-01-01
In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
Zhang, Yudong; Yang, Jiquan; Yang, Jianfei; Liu, Aijun; Sun, Ping
2016-01-01
Aim. It can help improve the hospital throughput to accelerate magnetic resonance imaging (MRI) scanning. Patients will benefit from less waiting time. Task. In the last decade, various rapid MRI techniques on the basis of compressed sensing (CS) were proposed. However, both computation time and reconstruction quality of traditional CS-MRI did not meet the requirement of clinical use. Method. In this study, a novel method was proposed with the name of exponential wavelet iterative shrinkage-thresholding algorithm with random shift (abbreviated as EWISTARS). It is composed of three successful components: (i) exponential wavelet transform, (ii) iterative shrinkage-thresholding algorithm, and (iii) random shift. Results. Experimental results validated that, compared to state-of-the-art approaches, EWISTARS obtained the least mean absolute error, the least mean-squared error, and the highest peak signal-to-noise ratio. Conclusion. EWISTARS is superior to state-of-the-art approaches. PMID:27066068
International Nuclear Information System (INIS)
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 ξ and θ. 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(ξ, θ), 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.
Asymptotic perturbation theory of waves
Ostrovsky, Lev
2014-01-01
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theor
Institute of Scientific and Technical Information of China (English)
WU Kai-Su; CHEN Yong-Shou; LIU Zu-Hua; LIN Cheng-Jian; ZHANG Huan-Qiao
2003-01-01
The cross section of the direct neutron capture reaction 12C(n,7)13C(l/2+) is calculated with the asymptotic normalization coefficient method. The result is in good agreement with a recent experiment at low energy. An enormous enhancement of cross section is found for this direct neutron capture in which a p-wave neutron is captured into an 2?i/2 orbit with neutron halo. The possible effect of the neutron halo structure presented in this reaction on the s-process in astrophysics is discussed in general.
International Nuclear Information System (INIS)
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
Directory of Open Access Journals (Sweden)
Junlin Shen
Full Text Available OBJECTIVES: To evaluate the clinical value of noise-based tube current reduction method with iterative reconstruction for obtaining consistent image quality with dose optimization in prospective electrocardiogram (ECG-triggered coronary CT angiography (CCTA. MATERIALS AND METHODS: We performed a prospective randomized study evaluating 338 patients undergoing CCTA with prospective ECG-triggering. Patients were randomly assigned to fixed tube current with filtered back projection (Group 1, n = 113, noise-based tube current with filtered back projection (Group 2, n = 109 or with iterative reconstruction (Group 3, n = 116. Tube voltage was fixed at 120 kV. Qualitative image quality was rated on a 5-point scale (1 = impaired, to 5 = excellent, with 3-5 defined as diagnostic. Image noise and signal intensity were measured; signal-to-noise ratio was calculated; radiation dose parameters were recorded. Statistical analyses included one-way analysis of variance, chi-square test, Kruskal-Wallis test and multivariable linear regression. RESULTS: Image noise was maintained at the target value of 35HU with small interquartile range for Group 2 (35.00-35.03HU and Group 3 (34.99-35.02HU, while from 28.73 to 37.87HU for Group 1. All images in the three groups were acceptable for diagnosis. A relative 20% and 51% reduction in effective dose for Group 2 (2.9 mSv and Group 3 (1.8 mSv were achieved compared with Group 1 (3.7 mSv. After adjustment for scan characteristics, iterative reconstruction was associated with 26% reduction in effective dose. CONCLUSION: Noise-based tube current reduction method with iterative reconstruction maintains image noise precisely at the desired level and achieves consistent image quality. Meanwhile, effective dose can be reduced by more than 50%.
