On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

International Nuclear Information System (INIS)

An Hengbin; Mo Zeyao; Xu Xiaowen; Liu Xu

2009-01-01

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.

Colorado Conference on iterative methods. Volume 1

Energy Technology Data Exchange (ETDEWEB)

NONE

1994-12-31

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

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

Directory of Open Access Journals (Sweden)

Wilson Rodríguez Calderón

2015-04-01

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

Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

DEFF Research Database (Denmark)

Miansari, Mo; Miansari, Me; Barari, Amin

2009-01-01

In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

KAUST Repository

Desmal, Abdulla

2015-07-29

A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow

International Nuclear Information System (INIS)

Knoll, D.A.

1998-01-01

The authors study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. They use Newton's method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. They investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, mesh sequencing, and a pseudotransient continuation technique is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a mesh sequencing implementation provides significant CPU savings for fine grid calculations. Performance comparisons of modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented

Multi-Level iterative methods in computational plasma physics

International Nuclear Information System (INIS)

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

1999-01-01

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

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

Science.gov (United States)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Science.gov (United States)

Xu, Feng; Deshpande, Manohar

2012-01-01

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

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

Directory of Open Access Journals (Sweden)

Mehmet Tarik Atay

2013-01-01

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

Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow

Energy Technology Data Exchange (ETDEWEB)

Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

1996-12-31

We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.

An iterative method for nonlinear demiclosed monotone-type operators

International Nuclear Information System (INIS)

Chidume, C.E.

1991-01-01

It is proved that a well known fixed point iteration scheme which has been used for approximating solutions of certain nonlinear demiclosed monotone-type operator equations in Hilbert spaces remains applicable in real Banach spaces with property (U, α, m+1, m). These Banach spaces include the L p -spaces, p is an element of [2,∞]. An application of our results to the approximation of a solution of a certain linear operator equation in this general setting is also given. (author). 19 refs

Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence

International Nuclear Information System (INIS)

Bloomberg, D.S.; Castelli, V.

1985-01-01

The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor β in the MH approach varies inversely with permeability μ, and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for β 3 , the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on β, degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for βless than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix

A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

Directory of Open Access Journals (Sweden)

Pratibha Joshi

2014-12-01

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

Conformable variational iteration method

Directory of Open Access Journals (Sweden)

Omer Acan

2017-02-01

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

Nonlinear ordinary differential equations analytical approximation and numerical methods

CERN Document Server

Hermann, Martin

2016-01-01

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

Strong convergence of modified Ishikawa iterations for nonlinear ...

Indian Academy of Sciences (India)

interval [0, 1]. The second iteration process is referred to as Ishikawa's iteration process [11] which is .... Let E be a smooth Banach space with dual E∗ ..... and applications, in: Theory and Applications of Nonlinear Operators of Accretive and.

Estimation of POL-iteration methods in fast running DNBR code

Energy Technology Data Exchange (ETDEWEB)

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

2016-05-15

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

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

Science.gov (United States)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

Directory of Open Access Journals (Sweden)

Chi-Chang Wang

2013-09-01

Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

Iterative solution of a nonlinear system arising in phase change problems

International Nuclear Information System (INIS)

Williams, M.A.

1987-01-01

We consider several iterative methods for solving the nonlinear system arising from an enthalpy formulation of a phase change problem. We present the formulation of the problem. Implicit discretization of the governing equations results in a mildly nonlinear system at each time step. We discuss solving this system using Jacobi, Gauss-Seidel, and SOR iterations and a new modified preconditioned conjugate gradient (MPCG) algorithm. The new MPCG algorithm and its properties are discussed in detail. Numerical results are presented comparing the performance of the SOR algorithm and the MPCG algorithm with 1-step SSOR preconditioning. The MPCG algorithm exhibits a superlinear rate of convergence. The SOR algorithm exhibits a linear rate of convergence. Thus, the MPCG algorithm requires fewer iterations to converge than the SOR algorithm. However in most cases, the SOR algorithm requires less total computation time than the MPCG algorithm. Hence, the SOR algorithm appears to be more appropriate for the class of problems considered. 27 refs., 11 figs

Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces

International Nuclear Information System (INIS)

Jin, Qinian

2012-01-01

By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

Geometric properties of Banach spaces and nonlinear iterations

CERN Document Server

Chidume, Charles

2009-01-01

Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...

A Fibonacci-like Iterated Nonlinear Map

NARCIS (Netherlands)

Asveld, P.R.J.; van der Weele, J.P.; Valkering, T.P.

1990-01-01

We study a second-order Fibonacci-like iterated nonlinear map that contains two parameters of which one is kept fixed, whereas the other one varies from 0 to 1. This gives rise to some complicated behavior which is displayed in a few interesting pictures.

A Fibonacci-like Iterated Nonlinear Map

NARCIS (Netherlands)

Asveld, P.R.J.

1989-01-01

We study a second-order Fibonacci-like iterated nonlinear map that contains two parameters of which one is kept fixed, whereas the other one varies from 0 to 1. This gives rise to some complicated behavior which is displayed in a few interesting pictures.

Iterative solutions of nonlinear equations with strongly accretive or strongly pseudocontractive maps

International Nuclear Information System (INIS)

Chidume, C.E.

1994-03-01

Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudo-contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided. (author). 38 refs

Nonlinear iterative strategy for NEM refinement and extension

International Nuclear Information System (INIS)

Engrand, P.R.; Maldonado, G.I.; Al-Chalabi, R.; Turinsky, P.J.

1992-01-01

The work discussed in this paper is related to the nonlinear iterative strategy developed by Smith to solve the nodal expansion method (NEM) representation of the neutron diffusion equations. The authors show how it is possible to save computation time by taking advantage of the reducibility of the matrices that have to be inverted when employing this strategy. In addition, they show how this strategy can be adapted in an easy and efficient manner to time-dependent problems

An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

Science.gov (United States)

Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.

2009-12-01

A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.

Iterative algorithm for the volume integral method for magnetostatics problems

International Nuclear Information System (INIS)

Pasciak, J.E.

1980-11-01

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

A sparse electromagnetic imaging scheme using nonlinear landweber iterations

KAUST Repository

Desmal, Abdulla

2015-10-26

Development and use of electromagnetic inverse scattering techniques for imagining sparse domains have been on the rise following the recent advancements in solving sparse optimization problems. Existing techniques rely on iteratively converting the nonlinear forward scattering operator into a sequence of linear ill-posed operations (for example using the Born iterative method) and applying sparsity constraints to the linear minimization problem of each iteration through the use of L0/L1-norm penalty term (A. Desmal and H. Bagci, IEEE Trans. Antennas Propag, 7, 3878–3884, 2014, and IEEE Trans. Geosci. Remote Sens., 3, 532–536, 2015). It has been shown that these techniques produce more accurate and sharper images than their counterparts which solve a minimization problem constrained with smoothness promoting L2-norm penalty term. But these existing techniques are only applicable to investigation domains involving weak scatterers because the linearization process breaks down for high values of dielectric permittivity.

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

Science.gov (United States)

Zeng, Gengsheng L

2017-10-01

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

Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media

KAUST Repository

Efendiev, Y.

2012-08-01

In this paper, we study robust iterative solvers for finite element systems resulting in approximation of steady-state Richards\\' equation in porous media with highly heterogeneous conductivity fields. It is known that in such cases the contrast, ratio between the highest and lowest values of the conductivity, can adversely affect the performance of the preconditioners and, consequently, a design of robust preconditioners is important for many practical applications. The proposed iterative solvers consist of two kinds of iterations, outer and inner iterations. Outer iterations are designed to handle nonlinearities by linearizing the equation around the previous solution state. As a result of the linearization, a large-scale linear system needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer iterations is independent of the contrast. Second, based on the recently developed iterative methods, we construct a class of preconditioners that yields convergence rate that is independent of the contrast. Thus, the proposed iterative solvers are optimal with respect to the large variation in the physical parameters. Since the same preconditioner can be reused in every outer iteration, this provides an additional computational savings in the overall solution process. Numerical tests are presented to confirm the theoretical results. © 2012 Global-Science Press.

Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

Science.gov (United States)

Wei, Qinglai; Liu, Derong; Lin, Hanquan

2016-03-01

In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

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

Directory of Open Access Journals (Sweden)

D. G. Patalakh

2018-02-01

Full Text Available Purpose. Development of calculation of electromagnetic and electromechanic transients is in asynchronous engines without iterations. Methodology. Numeral methods of integration of usual differential equations, programming. Findings. As the system of equations, describing the dynamics of asynchronous engine, contents the products of rotor and stator currents and product of rotation frequency of rotor and currents, so this system is nonlinear one. The numeral solution of nonlinear differential equations supposes an iteration process on every step of integration. Time-continuing and badly converging iteration process may be the reason of calculation slowing. The improvement of numeral method by the way of an iteration process removing is offered. As result the modeling time is reduced. The improved numeral method is applied for integration of differential equations, describing the dynamics of asynchronous engine. Originality. The improvement of numeral method allowing to execute numeral integrations of differential equations containing product of functions is offered, that allows to avoid an iteration process on every step of integration and shorten modeling time. Practical value. On the basis of the offered methodology the universal program of modeling of electromechanics processes in asynchronous engines could be developed as taking advantage on fast-acting.

Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method

International Nuclear Information System (INIS)

Langemann, Dirk; Tasche, Manfred

2008-01-01

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

Iterative ensemble variational methods for nonlinear data assimilation: Application to transport and atmospheric chemistry

International Nuclear Information System (INIS)

Haussaire, Jean-Matthieu

2017-01-01

Data assimilation methods are constantly evolving to adapt to the various application domains. In atmospheric sciences, each new algorithm has first been implemented on numerical weather prediction models before being ported to atmospheric chemistry models. It has been the case for 4D variational methods and ensemble Kalman filters for instance. The new 4D ensemble variational methods (4D EnVar) are no exception. They were developed to take advantage of both variational and ensemble approaches and they are starting to be used in operational weather prediction centers, but have yet to be tested on operational atmospheric chemistry models. The validation of new data assimilation methods on these models is indeed difficult because of the complexity of such models. It is hence necessary to have at our disposal low-order models capable of synthetically reproducing key physical phenomena from operational models while limiting some of their hardships. Such a model, called L95-GRS, has therefore been developed. Il combines the simple meteorology from the Lorenz-95 model to a tropospheric ozone chemistry module with 7 chemical species. Even though it is of low dimension, it reproduces some of the physical and chemical phenomena observable in real situations. A data assimilation method, the iterative ensemble Kalman smoother (IEnKS), has been applied to this model. It is an iterative 4D EnVar method which solves the full non-linear variational problem. This application validates 4D EnVar methods in the context of non-linear atmospheric chemistry, but also raises the first limits of such methods, most noticeably when they are applied to weakly coupled stable models. After this experiment, results have been extended to a realistic atmospheric pollution prediction model. 4D EnVar methods, via the IEnKS, have once again shown their potential to take into account the non-linearity of the chemistry model in a controlled environment, with synthetic observations. However, the

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

International Nuclear Information System (INIS)

Yusufoglu, Elcin; Erbas, Baris

2008-01-01

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

Iterative analysis of concrete gravity dam-nonlinear foundation ...

African Journals Online (AJOL)

The solution of the coupled system is accomplished by solving the two systems separately and then considering the interaction effects at the soil–structure interface enforced by a developed iterative scheme. Emphasis has been laid on the study of material nonlinearity of the foundation material in the interaction analysis.

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

International Nuclear Information System (INIS)

Tatari, Mehdi; Dehghan, Mehdi

2007-01-01

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

Nonlinear response matrix methods for radiative transfer

International Nuclear Information System (INIS)

Miller, W.F. Jr.; Lewis, E.E.

1987-01-01

A nonlinear response matrix formalism is presented for the solution of time-dependent radiative transfer problems. The essential feature of the method is that within each computational cell the temperature is calculated in response to the incoming photons from all frequency groups. Thus the updating of the temperature distribution is placed within the iterative solution of the spaceangle transport problem, instead of being placed outside of it. The method is formulated for both grey and multifrequency problems and applied in slab geometry. The method is compared to the more conventional source iteration technique. 7 refs., 1 fig., 4 tabs

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

Directory of Open Access Journals (Sweden)

Muhammad Aslam Noor

2008-01-01

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

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

International Nuclear Information System (INIS)

Alves, Carlos; Kress, Rainer; Serranho, Pedro

2009-01-01

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

A block-iterative nodal integral method for forced convection problems

International Nuclear Information System (INIS)

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

1992-01-01

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

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

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Mashinchi Joubari

2015-01-01

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

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

NARCIS (Netherlands)

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

2017-01-01

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

Natural Preconditioning and Iterative Methods for Saddle Point Systems

KAUST Repository

Pestana, Jennifer

2015-01-01

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

A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging

KAUST Repository

Desmal, Abdulla

2015-03-01

A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

Science.gov (United States)

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

Convergence analysis of the nonlinear iterative method for two-phase flow in porous media associated with nanoparticle injection

KAUST Repository

El-Amin, Mohamed

2017-08-29

Purpose In this paper, we introduce modeling, numerical simulation, and convergence analysis of the problem nanoparticles transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles concentration, deposited nanoparticles concentration on the pore-walls, and entrapped nanoparticles concentration in pore-throats. Design/methodology/approach Nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated. Findings We stated and proved three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions. The theorem is proved by induction states that after a number of iterations the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, while the error estimations are presented in table for different values of number of time steps, number of iterations and mesh size. Research limitations/implications The domain of the computations is relatively small however, it is straightforward to extend this method

Variational iteration method for solving coupled-KdV equations

International Nuclear Information System (INIS)

Assas, Laila M.B.

2008-01-01

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

Bounds for nonlinear composites via iterated homogenization

Science.gov (United States)

Ponte Castañeda, P.

2012-09-01

Improved estimates of the Hashin-Shtrikman-Willis type are generated for the class of nonlinear composites consisting of two well-ordered, isotropic phases distributed randomly with prescribed two-point correlations, as determined by the H-measure of the microstructure. For this purpose, a novel strategy for generating bounds has been developed utilizing iterated homogenization. The general idea is to make use of bounds that may be available for composite materials in the limit when the concentration of one of the phases (say phase 1) is small. It then follows from the theory of iterated homogenization that it is possible, under certain conditions, to obtain bounds for more general values of the concentration, by gradually adding small amounts of phase 1 in incremental fashion, and sequentially using the available dilute-concentration estimate, up to the final (finite) value of the concentration (of phase 1). Such an approach can also be useful when available bounds are expected to be tighter for certain ranges of the phase volume fractions. This is the case, for example, for the "linear comparison" bounds for porous viscoplastic materials, which are known to be comparatively tighter for large values of the porosity. In this case, the new bounds obtained by the above-mentioned "iterated" procedure can be shown to be much improved relative to the earlier "linear comparison" bounds, especially at low values of the porosity and high triaxialities. Consistent with the way in which they have been derived, the new estimates are, strictly, bounds only for the class of multi-scale, nonlinear composites consisting of two well-ordered, isotropic phases that are distributed with prescribed H-measure at each stage in the incremental process. However, given the facts that the H-measure of the sequential microstructures is conserved (so that the final microstructures can be shown to have the same H-measure), and that H-measures are insensitive to length scales, it is conjectured

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

African Journals Online (AJOL)

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

Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

International Nuclear Information System (INIS)

Koteras, J.R.

1996-01-01

The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

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

OpenAIRE

Darzi R; Neamaty A

2010-01-01

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

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

Science.gov (United States)

Pakdemirli, Mehmet

2016-01-01

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

A different approach to estimate nonlinear regression model using numerical methods

Science.gov (United States)

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

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

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

Directory of Open Access Journals (Sweden)

A. A. Hemeda

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

R. Darzi

2010-01-01

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

TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

Energy Technology Data Exchange (ETDEWEB)

Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

1996-12-31

This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

An hp symplectic pseudospectral method for nonlinear optimal control

Science.gov (United States)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

NITSOL: A Newton iterative solver for nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

DEFF Research Database (Denmark)

Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

2010-01-01

of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....

Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Energy Technology Data Exchange (ETDEWEB)

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

Study of a Biparametric Family of Iterative Methods

Directory of Open Access Journals (Sweden)

B. Campos

2014-01-01

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

Copper Mountain conference on iterative methods: Proceedings: Volume 1

Energy Technology Data Exchange (ETDEWEB)

NONE

1996-10-01

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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

International Nuclear Information System (INIS)

Jin Qinian

2008-01-01

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

Iterated non-linear model predictive control based on tubes and contractive constraints.

Science.gov (United States)

Murillo, M; Sánchez, G; Giovanini, L

2016-05-01

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Methods for Large-Scale Nonlinear Optimization.