International Nuclear Information System (INIS)
As part of the ITER Conceptual Design Activity (CDA), three workshops were held on plasma diagnostics. From these conference, a set of diagnostics for the full operation of ITER has been developed. This report summarizes the results of these design and discussion activities, and the incorporation of the concepts developed into the overall ITER experiment. Refs, figs and tabs
International Nuclear Information System (INIS)
We study convergence of the integral transport matrix method (ITMM) based on block-Jacobi strategy for solving diamond-differenced SN equations for two-dimensional transport problems. This is a spatial domain decomposition method applied in massively parallel computations. We consider the case of one cell per subdomain. A Fourier analysis of the equations for S2 is performed. The analysis shows that the iteration method in this particular case loses its effectiveness. Numerical results of finite-medium problems are presented to demonstrate the behavior of the ITMM for the DD scheme that was theoretically predicted. (author)
Performance of MCAO on the E-ELT using the Fractal Iterative Method for fast atmospheric tomography
Tallon, Michel; Béchet, Clémentine; Tallon-Bosc, Isabelle; Le Louarn, Miska; Thiébaut, Éric; Clare, Richard; Marchetti, Enrico
2011-09-01
Adaptive optics (AO) on Extremely Large Telescopes (ELTs) must overcome the difficulty of solving a huge number of equations in real time, especially when atmospheric tomography is involved. This is particularly the case for multi-conjugate or multi-objects AO systems. The Fractal Iterative Method (FrIM) has been introduced as a fast iterative algorithm for minimum variance wavefront reconstruction and control on ELTs. In particular, it includes an accurate fast computation of turbulence priors by using the so-called fractal operator. We present the first results obtained with FrIM in closed-loop in the context of atmospheric tomography. The method has been tested on Octopus, the end-to-end AO simulator at ESO, by considering MAORY, the multi-conjugate AO module planed for the E-ELT. This module aims at correcting a 2 arcmin field-of-view, by using 3 deformable mirrors, 6 Sodium laser guide stars, and 3 natural guide stars for low-order wavefront sensing. We show the performance obtained in different conditions and analyze the effect of some parameters of FrIM, like the weight of the priors, or the number of conjugate gradient iterations for solving the reconstruction. We show how the duration of the simulations can be shortened on such a large aperture, with the introduction of artificial vibrations in the simulation. The results are also compared to a more classical approach using matrix-vector multiplication.
International Nuclear Information System (INIS)
The Tokamak Exhaust Processing (TEP) system within the Tritium Plant of ITER needs to be designed such that tritium is recovered from all exhaust gases produced during different modes and operational conditions of the vacuum vessel. The reference process for the TEP system of ITER is called CAPER and comprises three different, consecutive steps to recover hydrogen isotopes at highest purity for direct transfer to the cryogenic Isotope Separation system. The second step ('impurity processing', IP) is carried out in a closed loop involving heterogeneously catalyzed cracking or conversion reactions to liberate tritium from tritiated hydrocarbons or tritiated water combined with permeation of hydrogen isotopes through a Pd/Ag permeator. This combination shifts chemical equilibria towards dehydrogenation and, therefore, enables detritiation factors higher than 1000 in the IP stage. Such a high decontamination factor requires the optimal performance of the permeator, which on the other hand is operated under conditions which provoke coking of the permeator membrane by hydrocarbon cracking. For this reason the permeator in the impurity processing loop needs to be repeatedly regenerated in order to sustain decontamination factors higher/in the order of 1000. At the Tritium Laboratory Karlsruhe (TLK) a method to measure the actual performance of the second stage of the CAPER process has been developed. This method has been successfully tested with the CAPER facility and appears feasible for the TEP system of ITER
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Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.
International Nuclear Information System (INIS)
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. It discretizes only the surface of the radiating object and gives rise to linear systems that are smaller in size compared to those arising from finite element or finite difference discretizations. However, these systems are prohibitively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address the iterative solution via preconditioned Krylov methods of electromagnetic scattering problems expressed in an integral formulation, with main focus on the design of the pre-conditioner. We consider an approximate inverse method based on the Frobenius-norm minimization with a pattern prescribed in advance. The pre-conditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the pre-conditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe the implementation of the approximate inverse in an out-of-core parallel code that uses multipole techniques for the matrix-vector products, and show results on the numerical scalability of our method on systems of size up to one million unknowns. We propose an embedded iterative scheme based on the GMRES method and combined with multipole techniques, aimed at improving the robustness of the approximate inverse for large problems. We prove by numerical experiments that the proposed scheme enables the solution of very large and difficult problems efficiently at reduced computational and memory cost. Finally we perform a preliminary study on a spectral two-level pre-conditioner to enhance the robustness of our method. This numerical technique exploits spectral information of the preconditioned systems to build a low rank-update of the pre-conditioner. (authors)
Convergence Analysis of an Iterative Targeting Method for Keyhole Robotic Surgery
Mirko Daniele Comparetti; Elena De Momi; Tim Beyl; Mirko Kunze; Jörg Raczkowsky; Giancarlo Ferrigno
2014-01-01
In surgical procedures, robots can accurately position and orient surgical instruments. Intraoperatively, external sensors can localize the instrument and compute the targeting movement of the robot, based on the transformation between the coordinate frame of the robot and the sensor. This paper addresses the assessment of the robustness of an iterative targeting algorithm in perturbed conditions. Numerical simulations and experiments (with a robot with seven degrees of freedom and an opti...
Xue, Haile; Shen, Xueshun; Chou, Jifan
2015-10-01
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
International Nuclear Information System (INIS)
Highlights: • Nonoverlapping local/global (NLG) iteration method for reactor transient calculation is developed. • In NLG iteration, local kernel is 2D/1D fusion transport method and global wrapper is p-CMFD. • Neighboring spectral index (NSI) method is developed for rod cusping correction. • NLG iteration gives identical results to the reference solution by p-CMFD acceleration. • NLG iteration is somewhat slower in present implementation compared to p-CMFD acceleration, but has great potential in parallelization. - Abstract: As modern computing power grows, whole-core transport calculations become more viable. However, the computing time and memory requirement remain major burdens. As a candidate for whole-core transport calculation methods, nonoverlapping local/global (NLG) iteration has recently been developed. In this study, the NLG iteration method is extended to make it capable of transient calculations of 3-D heterogeneous problems. It is then implemented in an in-house code, CRX-2K. Transient NLG iteration uses the 2-D/1-D fusion method as a local transport kernel, with the transient p-CMFD equation adopted as a global wrapper. In addition, a neighboring spectral index (NSI) weighting method is suggested as a tool for correcting the rod cusping phenomenon for rod ejection problems. Four problems, including a 3-D heterogeneous problem, are computed. Numerical results show that the NLG iteration converges to the reference solution obtained by means of the whole-core p-CMFD acceleration, and the NSI weighting method is accurate to correct the rod cusping phenomenon. The NLG iteration in present implementation takes more computing times (still less than 2 times) than the whole-core p-CMFD acceleration, but has great potential in parallelization
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Directory of Open Access Journals (Sweden)
Shihua Cao
2014-03-01
Full Text Available Anomaly event detection is one of the research hotspots in wireless sensor networks. Aiming at the disadvantages of current detection solutions, a novel anomaly event detection algorithm based on compressed sensing and iteration is proposed. Firstly, a measured value can be sensed in each node, based on the compressed sensing. Then the problem of anomaly event detection is modeled as the minimization problem of weighted l1 norm, and OMP algorithm is adopted for solving the problem iteratively. And then the result of problem solving is judged according to detection functions. Finally, in the light of the judgment results, the weight value is updated for beginning a new round iteration. The loop won't stop until all the anomaly events are detected in wireless sensor networks. Simulation experimental results show the proposed algorithm has a better omission detection rate and false alarm rate in different noisy environments. In addition, the detection quality of this algorithm is higher than those of the traditional ones.
Asymptotic freedom for nonrelativistic confinement
International Nuclear Information System (INIS)
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle nonrelativistic confining potential model. In this model, asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given, and explicit examples are given for the case of a harmonic oscillator
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Asymptotic evolution of quantum Markov chains
International Nuclear Information System (INIS)
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.
Extended Analytic Device Optimization Employing Asymptotic Expansion
Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred
2013-01-01
Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.
International Nuclear Information System (INIS)
A new multidimensional semi-analytical benchmark capability is developed. The key feature in the solution is the point kernel formulation. The 3D nature of the source is inherited in the flux making this a true multidimensional test. In addition, an efficient numerical scheme, called iterative interpolation, is used to evaluate the required point kernel solution and maintain benchmark accuracy. The EVENT finite element transport algorithm is compared to the point source solution as the first step of embedding the benchmark directly with the EVENT code. Additional code comparisons will be presented. (authors)
An iterative method for controlling reactive power flow in boundary transformers
Energy Technology Data Exchange (ETDEWEB)
Trigo, Angel L.; Martinez, Jose L.; Riquelme, Jesus; Romero, Esther [Department of Electrical Engineering, University of Seville (Spain)
2011-02-15
This paper presents an operational tool designed to help the system operator to control the reactive power flow in transmission-subtransmission boundary transformers. The main objective is to determine the minimum number of control actions necessary to ensure that reactive power flows in transmission/subtransmission transformers remain within limits. The proposed iterative procedure combines the use of a linear programming problem and a load flow tool. The linear programming assumes a linear behaviour between dependent and control variables around an operating point, modelled with sensitivities. Experimental results regarding IEEE systems are provided comparing the performance of the proposed approach with that of a conventional optimal power flow. (author)
An iterative method for calculating gamma-ray build-up factors in multi-layer shields
International Nuclear Information System (INIS)
Point kernel codes that simulate gamma-ray transport often use build-up factors to take scattered photons into account. This study introduces a new method, for computing multi-layer shield build-up factors. This method, based on an empirical formula for calculating double-layer shield build-up factors, is iterative. For an N-layer shield, each iteration of the method treats the first and the second layer of the shield. It replaces these layers by a single equivalent layer composed of an appropriate material and, hence, it turns the N-layer shield into an (N - 1)-layer shield. In order to determine the equivalent layer of an appropriate material, a neural network approach is developed: some neural networks trained on a large set of various configurations provide the equivalent material for any double-layer configuration. The method is implemented into MERCURE-6.3 straight-line attenuation code and is validated by comparison between MERCURE-6.3 results and reference data for one-dimensional geometries. Reference data obtained from transport calculations performed using the Sn transport code TWODANT. The comparisons prove the accuracy and sturdiness of the method. (authors)
Institute of Scientific and Technical Information of China (English)
Shuang-suo Zhao; Zhang-hua Luo; Guo-feng Zhang
2000-01-01
This paper presents optimum an one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix A and high order matrix B: Y = (A B)Y +Ф. On parallel computers (also on serial computer) the former will be efficient, even very efficient under certain conditions, the latter will be universally very efficient.