Science.gov (United States)

1980-05-01

STANFORD, CALIFORNIA 94305 METHODS FOR LARGE-SCALE NONLINEAR OPTIMIZATION by Philip E. Gill, Waiter Murray, I Michael A. Saunden, and Masgaret H. Wright...typical iteration can be partitioned so that where B is an m X m basise matrix. This partition effectively divides the vari- ables into three classes... attention is given to the standard of the coding or the documentation. A much better way of obtaining mathematical software is from a software library

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

Science.gov (United States)

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

2015-06-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1994-12-31

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

An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Directory of Open Access Journals (Sweden)

Eman S. Alaidarous

2013-01-01

Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

Iterative solution for nonlinear integral equations of Hammerstein type

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1990-12-01

Let E be a real Banach space with a uniformly convex dual, E*. Suppose N is a nonlinear set-valued accretive map of E into itself with open domain D; K is a linear single-valued accretive map with domain D(K) in E such that Im(N) is contained in D(K); K -1 exists and satisfies -1 x-K -1 y,j(x-y)>≥β||x-y|| 2 for each x, y is an element of Im(K) and some constant β > 0, where j denotes the single-valued normalized duality map on E. Suppose also that for each h is an element Im(K) the equation h is an element x+KNx has a solution x* in D. An iteration method is constructed which converges strongly to x*. Explicit error estimates are also computed. (author). 25 refs

New Efficient Fourth Order Method for Solving Nonlinear Equations

Directory of Open Access Journals (Sweden)

Farooq Ahmad

2013-12-01

Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian

2016-07-26

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian; Yang, Chao; Sun, Shuyu

2016-01-01

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Implementation of non-linear filters for iterative penalized maximum likelihood image reconstruction

International Nuclear Information System (INIS)

Liang, Z.; Gilland, D.; Jaszczak, R.; Coleman, R.

1990-01-01

In this paper, the authors report on the implementation of six edge-preserving, noise-smoothing, non-linear filters applied in image space for iterative penalized maximum-likelihood (ML) SPECT image reconstruction. The non-linear smoothing filters implemented were the median filter, the E 6 filter, the sigma filter, the edge-line filter, the gradient-inverse filter, and the 3-point edge filter with gradient-inverse filter, and the 3-point edge filter with gradient-inverse weight. A 3 x 3 window was used for all these filters. The best image obtained, by viewing the profiles through the image in terms of noise-smoothing, edge-sharpening, and contrast, was the one smoothed with the 3-point edge filter. The computation time for the smoothing was less than 1% of one iteration, and the memory space for the smoothing was negligible. These images were compared with the results obtained using Bayesian analysis

Domain decomposition based iterative methods for nonlinear elliptic finite element problems

Energy Technology Data Exchange (ETDEWEB)

Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

1994-12-31

The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

Optimal analytic method for the nonlinear Hasegawa-Mima equation

Science.gov (United States)

Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

2014-05-01

The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

Directory of Open Access Journals (Sweden)

H. Montazeri

2012-01-01

Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

International Nuclear Information System (INIS)

Di Dong; Yiming Long.

1994-10-01

In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

Science.gov (United States)

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

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

1990-01-01

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

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

Science.gov (United States)

Jin, Qinian; Wang, Wei

2018-03-01

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

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

KAUST Repository

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

2016-01-01

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

An approximation method for nonlinear integral equations of Hammerstein type

International Nuclear Information System (INIS)

Chidume, C.E.; Moore, C.

1989-05-01

The solution of a nonlinear integral equation of Hammerstein type in Hilbert spaces is approximated by means of a fixed point iteration method. Explicit error estimates are given and, in some cases, convergence is shown to be at least as fast as a geometric progression. (author). 25 refs

Advances in iterative methods

International Nuclear Information System (INIS)

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

1981-01-01

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

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

Science.gov (United States)

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

1994-01-01

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

Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

Directory of Open Access Journals (Sweden)

Fan Yuxin

2014-12-01

Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.

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

KAUST Repository

Sandhu, Ali Imran

2016-04-10

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

Construction of a path of MHD equilibrium solutions by an iterative method

International Nuclear Information System (INIS)

Kikuchi, Fumio.

1979-09-01

This paper shows a constructive proof of the existence of a path of solutions to a nonlinear eigenvalue problem expressed by -Δu = lambda u + in Ω, and u = -1 on deltaΩ where Ω is a two-dimensional domain with a boundary deltaΩ. This problem arises from the ideal MHD equilibria in tori. The existence proof is based on the principle of contraction mappings, which is widely employed in nonlinear problems such as those associated with bifurcation phenomena. Some comments are also given on the application of the present iteration techniques to numerical method. (author)

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

KAUST Repository

Elsheikh, Ahmed H.

2013-05-01

A novel multi-modal parameter estimation algorithm is introduced. Parameter estimation is an ill-posed inverse problem that might admit many different solutions. This is attributed to the limited amount of measured data used to constrain the inverse problem. The proposed multi-modal model calibration algorithm uses an iterative stochastic ensemble method (ISEM) for parameter estimation. ISEM employs an ensemble of directional derivatives within a Gauss-Newton iteration for nonlinear parameter estimation. ISEM is augmented with a clustering step based on k-means algorithm to form sub-ensembles. These sub-ensembles are used to explore different parts of the search space. Clusters are updated at regular intervals of the algorithm to allow merging of close clusters approaching the same local minima. Numerical testing demonstrates the potential of the proposed algorithm in dealing with multi-modal nonlinear parameter estimation for subsurface flow models. © 2013 Elsevier B.V.

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.

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

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

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

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

A family of conjugate gradient methods for large-scale nonlinear equations.

Science.gov (United States)

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Parallel supercomputing: Advanced methods, algorithms, and software for large-scale linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Carey, G.F.; Young, D.M.

1993-12-31

The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.

Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2016-03-01

Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

A family of conjugate gradient methods for large-scale nonlinear equations

Directory of Open Access Journals (Sweden)

Dexiang Feng

2017-09-01

Full Text Available Abstract In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2014-01-01

Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...

Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Directory of Open Access Journals (Sweden)

Reza Mokhtari

2012-01-01

Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.

Iterative Splitting Methods for Differential Equations

CERN Document Server

Geiser, Juergen

2011-01-01

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

Iterative nonlinear unfolding code: TWOGO

International Nuclear Information System (INIS)

Hajnal, F.

1981-03-01

a new iterative unfolding code, TWOGO, was developed to analyze Bonner sphere neutron measurements. The code includes two different unfolding schemes which alternate on successive iterations. The iterative process can be terminated either when the ratio of the coefficient of variations in terms of the measured and calculated responses is unity, or when the percentage difference between the measured and evaluated sphere responses is less than the average measurement error. The code was extensively tested with various known spectra and real multisphere neutron measurements which were performed inside the containments of pressurized water reactors

Iteration and accelerator dynamics

International Nuclear Information System (INIS)

Peggs, S.

1987-10-01

Four examples of iteration in accelerator dynamics are studied in this paper. The first three show how iterations of the simplest maps reproduce most of the significant nonlinear behavior in real accelerators. Each of these examples can be easily reproduced by the reader, at the minimal cost of writing only 20 or 40 lines of code. The fourth example outlines a general way to iteratively solve nonlinear difference equations, analytically or numerically

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

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

Nonlinear Burn Control and Operating Point Optimization in ITER

Science.gov (United States)

Boyer, Mark; Schuster, Eugenio

2013-10-01

Control of the fusion power through regulation of the plasma density and temperature will be essential for achieving and maintaining desired operating points in fusion reactors and burning plasma experiments like ITER. In this work, a volume averaged model for the evolution of the density of energy, deuterium and tritium fuel ions, alpha-particles, and impurity ions is used to synthesize a multi-input multi-output nonlinear feedback controller for stabilizing and modulating the burn condition. Adaptive control techniques are used to account for uncertainty in model parameters, including particle confinement times and recycling rates. The control approach makes use of the different possible methods for altering the fusion power, including adjusting the temperature through auxiliary heating, modulating the density and isotopic mix through fueling, and altering the impurity density through impurity injection. Furthermore, a model-based optimization scheme is proposed to drive the system as close as possible to desired fusion power and temperature references. Constraints are considered in the optimization scheme to ensure that, for example, density and beta limits are avoided, and that optimal operation is achieved even when actuators reach saturation. Supported by the NSF CAREER award program (ECCS-0645086).

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

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

International Nuclear Information System (INIS)

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

2014-01-01

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

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.

A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-08-01

Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

Nonlinear acceleration of SN transport calculations

Energy Technology Data Exchange (ETDEWEB)

Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

2010-12-20

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

Science.gov (United States)

Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati

2016-10-01

The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

Milestones in the Development of Iterative Solution Methods

Directory of Open Access Journals (Sweden)

Owe Axelsson

2010-01-01

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

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

Science.gov (United States)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

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...