Asymptotic fixed points for nonlinear contractions
Directory of Open Access Journals (Sweden)
Yong-Zhuo Chen
2005-06-01
Full Text Available Recently, W. A. Kirk proved an asymptotic fixed point theorem for nonlinear contractions by using ultrafilter methods. In this paper, we prove his theorem under weaker assumptions. Furthermore, our proof does not use ultrafilter methods.
A self-calibration method for the edge Thomson scattering diagnostic in ITER
International Nuclear Information System (INIS)
Calibration of spectral transmissivity of the collection and transmission optics is one of the most crucial issues for the Thomson scattering diagnostic system. Radioactivation of the vacuum vessel in ITER makes it difficult to calibrate spectral transmissivity in areas near the vacuum vessel. By using an additional calibration laser whose wavelength differs from those of the diagnostic laser and equipping two lasers with Thomson scattering lights, we can obtain the electron temperature and the relative transmissivity of each spectral channel of the polychromator from the Thomson scattering signal itself. A ruby laser is a promising candidate as a calibration laser because the wavelength does not diverge greatly from that of a diagnostic laser and from the lower limit of an observable wavelength. Even if the signal-noise ratio degrades, the available electron temperature data during calibration operations remain largely unaffected. A degrading signal-noise ratio increases statistical error in electron temperature data and relative spectral transmissivity. Even when the spectral transmissivity is unknown, electron temperature data may be obtained within a 10% margin of error, which fulfills the requirements for edge electron temperature measurement in ITER. (author)
Tian, Zhen; Jia, Xun; Jiang, Steve B
2013-01-01
In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of unit intensity. However, due to the limitation of computer memory and the requirement on computational efficiency, in practice matrix elements of small values are usually truncated, which inevitably compromises the quality of the resulting plan. A fixed-point iteration scheme has been applied in IMRT optimization to solve this problem, which has been reported to be effective and efficient based on the observations of the numerical experiments. In this paper, we aim to point out the mathematics behind this scheme and to answer the following three questions: 1) whether the fixed-point iteration algorithm converges or not? 2) when it converges, whether the fixed point solution is same as the original solution obtained with the complete DDC matrix? 3) if not the same, wh...
Energy Technology Data Exchange (ETDEWEB)
Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)
1994-12-31
What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).
On asymptotic extension dimension
Repovš, Dušan; Zarichnyi, Mykhailo
2011-01-01
The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-07-01
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell's equations. An iterative constraint method was developed to satisfy Maxwell's equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell's equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material's magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
Directory of Open Access Journals (Sweden)
Alam Kamran M.
2013-01-01
Full Text Available In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter β=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter β and the thickness δ of the fluid film on the fluid velocities.
Energy Technology Data Exchange (ETDEWEB)
Nevanlinna, O. [Helsinki Univ. of Technology, Espoo (Finland)
1994-12-31
This note summarizes some results on (a monitored version of) the Arnoldi method in Hilbert spaces. The interest in working in infinite dimensional spaces comes partly from the fact that only then can one have meaningful asymptotical statements (which hopefully give some light to the convergence of Arnoldi in large dimensional problems with iteration indices far less than the dimension).