An iterative method for the canard explosion in general planar systems

DEFF Research Database (Denmark)

Brøns, Morten

2013-01-01

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

A linear iterative unfolding method

International Nuclear Information System (INIS)

László, András

2012-01-01

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

Generalized multiscale finite element methods. nonlinear elliptic equations

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

2013-01-01

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

Decentralized Gauss-Newton method for nonlinear least squares on wide area network

Science.gov (United States)

Liu, Lanchao; Ling, Qing; Han, Zhu

2014-10-01

This paper presents a decentralized approach of Gauss-Newton (GN) method for nonlinear least squares (NLLS) on wide area network (WAN). In a multi-agent system, a centralized GN for NLLS requires the global GN Hessian matrix available at a central computing unit, which may incur large communication overhead. In the proposed decentralized alternative, each agent only needs local GN Hessian matrix to update iterates with the cooperation of neighbors. The detail formulation of decentralized NLLS on WAN is given, and the iteration at each agent is defined. The convergence property of the decentralized approach is analyzed, and numerical results validate the effectiveness of the proposed algorithm.

On iterative solution of nonlinear functional equations in a metric space

Directory of Open Access Journals (Sweden)

Rabindranath Sen

1983-01-01

Full Text Available Given that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where u∈R, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,…. We use Kannan's criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu=Pmu, where u∈R, n and m positive integers, are also treated.

Open-closed-loop iterative learning control for a class of nonlinear systems with random data dropouts

Science.gov (United States)

Cheng, X. Y.; Wang, H. B.; Jia, Y. L.; Dong, YH

2018-05-01

In this paper, an open-closed-loop iterative learning control (ILC) algorithm is constructed for a class of nonlinear systems subjecting to random data dropouts. The ILC algorithm is implemented by a networked control system (NCS), where only the off-line data is transmitted by network while the real-time data is delivered in the point-to-point way. Thus, there are two controllers rather than one in the control system, which makes better use of the saved and current information and thereby improves the performance achieved by open-loop control alone. During the transfer of off-line data between the nonlinear plant and the remote controller data dropout occurs randomly and the data dropout rate is modeled as a binary Bernoulli random variable. Both measurement and control data dropouts are taken into consideration simultaneously. The convergence criterion is derived based on rigorous analysis. Finally, the simulation results verify the effectiveness of the proposed method.

Iterative solution of nonlinear equations with strongly accretive operators

International Nuclear Information System (INIS)

Chidume, C.E.

1991-10-01

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Suppose T:K→K is a strongly accretive map such that for each f is an element of K the equation Tx=f has a solution in K. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly to a solution of the equation Tx=f. Furthermore, our method shows that such a solution is necessarily unique. Explicit error estimates are given. Our results resolve in the affirmative two open problems (J. Math. Anal. Appl. Vol 151(2) (1990), p. 460) and generalize important known results. (author). 32 refs

Non-linear iterative strategy for nem refinement and extension

International Nuclear Information System (INIS)

Engrand, P.R.; Maldonado, G.I.; Al-Chalabi, R.; Turinsky, P.J.

1994-10-01

The following work is related to the non-linear iterative strategy developed by K. Smith to solve the Nodal Expansion Method (NEM) representation of the neutron diffusion equations. We show how to improve this strategy and how to adapt it to time dependant problems. This work has been done in the NESTLE code, developed at North Carolina State University. When using Smith's strategy, one ends up with a two-node problem which corresponds to a matrix with a fixed structure and a size of 16 x 16 (for a 2 group representation). We show how to reduce this matrix into 2 equivalent systems which sizes are 4 x 4 and 8 x 8. The whole problem needs many of these 2 node problems solution. Therefore the gain in CPU time reaches 45% in the nodal part of the code. To adapt Smith's strategy to time dependent problems, the idea is to get the same structure of the 2 node problem system as in steady-state calculation. To achieve this, one has to approximate the values of the past time-step and of the previous by a second order polynomial and to treat it as a source term. We show here how to make this approximation consistent and accurate. (authors). 1 tab., 2 refs

Nonlinear acceleration of S_n transport calculations

International Nuclear Information System (INIS)

Fichtl, Erin D.; Warsa, James S.; Calef, Matthew T.

2011-01-01

The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we employ a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application. (author)

Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.

Science.gov (United States)

Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.

1997-08-01

A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.

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.

Multicore Performance of Block Algebraic Iterative Reconstruction Methods

DEFF Research Database (Denmark)

Sørensen, Hans Henrik B.; Hansen, Per Christian

2014-01-01

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

A New Iteration Multivariate Pad e´ Approximation Technique for ...

African Journals Online (AJOL)

In this paper, the Laplace transform, the New iteration method and the Multivariate Pade´ approximation technique are employed to solve nonlinear fractional partial differential equations whose fractional derivatives are described in the sense of Caputo. The Laplace transform is used to ”fully” determine the initial iteration ...

Non-linear analysis of skew thin plate by finite difference method

International Nuclear Information System (INIS)

Kim, Chi Kyung; Hwang, Myung Hwan

2012-01-01

This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed

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.

A semi-analytical iterative technique for solving chemistry problems

Directory of Open Access Journals (Sweden)

Majeed Ahmed AL-Jawary

2017-07-01

Full Text Available The main aim and contribution of the current paper is to implement a semi-analytical iterative method suggested by Temimi and Ansari in 2011 namely (TAM to solve two chemical problems. An approximate solution obtained by the TAM provides fast convergence. The current chemical problems are the absorption of carbon dioxide into phenyl glycidyl ether and the other system is a chemical kinetics problem. These problems are represented by systems of nonlinear ordinary differential equations that contain boundary conditions and initial conditions. Error analysis of the approximate solutions is studied using the error remainder and the maximal error remainder. Exponential rate for the convergence is observed. For both problems the results of the TAM are compared with other results obtained by previous methods available in the literature. The results demonstrate that the method has many merits such as being derivative-free, and overcoming the difficulty arising in calculating Adomian polynomials to handle the non-linear terms in Adomian Decomposition Method (ADM. It does not require to calculate Lagrange multiplier in Variational Iteration Method (VIM in which the terms of the sequence become complex after several iterations, thus, analytical evaluation of terms becomes very difficult or impossible in VIM. No need to construct a homotopy in Homotopy Perturbation Method (HPM and solve the corresponding algebraic equations. The MATHEMATICA® 9 software was used to evaluate terms in the iterative process.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

Science.gov (United States)

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

A MODIFIED DECOMPOSITION METHOD FOR SOLVING NONLINEAR PROBLEM OF FLOW IN CONVERGING- DIVERGING CHANNEL

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MOHAMED KEZZAR

2015-08-01

Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.

APPLICATION OF FINITE ELEMENT METHOD TAKING INTO ACCOUNT PHYSICAL AND GEOMETRIC NONLINEARITY FOR THE CALCULATION OF PRESTRESSED REINFORCED CONCRETE BEAMS

Directory of Open Access Journals (Sweden)

Vladimir P. Agapov

2017-01-01

Full Text Available Abstract. Objectives Modern building codes prescribe the calculation of building structures taking into account the nonlinearity of deformation. To achieve this goal, the task is to develop a methodology for calculating prestressed reinforced concrete beams, taking into account physical and geometric nonlinearity. Methods The methodology is based on nonlinear calculation algorithms implemented and tested in the computation complex PRINS (a program for calculating engineering constructions for other types of construction. As a tool for solving this problem, the finite element method is used. Non-linear calculation of constructions is carried out by the PRINS computational complex using the stepwise iterative method. In this case, an equation is constructed and solved at the loading step, using modified Lagrangian coordinates. Results The basic formulas necessary for both the formation and the solution of a system of nonlinear algebraic equations by the stepwise iteration method are given, taking into account the loading, unloading and possible additional loading. A method for simulating prestressing is described by setting the temperature action on the reinforcement and stressing steel rod. Different approaches to accounting for physical and geometric nonlinearity of reinforced concrete beam rods are considered. A calculation example of a flat beam is given, in which the behaviour of the beam is analysed at various stages of its loading up to destruction. Conclusion A program is developed for the calculation of flat and spatially reinforced concrete beams taking into account the nonlinearity of deformation. The program is adapted to the computational complex PRINS and as part of this complex is available to a wide range of engineering, scientific and technical specialists. 

Information operator approach and iterative regularization methods for atmospheric remote sensing

International Nuclear Information System (INIS)

Doicu, A.; Hilgers, S.; Bargen, A. von; Rozanov, A.; Eichmann, K.-U.; Savigny, C. von; Burrows, J.P.

2007-01-01

In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO 2 retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen

A combined modification of Newton`s method for systems of nonlinear equations

Energy Technology Data Exchange (ETDEWEB)

Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)

1996-12-31

To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.

Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

Energy Technology Data Exchange (ETDEWEB)

Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

2006-09-28

A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

Combined algorithms in nonlinear problems of magnetostatics

International Nuclear Information System (INIS)

Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

1988-01-01

To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

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.

Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

NARCIS (Netherlands)

Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

Regularized iterative integration combined with non-linear diffusion filtering for phase-contrast x-ray computed tomography.

Science.gov (United States)

Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter

2014-12-29

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

Nonlinear wave equations

CERN Document Server

Li, Tatsien

2017-01-01

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

Leapfrog variants of iterative methods for linear algebra equations

Science.gov (United States)

Saylor, Paul E.

1988-01-01

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

The nonlinear response of the complex structural system in nuclear reactors using dynamic substructure method

International Nuclear Information System (INIS)

Zheng, Z.C.; Xie, G.; Du, Q.H.

1987-01-01

Because of the existence of nonlinear characteristics in practical engineering structures, such as large steam turbine-foundation system and offshore platform, it is necessary to predict nonlinear dynamic responses for these very large and complex structural systems subjected extreme load. Due to the limited storage and high executing cost of computers, there are still some difficulties in the analysis for such systems although the traditional finite element methods provide basic available methods to the problems. The dynamic substructure methods, which were developed as a branch of general structural dynamics in the past more than 20 years and have been widely used from aircraft, space vehicles to other mechanical and civil engineering structures, present a powerful method to the analysis of very large structural systems. The key to success is due to the considerable reduction in the number of degrees of freedom while not changing the physical essence of the problems investigated. The dynamic substructure method has been extended to nonlinear system and applicated to the analysis of nonlinear dynamic response of an offshore platform by Z.C. Zheng, et al. (1983, 1985a, b, c). In this paper, the method is presented to analyze dynamic responses of the systems contained intrinsic nonlinearities and with nonlinear attachments and nonlinear supports of nuclear structural systems. The efficiency of the method becomes more clear for nonlinear dynamic problems due to the adoption of iterating processes. For simplicity, the analysis procedure is demonstrated briefly. The generalized substructure method of nonlinear systems is similar to linear systems, only the nonlinear terms are treated as pseudo-forces. Interface coordinates are classified into two categories, the connecting interface coordinates which connect with each other directly in the global system and the linking interface coordinates which link to each other through attachments. (orig./GL)

Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices

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Alicia Cordero

2018-01-01

Full Text Available We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order 15.5156 and a very high efficiency index 15.51561/4≈1.9847. Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.

Iteration of ultrasound aberration correction methods

Science.gov (United States)

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

2004-05-01

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

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

Science.gov (United States)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

An Iterative Brinkman penalization for particle vortex methods

DEFF Research Database (Denmark)

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

2013-01-01

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

Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

International Nuclear Information System (INIS)

Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

2008-01-01

He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

Directory of Open Access Journals (Sweden)

Qianqian Tong

2017-12-01

Full Text Available The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young’s modulus and Poisson’s ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg–Marquardt (LM algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

DEFF Research Database (Denmark)

Hansen, Per Christian; Saxild-Hansen, Maria

2012-01-01

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

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

International Nuclear Information System (INIS)

Mukoyama, T.; Vegh, J.

1980-01-01

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

A comparison theorem for the SOR iterative method

Science.gov (United States)

Sun, Li-Ying

2005-09-01

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

A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded

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

DEFF Research Database (Denmark)

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

2011-01-01

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

The danger of iteration methods

International Nuclear Information System (INIS)

Villain, J.; Semeria, B.

1983-01-01

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

AIR Tools II: algebraic iterative reconstruction methods, improved implementation

DEFF Research Database (Denmark)

Hansen, Per Christian; Jørgensen, Jakob Sauer

2017-01-01

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

A transport synthetic acceleration method for transport iterations

International Nuclear Information System (INIS)

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

1997-01-01

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

Iterative solution of the semiconductor device equations

Energy Technology Data Exchange (ETDEWEB)

Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)

1996-12-31

Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

Iterative method for Amado's model

International Nuclear Information System (INIS)

Tomio, L.

1980-01-01

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

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Directory of Open Access Journals (Sweden)

Xiaobing Kong

2013-01-01

Full Text Available Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR demonstrate the effectiveness of the proposed method.

A Modal-Based Substructure Method Applied to Nonlinear Rotordynamic Systems

Directory of Open Access Journals (Sweden)

Helmut J. Holl

2009-01-01

Full Text Available The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.

Application of nonlinear Krylov acceleration to radiative transfer problems

International Nuclear Information System (INIS)

Till, A. T.; Adams, M. L.; Morel, J. E.

2013-01-01

The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)

Iterative Reconstruction Methods for Inverse Problems in Tomography with Hybrid Data

DEFF Research Database (Denmark)

Sherina, Ekaterina

. The goal of these modalities is to quantify physical parameters of materials or tissues inside an object from given interior data, which is measured everywhere inside the object. The advantage of these modalities is that large variations in physical parameters can be resolved and therefore, they have...... data is precisely the reason why reconstructions with a high contrast and a high resolution can be expected. The main contributions of this thesis consist in formulating the underlying mathematical problems with interior data as nonlinear operator equations, theoretically analysing them within...... iteration and the Levenberg-Marquardt method are employed for solving the problems. The first problem considered in this thesis is a problem of conductivity estimation from interior measurements of the power density, known as Acousto-Electrical Tomography. A special case of limited angle tomography...

Power system state estimation using an iteratively reweighted least squares method for sequential L{sub 1}-regression

Energy Technology Data Exchange (ETDEWEB)

Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)

2006-02-15

This paper presents an implementation of the least absolute value (LAV) power system state estimator based on obtaining a sequence of solutions to the L{sub 1}-regression problem using an iteratively reweighted least squares (IRLS{sub L1}) method. The proposed implementation avoids reformulating the regression problem into standard linear programming (LP) form and consequently does not require the use of common methods of LP, such as those based on the simplex method or interior-point methods. It is shown that the IRLS{sub L1} method is equivalent to solving a sequence of linear weighted least squares (LS) problems. Thus, its implementation presents little additional effort since the sparse LS solver is common to existing LS state estimators. Studies on the termination criteria of the IRLS{sub L1} method have been carried out to determine a procedure for which the proposed estimator is more computationally efficient than a previously proposed non-linear iteratively reweighted least squares (IRLS) estimator. Indeed, it is revealed that the proposed method is a generalization of the previously reported IRLS estimator, but is based on more rigorous theory. (author)

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

Science.gov (United States)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

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

Directory of Open Access Journals (Sweden)

Mahmoud Bayat

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

Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

Science.gov (United States)

Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

2018-02-01

Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

Nonlinear Least Square Based on Control Direction by Dual Method and Its Application

Directory of Open Access Journals (Sweden)

Zhengqing Fu

2016-01-01

Full Text Available A direction controlled nonlinear least square (NLS estimation algorithm using the primal-dual method is proposed. The least square model is transformed into the primal-dual model; then direction of iteration can be controlled by duality. The iterative algorithm is designed. The Hilbert morbid matrix is processed by the new model and the least square estimate and ridge estimate. The main research method is to combine qualitative analysis and quantitative analysis. The deviation between estimated values and the true value and the estimated residuals fluctuation of different methods are used for qualitative analysis. The root mean square error (RMSE is used for quantitative analysis. The results of experiment show that the model has the smallest residual error and the minimum root mean square error. The new estimate model has effectiveness and high precision. The genuine data of Jining area in unwrapping experiments are used and the comparison with other classical unwrapping algorithms is made, so better results in precision aspects can be achieved through the proposed algorithm.

Stopping test of iterative methods for solving PDE

International Nuclear Information System (INIS)

Wang Bangrong

1991-01-01

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

A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis

Science.gov (United States)

Landi, G.; Loli Piccolomini, E.; Nagy, J. G.

2017-09-01

Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.

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

Czech Academy of Sciences Publication Activity Database

Morikuni, Keiichi; Hayami, K.

2015-01-01

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

Iterative approach as alternative to S-matrix in modal methods

Science.gov (United States)

Semenikhin, Igor; Zanuccoli, Mauro

2014-12-01

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

Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

Directory of Open Access Journals (Sweden)

Huan Ma

2015-01-01

Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations

KAUST Repository

Giraldi, Loic; Nouy, Anthony

2017-01-01

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.

Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations

KAUST Repository

Giraldi, Loic

2017-06-30

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.