Energy Technology Data Exchange (ETDEWEB)
Zayed, Elsayed M.E. [Dept. of Mathematics, Zagazig Univ. (Egypt); Abdel Rahman, Hanan M. [Dept. of Basic Sciences, Higher Technological Inst., Tenth of Ramadan City (Egypt)
2010-01-15
In this article, two powerful analytical methods called the variational iteration method (VIM) and the variational homotopy perturbation method (VHPM) are introduced to obtain the exact and the numerical solutions of the (2+1)-dimensional Korteweg-de Vries-Burgers (KdVB) equation and the (1+1)-dimensional Sharma-Tasso-Olver equation. The main objective of the present article is to propose alternative methods of solutions, which avoid linearization and physical unrealistic assumptions. The results show that these methods are very efficient, convenient and can be applied to a large class of nonlinear problems. (orig.)
Ali, Iftikhar; Chanane, Bilal; Malik, Nadeem A.
2014-01-01
We consider a time fractional differential equation of order $\\alpha$, $0 0, \\quad c(x,0)=f(x). $$ where ${}^C_0\\mathcal{D}_t^{\\alpha}$ is the Caputo fractional derivative of order $\\alpha$, $A$ is a linear differential operator, $q(x,t)$ is a source term, and $f(x)$ is the inital condition. Approximate (truncated) series solutions are obtained by means of the Variational Iteration Method (VIM). We find the series solutions for different cases of the source term, in a form that is readily imp...
Abedin, Kazi Monowar; Mujibur Rahman, S. M.
2012-03-01
We have applied the iterative Fresnel integrals method for the computation and simulation of the Fresnel diffraction images created by double apertures in one and two dimensions. Necessary formalism has been derived and the relevant computation algorithms have been developed for this application. The computer simulated images show an interesting combination of Fresnel diffraction images with mutual interference effects between the light diffracted from the two apertures. Transition to the expected Fraunhofer diffraction pattern for double apertures or slits is also observed by the simulations.
Iterative Estimation of Constrained Rank-One Matrices in Noise
Rangan, Sundeep
2012-01-01
We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and positivity that arise commonly in learning problems. We propose a simple iterative procedure that reduces the problem to a sequence of scalar estimation computations. The method is similar to approximate message passing techniques based on Gaussian approximations of loopy belief propagation that have been used recently in compressed sensing. Leveraging analysis methods by Bayati and Montanari, we show that the asymptotic behavior of the estimates from the proposed iterative procedure is described by a simple scalar equivalent model, where the distribution of the estimates is identical to certain scalar estimates of the variables in Gaussian noise. Moreover, the effective Gaussian noise level is described by a set of state evolution equations. The proposed method thus provides a co...
Novel iterative reconstruction method with optimal dose usage for partially redundant CT-acquisition
Bruder, H.; Raupach, R.; Sunnegardh, J.; Allmendinger, T.; Klotz, E.; Stierstorfer, K.; Flohr, T.
2015-11-01
In CT imaging, a variety of applications exist which are strongly SNR limited. However, in some cases redundant data of the same body region provide additional quanta. Examples: in dual energy CT, the spatial resolution has to be compromised to provide good SNR for material decomposition. However, the respective spectral dataset of the same body region provides additional quanta which might be utilized to improve SNR of each spectral component. Perfusion CT is a high dose application, and dose reduction is highly desirable. However, a meaningful evaluation of perfusion parameters might be impaired by noisy time frames. On the other hand, the SNR of the average of all time frames is extremely high. In redundant CT acquisitions, multiple image datasets can be reconstructed and averaged to composite image data. These composite image data, however, might be compromised with respect to contrast resolution and/or spatial resolution and/or temporal resolution. These observations bring us to the idea of transferring high SNR of composite image data to low SNR ‘source’ image data, while maintaining their resolution. It has been shown that the noise characteristics of CT image data can be improved by iterative reconstruction (Popescu et al 2012 Book of Abstracts, 2nd CT Meeting (Salt Lake City, UT) p 148). In case of data dependent Gaussian noise it can be modelled with image-based iterative reconstruction at least in an approximate manner (Bruder et al 2011 Proc. SPIE 7961 79610J). We present a generalized update equation in image space, consisting of a linear combination of the previous update, a correction term which is constrained by the source image data, and a regularization prior, which is initialized by the composite image data. This iterative reconstruction approach we call bimodal reconstruction (BMR). Based on simulation data it is shown that BMR can improve low contrast detectability, substantially reduces the noise power and has the potential to recover
Strong Convergence of Modified Ishikawa Iterations for Nonlinear Mappings
Indian Academy of Sciences (India)
Yongfu Su; Xiaolong Qin
2007-02-01
In this paper, we prove a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive mappings in Banach space. Our results extend and improve the recent results by Nakajo, Takahashi, Kim, $Xu$, Matsushita and some others.