Properties of a class of block-iterative methods

International Nuclear Information System (INIS)

Elfving, Tommy; Nikazad, Touraj

2009-01-01

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

An iterative fast sweeping based eikonal solver for tilted orthorhombic media

KAUST Repository

Waheed, Umair bin

2014-08-01

Computing first-arrival traveltimes of quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, and requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects of the higher order nonlinear terms. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an algorithm for first-arrival traveltime computations in tilted anisotropic media. We demonstrate our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests demonstrate that the proposed method can match the first arrivals obtained by wavefield extrapolation, even for strong anisotropy and complex structures. Therefore, for the cases where oneor two-point ray tracing fails, our method may be a potential substitute for computing traveltimes. Our approach can be extended to anisotropic media with lower symmetries, such as monoclinic or even triclinic media.

An iterative fast sweeping based eikonal solver for tilted orthorhombic media

KAUST Repository

Waheed, Umair bin; Yarman, Can Evren; Flagg, Garret

2014-01-01

Computing first-arrival traveltimes of quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, and requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects of the higher order nonlinear terms. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an algorithm for first-arrival traveltime computations in tilted anisotropic media. We demonstrate our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests demonstrate that the proposed method can match the first arrivals obtained by wavefield extrapolation, even for strong anisotropy and complex structures. Therefore, for the cases where oneor two-point ray tracing fails, our method may be a potential substitute for computing traveltimes. Our approach can be extended to anisotropic media with lower symmetries, such as monoclinic or even triclinic media.

Copper Mountain conference on iterative methods: Proceedings: Volume 2

Energy Technology Data Exchange (ETDEWEB)

NONE

1996-10-01

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

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

Science.gov (United States)

Debussche, A.; Dubois, T.; Temam, R.

1993-01-01

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

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

OpenAIRE

Manton, Jonathan H.

2012-01-01

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

An iterative reconstruction from truncated projection data

International Nuclear Information System (INIS)

Anon.

1985-01-01

Various methods have been proposed for tomographic reconstruction from truncated projection data. In this paper, a reconstructive method is discussed which consists of iterations of filtered back-projection, reprojection and some nonlinear processings. First, the method is so constructed that it converges to a fixed point. Then, to examine its effectiveness, comparisons are made by computer experiments with two existing reconstructive methods for truncated projection data, that is, the method of extrapolation based on the smooth assumption followed by filtered back-projection, and modified additive ART

Regarding overrelaxation for accelerating an iteration process

International Nuclear Information System (INIS)

Vondy, D.R.

1984-06-01

The solution for a vector that satisfies a set of coupled equations is often obtained economically in iteration. Application of an overrelaxation coefficient to augment the calculated iterate changes is done to accelerate the rate of convergence. This scheme is simple to implement and often effective. Much is known theoretically about the iterative behavior when the system of equations is linear, although there are complexities that are not widely known. Extensive use is made of the scheme even to non-linear systems of equations where behavior depends on the situation. Of much concern to the developer of solution methods (typically an engineer or applied mathematician) is implementing an effective procedure at a modest investment in development and testing. Applications are described to thermal cell and neutron diffusion modeling

Multisplitting for linear, least squares and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Renaut, R.

1996-12-31

In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.

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

Science.gov (United States)

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

2017-07-01

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

Parameter Estimation of Nonlinear Models in Forestry.

OpenAIRE

Fekedulegn, Desta; Mac Siúrtáin, Máirtín Pádraig; Colbert, Jim J.

1999-01-01

Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinnin...

Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

International Nuclear Information System (INIS)

Cook, W.A.

1978-10-01

Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

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.

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

Indian Academy of Sciences (India)

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

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin

2010-10-28

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

KAUST Repository

Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel

2010-01-01

A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.

KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

International Nuclear Information System (INIS)

Westley, G.W.

1975-01-01

1 - Description of problem or function: KEELE is a linearly constrained nonlinear programming algorithm for locating a local minimum of a function of n variables with the variables subject to linear equality and/or inequality constraints. 2 - Method of solution: A variable metric procedure is used where the direction of search at each iteration is obtained by multiplying the negative of the gradient vector by a positive definite matrix which approximates the inverse of the matrix of second partial derivatives associated with the function. 3 - Restrictions on the complexity of the problem: Array dimensions limit the number of variables to 20 and the number of constraints to 50. These can be changed by the user

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

Directory of Open Access Journals (Sweden)

Marinca Vasile

2017-10-01

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

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

Science.gov (United States)

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

2017-10-01

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

Multiparameter extrapolation and deflation methods for solving equation systems

Directory of Open Access Journals (Sweden)

A. J. Hughes Hallett

1984-01-01

Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

Science.gov (United States)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

The use of iteration factors in the solution of the NLTE line transfer problem-II. Multilevel atom

International Nuclear Information System (INIS)

Kuzmanovska-Barandovska, O.; Atanackovic, O.

2010-01-01

The iteration factors method (IFM) developed in Paper I (Atanackovic-Vukmanovic and Simonneau, 1994) to solve the NLTE line transfer problem for a two-level atom model, is extended here to deal with a multilevel atom case. At the beginning of each iteration step, for each line transition, angle and frequency averaged depth-dependent iteration factors are computed from the formal solution of radiative transfer (RT) equation and used to close the system of the RT equation moments, non-linearly coupled with the statistical equilibrium (SE) equations. Non-linear coupling of the atomic level populations and the corresponding line radiation field intensities is tackled in two ways. One is based on the linearization of the equations with respect to the relevant variables, and the other on the use of the old (known from the previous iteration) level populations in the line-opacity-like terms of the SE equations. In both cases the use of quasi-invariant iteration factors provided very fast and accurate solution. The properties of the proposed procedures are investigated in detail by applying them to the solution of the prototype multilevel RT problem of Avrett and Loeser , and compared with the properties of some other methods.

Post-convergence automatic differentiation of iterative schemes

International Nuclear Information System (INIS)

Azmy, Y.Y.

1997-01-01

A new approach for performing automatic differentiation (AD) of computer codes that embody an iterative procedure, based on differentiating a single additional iteration upon achieving convergence, is described and implemented. This post-convergence automatic differentiation (PAD) technique results in better accuracy of the computed derivatives, as it eliminates part of the derivatives convergence error, and a large reduction in execution time, especially when many iterations are required to achieve convergence. In addition, it provides a way to compute derivatives of the converged solution without having to repeat the entire iterative process every time new parameters are considered. These advantages are demonstrated and the PAD technique is validated via a set of three linear and nonlinear codes used to solve neutron transport and fluid flow problems. The PAD technique reduces the execution time over direct AD by a factor of up to 30 and improves the accuracy of the derivatives by up to two orders of magnitude. The PAD technique's biggest disadvantage lies in the necessity to compute the iterative map's Jacobian, which for large problems can be prohibitive. Methods are discussed to alleviate this difficulty

Implicit solvers for large-scale nonlinear problems

International Nuclear Information System (INIS)

Keyes, David E; Reynolds, Daniel R; Woodward, Carol S

2006-01-01

Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications

LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

International Nuclear Information System (INIS)

Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

2015-01-01

This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

OpenAIRE

De Sterck, Hans

2011-01-01

A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...

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

International Nuclear Information System (INIS)

McCormick, Stephen F.

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-03-25

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

A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from M/G/1-Type Markov Chains

Directory of Open Access Journals (Sweden)

Pei-Chang Guo

2017-01-01

Full Text Available For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution G or R can be found by Newton-like methods. We prove monotone convergence results for the Newton-Shamanskii iteration for this class of equations. Starting with zero initial guess or some other suitable initial guess, the Newton-Shamanskii iteration provides a monotonically increasing sequence of nonnegative matrices converging to the minimal nonnegative solution. A Schur decomposition method is used to accelerate the Newton-Shamanskii iteration. Numerical examples illustrate the effectiveness of the Newton-Shamanskii iteration.

Accuracy improvement of a hybrid robot for ITER application using POE modeling method

International Nuclear Information System (INIS)

Wang, Yongbo; Wu, Huapeng; Handroos, Heikki

2013-01-01

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.

System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time

DEFF Research Database (Denmark)

Sun, Zhen; Yang, Zhenyu

2011-01-01

An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent....

On a method of numerical calculation of nonlinear radial pulsations of stars

International Nuclear Information System (INIS)

Kosovichev, A.G.