Library designs for generic C++ sparse matrix computations of iterative methods
Energy Technology Data Exchange (ETDEWEB)
Pozo, R.
1996-12-31
A new library design is presented for generic sparse matrix C++ objects for use in iterative algorithms and preconditioners. This design extends previous work on C++ numerical libraries by providing a framework in which efficient algorithms can be written *independent* of the matrix layout or format. That is, rather than supporting different codes for each (element type) / (matrix format) combination, only one version of the algorithm need be maintained. This not only reduces the effort for library developers, but also simplifies the calling interface seen by library users. Furthermore, the underlying matrix library can be naturally extended to support user-defined objects, such as hierarchical block-structured matrices, or application-specific preconditioners. Utilizing optimized kernels whenever possible, the resulting performance of such framework can be shown to be competitive with optimized Fortran programs.
Directory of Open Access Journals (Sweden)
Phayap Katchang
2010-01-01
Full Text Available The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008, Peng et al. (2008, Peng and Yao (2009, as well as Plubtieng and Sriprad (2009 and some well-known results in the literature.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
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.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster
Asymptotic Resource Usage Bounds
Albert E.; Alonso D.; Arenas P.; Genaim S.; Puebla G.
2009-01-01
When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by ...
Asymptotic study of subcritical graph classes
Drmota, Michael; Kang, Mihyun; Kraus, Veronika; Rué, Juanjo
2010-01-01
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical"$ $ graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general method works both in the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp. $g_n$) of labelled (resp. unlabelled) graphs on $n$ vertices from a subcritical graph class ${\\cG}=\\cup_n {\\cG_n}$ satisfies asymptotically the universal behaviour
关于带W权Drazin逆的表示定理及迭代方法%THE REPRESENTATION FOR W-WEIGHTED DRAZIN INVERSE AND ITS ITERATIVE METHODS
Institute of Scientific and Technical Information of China (English)
卜凡斌
2004-01-01
To study singular linear system, Cline and Greville[8] proposed the concept of W-weighted Drazin inverse for the rectangular matrices,where the properties were also discussed. The computation for the W-weighted Drazin inverse is of much interest, which is mainly divided into two kinds of methods: direct method[2,4,6] and iterative method[3,5,7,9,12,13]. In this paper, we study the iterative method and successive matrix squaring(SMS) method for the W-weighted Drazin inverse and generalize the main results in [12,13].
Common fixed points of a finite family of asymptotically pseudocontractive maps
Directory of Open Access Journals (Sweden)
Osilike MO
2004-01-01
Full Text Available Convergence theorems for approximation of common fixed points of a finite family of asymptotically pseudocontractive mappings are proved in Banach spaces using an averaging implicit iteration process.
Energy Technology Data Exchange (ETDEWEB)
Reitz, Irmtraud; Hesse, Bernd-Michael; Nill, Simeon; Tuecking, Thomas; Oelfke, Uwe [DKFZ, Heidelberg (Germany)
2009-07-01
The problem of the enormous amount of scattered radiation in kV CBCT (kilo voltage cone beam computer tomography) is addressed. Scatter causes undesirable streak- and cup-artifacts and results in a quantitative inaccuracy of reconstructed CT numbers, so that an accurate dose calculation might be impossible. Image contrast is also significantly reduced. Therefore we checked whether an appropriate implementation of the fast iterative scatter correction algorithm we have developed for MV (mega voltage) CBCT reduces the scatter contribution in a kV CBCT as well. This scatter correction method is based on a superposition of pre-calculated Monte Carlo generated pencil beam scatter kernels. The algorithm requires only a system calibration by measuring homogeneous slab phantoms with known water-equivalent thicknesses. In this study we compare scatter corrected CBCT images of several phantoms to the fan beam CT images acquired with a reduced cone angle (a slice-thickness of 14 mm in the isocenter) at the same system. Additional measurements at a different CBCT system were made (different energy spectrum and phantom-to-detector distance) and a first order approach of a fast beam hardening correction will be introduced. The observed, image quality of the scatter corrected CBCT images is comparable concerning resolution, noise and contrast-to-noise ratio to the images acquired in fan beam geometry. Compared to the CBCT without any corrections the contrast of the contrast-and-resolution phantom with scatter correction and additional beam hardening correction is improved by a factor of about 1.5. The reconstructed attenuation coefficients and the CT numbers of the scatter corrected CBCT images are close to the values of the images acquired in fan beam geometry for the most pronounced tissue types. Only for extreme dense tissue types like cortical bone we see a difference in CT numbers of 5.2%, which can be improved to 4.4% with the additional beam hardening correction. Cupping