1984-01-01

Some features of using the finite difference method for numerical investigation of nonradial pulsations of stars were considered. The mathematical model of these pulsations is described by time-dependent gasdynaMic equations with gravity. A one-dimentional (spherically-symmetric) case is considered. It was obtained a two-parametric family of ultimate conservative difference schemes where the diffepence analogy of the main conservative laws as well as the additional relations for the balance to individual kinds of energy are performed. Such difference schemes provide more exact calculation of nonlinear flows with shocks as compared with the other difference schemes with the same order of approximation. The methods of numerical solution of implicit (absolute stable) difference schemes for a given family were considered. The coupled equations are solved through iterative Newton method Using martrix and separate successive eliminations. Numerical method can be used for calculation of large amplitude radial pulsations of stars

An iterative hyperelastic parameters reconstruction for breast cancer assessment

Science.gov (United States)

Mehrabian, Hatef; Samani, Abbas

2008-03-01

In breast elastography, breast tissues usually undergo large compressions resulting in significant geometric and structural changes, and consequently nonlinear mechanical behavior. In this study, an elastography technique is presented where parameters characterizing tissue nonlinear behavior is reconstructed. Such parameters can be used for tumor tissue classification. To model the nonlinear behavior, tissues are treated as hyperelastic materials. The proposed technique uses a constrained iterative inversion method to reconstruct the tissue hyperelastic parameters. The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. To mimic the breast geometry, we used a computational phantom, which comprises of a hemisphere connected to a cylinder. This phantom consists of two types of soft tissue to mimic adipose and fibroglandular tissues and a tumor. Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue.

Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

Directory of Open Access Journals (Sweden)

Nauman Raza

2016-01-01

Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

Ranking scientific publications: the effect of nonlinearity

Science.gov (United States)

Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; di, Zengru

2014-10-01

Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

Ranking scientific publications: the effect of nonlinearity.

Science.gov (United States)

Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; Di, Zengru

2014-10-17

Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

Maintaining the stability of nonlinear differential equations by the enhancement of HPM

International Nuclear Information System (INIS)

Hosein Nia, S.H.; Ranjbar, A.N.; Ganji, D.D.; Soltani, H.; Ghasemi, J.

2008-01-01

Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained. In this Letter, the need for stability verification is shown through some examples. Consequently, HPM is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic, even the selected linear part is not

Epsilon topological accelerating algorithms for difference method for initial-value problems

International Nuclear Information System (INIS)

Hristea, V.; Posirca, M.

1992-01-01

Linear and nonlinear parabolic equations can be solved by discretization methods which lead to linear and nonlinear algebraic systems. The iterative methods (e.g. Gauss - Seidel) show a very slow convergence and instability in the case of nonlinear equations. This paper proposes an ε topological algorithm for accelerating slow iterative methods used in the thermohydraulic code COBRA and the dynamic code ADEP. The results show an executing time approximately ten times lower than original algorithms. (Author)

Strength Reduction Method for Stability Analysis of Local Discontinuous Rock Mass with Iterative Method of Partitioned Finite Element and Interface Boundary Element

Directory of Open Access Journals (Sweden)

Tongchun Li

2015-01-01

element is proposed to solve the safety factor of local discontinuous rock mass. Slope system is divided into several continuous bodies and local discontinuous interface boundaries. Each block is treated as a partition of the system and contacted by discontinuous joints. The displacements of blocks are chosen as basic variables and the rigid displacements in the centroid of blocks are chosen as motion variables. The contact forces on interface boundaries and the rigid displacements to the centroid of each body are chosen as mixed variables and solved iteratively using the interface boundary equations. Flexibility matrix is formed through PFE according to the contact states of nodal pairs and spring flexibility is used to reflect the influence of weak structural plane so that nonlinear iteration is only limited to the possible contact region. With cohesion and friction coefficient reduced gradually, the states of all nodal pairs at the open or slip state for the first time are regarded as failure criterion, which can decrease the effect of subjectivity in determining safety factor. Examples are used to verify the validity of the proposed method.

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

Science.gov (United States)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

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

Iterative Regularization with Minimum-Residual Methods

DEFF Research Database (Denmark)

Jensen, Toke Koldborg; Hansen, Per Christian

2007-01-01

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

Iterative regularization with minimum-residual methods

DEFF Research Database (Denmark)

Jensen, Toke Koldborg; Hansen, Per Christian

2006-01-01

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

Mixed error compensation in a heterodyne interferometer using the iterated dual-EKF algorithm

International Nuclear Information System (INIS)

Lee, Woo Ram; Kim, Chang Rai; You, Kwan Ho

2010-01-01

The heterodyne laser interferometer has been widely used in the field of precise measurements. The limited measurement accuracy of a heterodyne laser interferometer arises from the periodic nonlinearity caused by non-ideal laser sources and imperfect optical components. In this paper, the iterated dual-EKF algorithm is used to compensate for the error caused by nonlinearity and external noise. With the iterated dual-EKF algorithm, the weight filter estimates the parameter uncertainties in the state equation caused by nonlinearity errors and has a high convergence rate of weight values due to the iteration process. To verify the performance of the proposed compensation algorithm, we present experimental results obtained by using the iterated dual-EKF algorithm and compare them with the results obtained by using a capacitance displacement sensor.

Mixed error compensation in a heterodyne interferometer using the iterated dual-EKF algorithm

Energy Technology Data Exchange (ETDEWEB)

Lee, Woo Ram; Kim, Chang Rai; You, Kwan Ho [Sungkyunkwan University, Suwon (Korea, Republic of)

2010-10-15

The heterodyne laser interferometer has been widely used in the field of precise measurements. The limited measurement accuracy of a heterodyne laser interferometer arises from the periodic nonlinearity caused by non-ideal laser sources and imperfect optical components. In this paper, the iterated dual-EKF algorithm is used to compensate for the error caused by nonlinearity and external noise. With the iterated dual-EKF algorithm, the weight filter estimates the parameter uncertainties in the state equation caused by nonlinearity errors and has a high convergence rate of weight values due to the iteration process. To verify the performance of the proposed compensation algorithm, we present experimental results obtained by using the iterated dual-EKF algorithm and compare them with the results obtained by using a capacitance displacement sensor.

Preconditioning of iterative methods - theory and applications

Czech Academy of Sciences Publication Activity Database

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

2015-01-01

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

Advances in dynamic relaxation techniques for nonlinear finite element analysis

International Nuclear Information System (INIS)

Sauve, R.G.; Metzger, D.R.

1995-01-01

Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

Nonlinear analysis of composite thin-walled helicopter blades

Science.gov (United States)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

KAUST Repository

Waheed, Umair bin; Yarman, Can Evren; Flagg, Garret

2015-01-01

Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken's extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.

An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

KAUST Repository

Waheed, Umair bin

2015-03-30

Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken\\'s extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.

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.

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

Directory of Open Access Journals (Sweden)

Oskar Cahueñas

2013-05-01

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

On varitional iteration method for fractional calculus

Directory of Open Access Journals (Sweden)

Wu Hai-Gen

2017-01-01

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

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Root-finding

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Petzold, L.R.

2005-01-01

1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user

Successive Over Relaxation Method Which Uses Matrix Norms for ...

African Journals Online (AJOL)

An algorithm for S.O.R functional iteration which uses matrix norms for the Jacobi iteration matrices rather than the usual Power method, feasible in Newton Operator for the solution of nonlinear system of equations is proposed. We modified the S.O.R. iterative method known as Multiphase S.O.R. method for Newton ...

On iteration-separable method on the multichannel scattering theory

International Nuclear Information System (INIS)

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

1975-01-01

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

Numerov iteration method for second order integral-differential equation

International Nuclear Information System (INIS)

Zeng Fanan; Zhang Jiaju; Zhao Xuan

1987-01-01

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

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

Science.gov (United States)

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

2007-09-01

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

Discounted Markov games : generalized policy iteration method

NARCIS (Netherlands)

Wal, van der J.

1978-01-01

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

Optimized iterative decoding method for TPC coded CPM

Science.gov (United States)

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

2018-05-01

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

AZTEC: A parallel iterative package for the solving linear systems

Energy Technology Data Exchange (ETDEWEB)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)

1996-12-31

We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

An iterative method for determination of a minimal eigenvalue

DEFF Research Database (Denmark)

Kristiansen, G.K.

1968-01-01

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

Iterative solution of linear equations in ODE codes. [Krylov subspaces

Energy Technology Data Exchange (ETDEWEB)

Gear, C. W.; Saad, Y.

1981-01-01

Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

DEFF Research Database (Denmark)

Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...

The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

Science.gov (United States)

Chen, Bochao; Li, Yong; Gao, Yixian

2018-05-01

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems

DEFF Research Database (Denmark)

Bayat, M.; Shahidi, M.; Barari, Amin

2011-01-01

approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...

Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.

Science.gov (United States)

Xie, Xianming

2016-08-22

A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

Science.gov (United States)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Efficacy of variational iteration method for chaotic Genesio system - Classical and multistage approach

International Nuclear Information System (INIS)

Goh, S.M.; Noorani, M.S.M.; Hashim, I.