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Iterative reconstruction method for PROPELLER MRI%基于迭代的PROPELLER MRI重建算法
Institute of Scientific and Technical Information of China (English)
郭红宇; 戴建平; 何砚发
2011-01-01
PROPELLER( periodically rotated overlapping parallel lines with enhanced reconstruction) is a new acquisition technique which can efficiently reduce motion artifacts in MRI imaging. Convolution gridding method usually necessitates lots of parameters optimization and a sampling density compensation step, so the quality of the reconstructed image cannot be ensured. In the paper, an iterative method is applied to reconstruct images for PROPELLER MRI. In the method, a cost function is iteratively minimized by using weighted pre-conditioned conjugate gradient algorithm. In order to improve computation, NUFFT (nonuniform fast Fourier transformation) is used to computing matrix-vector multiplication. Experimental comparison was made by using both digital phantom data and experimental PROPELLER imaging data. The results showed that the iterative method can improve signal to noise ratio of images and reduce ring artifacts of images in comparison with convolution gridding method. The homogeneity of images can be improved as well.%PROPELLER是磁共振成像中能有效消除运动伪影的一种新的采集技术.对于PROPELLER的重建,传统的卷积网格方法由于需要优化大量参数和采样密度补偿过程,重建图像的质量很难得到保证.本文提出使用迭代重建的方法进行PROPLLER的重建,通过加权预条件共轭梯度算法,迭代最小化代价函数,从而得到重建图像.为了提高速度,在每步迭代中.使用NUFFT计算矩阵一向量乘法.通过仿真数据和实际扫描数据比较验证,迭代算法相比卷积网格化方法提高了重建图像信噪比,消除了振铃伪影,并提高了图像的均匀性.
Asymptotic-group analysis of algebraic equations
Shamrovskii, A. D.; I. V. Andrianov; J. Awrejcewicz
2004-01-01
Both the method of asymptotic analysis and the theory of extension group are applied to study the Descates equation. The proposed algorithm allows to obtain various variants of simplification and can be easily generalized to their algebraic and differential equations.
Non-destructive methods for the defect detection in the ITER high heat flux components
Energy Technology Data Exchange (ETDEWEB)
Roccella, S., E-mail: selanna.roccella@enea.it [Associazione ENEA-Euratom sulla Fusione C.R.Frascati - 00044-Frascati, RM (Italy); Burrasca, G.; Cacciotti, E. [Associazione ENEA-Euratom sulla Fusione C.R.Frascati - 00044-Frascati, RM (Italy); Castillo, A. [Associazione Euratom-ENEA sulla Fusione, C.R.Casaccia, Via Anguillarese 301-00123 S. Maria di Galeria, RM (Italy); Universidad Politecnica de Valencia, Valencia (Spain); Mancini, A.; Pizzuto, A. [Associazione ENEA-Euratom sulla Fusione C.R.Frascati - 00044-Frascati, RM (Italy); Tati, A. [Associazione Euratom-ENEA sulla Fusione, C.R.Casaccia, Via Anguillarese 301-00123 S. Maria di Galeria, RM (Italy); Visca, E. [Associazione ENEA-Euratom sulla Fusione C.R.Frascati - 00044-Frascati, RM (Italy)
2011-10-15
This paper discusses the application of non-destructive testing (NDT) by ultrasonic technique for the control of the joining interfaces of the ITER divertor vertical target plasma facing units. The defect detection capability has to be proved for both metal to metal and metal to carbon/carbon fibre composite (CFC) joints because these two types of joints have to be realized for the manufacturing of the high heat flux units. In this paper the UT results coming from the investigation performed during the manufacturing, but also after the thermal fatigue testing (up to 20 MW/m{sup 2}) of six mock-ups manufactured using the Hot Radial Pressure technology (HRP) in ENEA labs are presented and compared with the evidences from the final destructive examination. Regarding the Cu/CFC joint, the effectiveness of the ultrasonic test has been deeply studied due to the high acoustic attenuation of CFC to ultrasonic waves. To investigate the possibility to use the ultrasonic technique for this type of joint, an 'ad hoc' flat Cu/CFC joint sample, that reproduces the actual annular joint interfaces, was manufactured. This flat sample has the advantage of being easily tested by probes with different geometry and frequency. UT results are compared with X-ray and eddy current testing of the same sample.
Convergence of path and an iterative method for families of nonexpansive mappings
International Nuclear Information System (INIS)
Let E be a real q-uniformly smooth Banach space with q ≥ 1+ dq. Let K be a closed, convex and nonempty subset of E. Let {Ti}i=1∞ be a family of nonexpansive self-mappings of K. For arbitrary fixed δ element of (0, 1) define a family of nonexpansive maps {Si }i=1∞ by Si := (1 - δ)I + δTi where I is the identity map of K. Let F :ntersectioni=∞F(Ti) ≠ 0. Assume either at least one of the T'i s is emicompact or E admits weakly sequentially continuous duality map. It is prove that the fixed point sequence {ztn} converges strongly to a common fixed point of the family {Ti}i=1∞, where tn = tnu + Σi≥1σi,nSiztn ,and {tn} is a sequence in (0, 1), satisfying appropriate conditions. As an application, it is prove that the iterative sequence {xn} defined by: x0 element of K, xn+1 = αnu + Σi≥1 σi,nSixn , n ≥ 0 onverges strongly to a common fixed point of the family {i right brace#i=1∞ where {αn} and {σi,n} are sequences in (0, 1) satisfying appropriate conditions. (author)
Non-destructive methods for the defect detection in the ITER high heat flux components
International Nuclear Information System (INIS)
This paper discusses the application of non-destructive testing (NDT) by ultrasonic technique for the control of the joining interfaces of the ITER divertor vertical target plasma facing units. The defect detection capability has to be proved for both metal to metal and metal to carbon/carbon fibre composite (CFC) joints because these two types of joints have to be realized for the manufacturing of the high heat flux units. In this paper the UT results coming from the investigation performed during the manufacturing, but also after the thermal fatigue testing (up to 20 MW/m2) of six mock-ups manufactured using the Hot Radial Pressure technology (HRP) in ENEA labs are presented and compared with the evidences from the final destructive examination. Regarding the Cu/CFC joint, the effectiveness of the ultrasonic test has been deeply studied due to the high acoustic attenuation of CFC to ultrasonic waves. To investigate the possibility to use the ultrasonic technique for this type of joint, an 'ad hoc' flat Cu/CFC joint sample, that reproduces the actual annular joint interfaces, was manufactured. This flat sample has the advantage of being easily tested by probes with different geometry and frequency. UT results are compared with X-ray and eddy current testing of the same sample.
WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Directory of Open Access Journals (Sweden)
Yu Miao
2008-08-01
Full Text Available In a real {sc Hilbert} space $H$, starting from an arbitrary initialpoint $x_0in H$, an iterative process is defined as follows:$x_{n+1}=a_nx_n+(1-a_nT^{lambda_{n+1}}_fy_n$, $y_n= b_nx_n+(1-b_nT^{eta_{n}}_gx_n$, $nge 0$, where$T^{lambda_{n+1}}_f x= Tx-lambda_{n+1} mu_f f(Tx$,$T^{eta_{n}}_g x= Tx-eta_{n} mu_g g(Tx$, ($forall xinH$, $T: Ho H$ a nonexpansive mappingwith $F(T eemptyset$ and $f$ (resp. $g$ $: Ho H$ an$eta_f$ (resp. $eta_g$-strongly monotone and $k_f$ (resp. $k_g$-Lipschitzianmapping, ${a_n}subset(0,1$, ${b_n}subset(0,1$ and ${lambda_n}subset[0,1$,${eta_n}subset[0,1$. Under some suitable conditions, severalconvergence results of the sequence ${x_n}$ are shown.
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
International Nuclear Information System (INIS)
A set of optical diagnostics is expected for measuring the plasma characteristics in ITER. Optical elements located inside discharge chambers are exposed to an intense radiation load, sputtering due to collisions with energetic atoms formed in the charge transfer processes, and contamination due to recondensation of materials sputtered from different parts of the construction of the chamber. Removing the films of the sputtered materials from the mirrors with the aid of pulsed laser radiation is an efficient cleaning method enabling recovery of the optical properties of the mirrors. In this work, we studied the efficiency of removal of metal oxide films by pulsed radiation of a fiber laser. Optimization of the laser cleaning conditions was carried out on samples representing metal substrates polished with optical quality with deposition of films on them imitating the chemical composition and conditions expected in ITER. It is shown that, by a proper selection of modes of radiation exposure to the surface with a deposited film, it is feasible to restore the original high reflection characteristics of optical elements