2009-01-01

This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.

Comparison of some nonlinear smoothing methods

International Nuclear Information System (INIS)

Bell, P.R.; Dillon, R.S.

1977-01-01

Due to the poor quality of many nuclear medicine images, computer-driven smoothing procedures are frequently employed to enhance the diagnostic utility of these images. While linear methods were first tried, it was discovered that nonlinear techniques produced superior smoothing with little detail suppression. We have compared four methods: Gaussian smoothing (linear), two-dimensional least-squares smoothing (linear), two-dimensional least-squares bounding (nonlinear), and two-dimensional median smoothing (nonlinear). The two dimensional least-squares procedures have yielded the most satisfactorily enhanced images, with the median smoothers providing quite good images, even in the presence of widely aberrant points

Nonlinear Krylov acceleration of reacting flow codes

Energy Technology Data Exchange (ETDEWEB)

Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)

1996-12-31

We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.

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

Directory of Open Access Journals (Sweden)

Yuan Li

2013-01-01

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

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

International Nuclear Information System (INIS)

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

2009-01-01

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

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

Directory of Open Access Journals (Sweden)

Humin Lei

2017-01-01

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

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

Institute of Scientific and Technical Information of China (English)

朱卫平; 黄黔

2002-01-01

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.

Variable aperture-based ptychographical iterative engine method

Science.gov (United States)

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

2018-02-01

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

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

Science.gov (United States)

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

2018-01-01

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

Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media

KAUST Repository

Efendiev, Y.; Galvis, J.; Kang, S. Ki; Lazarov, R.D.

2012-01-01

needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer

Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

DEFF Research Database (Denmark)

Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas

2018-01-01

. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....

Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery

Directory of Open Access Journals (Sweden)

Lingjun Liu

2017-01-01

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

Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Admissibility and Termination Analysis.

Science.gov (United States)

Wei, Qinglai; Liu, Derong; Lin, Qiao

In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.

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

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

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

Iterated interactions method. Realistic NN potential

International Nuclear Information System (INIS)

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

1991-01-01

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

Iterative learning control with sampled-data feedback for robot manipulators

Directory of Open Access Journals (Sweden)

Delchev Kamen

2014-09-01

Full Text Available This paper deals with the improvement of the stability of sampled-data (SD feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more, while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached

An Automated Baseline Correction Method Based on Iterative Morphological Operations.

Science.gov (United States)

Chen, Yunliang; Dai, Liankui

2018-05-01

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

Three dimensional iterative beam propagation method for optical waveguide devices

Science.gov (United States)

Ma, Changbao; Van Keuren, Edward

2006-10-01

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

Nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

Nonlinear differential equations

International Nuclear Information System (INIS)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

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.

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-15

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

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

Science.gov (United States)

Sun, Shu-Ting; Li, Xiao-Dong; Zhong, Ren-Xin

2017-10-01

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

Variable aperture-based ptychographical iterative engine method.

Science.gov (United States)

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

2018-02-01

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

A Study on the Analysis and Optimal Control of Nonlinear Systems via Walsh Function

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Tae; Kim, Tai Hoon; Ahn, Doo Soo [Sungkyunkwan University (Korea); Lee, Myung Kyu [Kyungsung University (Korea)

2000-07-01

This paper presents the new adaptive optimal scheme for the nonlinear systems, which is based on the Picard's iterative approximation and fast Walsh transform. It is well known that the Walsh function approach method is very difficult to apply for the analysis and optimal control of nonlinear systems. However, these problems can be easily solved by the improvement of the previous adaptive optimal scheme. The proposes method is easily applicable to the analysis and optimal control of nonlinear systems. (author). 15 refs., 6 figs., 1 tab.

A New Iterative Method for Equilibrium Problems and Fixed Point Problems

Directory of Open Access Journals (Sweden)

Abdul Latif

2013-01-01

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

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.

Compressively sampled MR image reconstruction using generalized thresholding iterative algorithm

Science.gov (United States)

Elahi, Sana; kaleem, Muhammad; Omer, Hammad

2018-01-01

Compressed sensing (CS) is an emerging area of interest in Magnetic Resonance Imaging (MRI). CS is used for the reconstruction of the images from a very limited number of samples in k-space. This significantly reduces the MRI data acquisition time. One important requirement for signal recovery in CS is the use of an appropriate non-linear reconstruction algorithm. It is a challenging task to choose a reconstruction algorithm that would accurately reconstruct the MR images from the under-sampled k-space data. Various algorithms have been used to solve the system of non-linear equations for better image quality and reconstruction speed in CS. In the recent past, iterative soft thresholding algorithm (ISTA) has been introduced in CS-MRI. This algorithm directly cancels the incoherent artifacts produced because of the undersampling in k -space. This paper introduces an improved iterative algorithm based on p -thresholding technique for CS-MRI image reconstruction. The use of p -thresholding function promotes sparsity in the image which is a key factor for CS based image reconstruction. The p -thresholding based iterative algorithm is a modification of ISTA, and minimizes non-convex functions. It has been shown that the proposed p -thresholding iterative algorithm can be used effectively to recover fully sampled image from the under-sampled data in MRI. The performance of the proposed method is verified using simulated and actual MRI data taken at St. Mary's Hospital, London. The quality of the reconstructed images is measured in terms of peak signal-to-noise ratio (PSNR), artifact power (AP), and structural similarity index measure (SSIM). The proposed approach shows improved performance when compared to other iterative algorithms based on log thresholding, soft thresholding and hard thresholding techniques at different reduction factors.

Parallel computation of multigroup reactivity coefficient using iterative method

Science.gov (United States)

Susmikanti, Mike; Dewayatna, Winter

2013-09-01

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

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

Energy Technology Data Exchange (ETDEWEB)

Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-01-22

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.

Comments on new iterative methods for solving linear systems

Directory of Open Access Journals (Sweden)

Wang Ke

2017-06-01

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

An ensemble based nonlinear orthogonal matching pursuit algorithm for sparse history matching of reservoir models

KAUST Repository

Fsheikh, Ahmed H.

2013-01-01

A nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of reservoir models is presented. 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 components of the basis functions with the residual. The discovered basis (aka support) is augmented across the nonlinear iterations. Once the basis functions are selected from the dictionary, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on approximate gradient estimation using an iterative stochastic ensemble method (ISEM). ISEM utilizes an ensemble of directional derivatives to efficiently approximate gradients. In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

Science.gov (United States)

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

A Nonmonotone Line Search Filter Algorithm for the System of Nonlinear Equations

Directory of Open Access Journals (Sweden)

Zhong Jin

2012-01-01

Full Text Available We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the sufficient reduction conditions and filter technique which leads to a flexibility and acceptance behavior comparable to monotone methods. The new algorithm is shown to be globally convergent and numerical experiments demonstrate its effectiveness.

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

Bierens, Herman J

1981-01-01

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

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

Science.gov (United States)

Trujillo Bueno, Javier; Manso Sainz, Rafael

1999-05-01

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

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Methods of nonlinear analysis

CERN Document Server

Bellman, Richard Ernest

1970-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

Performance of an iterative two-stage bayesian technique for population pharmacokinetic analysis of rich data sets

NARCIS (Netherlands)

Proost, Johannes H.; Eleveld, Douglas J.

2006-01-01

Purpose. To test the suitability of an Iterative Two-Stage Bayesian (ITSB) technique for population pharmacokinetic analysis of rich data sets, and to compare ITSB with Standard Two-Stage (STS) analysis and nonlinear Mixed Effect Modeling (MEM). Materials and Methods. Data from a clinical study with

A simple nonlinear dynamical computing device

International Nuclear Information System (INIS)

Miliotis, Abraham; Murali, K.; Sinha, Sudeshna; Ditto, William L.; Spano, Mark L.

2009-01-01

We propose and characterize an iterated map whose nonlinearity has a simple (i.e., minimal) electronic implementation. We then demonstrate explicitly how all the different fundamental logic gates can be implemented and morphed using this nonlinearity. These gates provide the full set of gates necessary to construct a general-purpose, reconfigurable computing device. As an example of how such chaotic computing devices can be exploited, we use an array of these maps to encode data and to process information. Each map can store one of M items, where M is variable and can be large. This nonlinear hardware stores data naturally in different bases or alphabets. We also show how this method of storing information can serve as a preprocessing tool for exact or inexact pattern-matching searches.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

Science.gov (United States)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Iterative reconstruction methods for Thermo-acoustic Tomography

International Nuclear Information System (INIS)

Marinesque, Sebastien

2012-01-01

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

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

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2014-01-01

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

Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods

DEFF Research Database (Denmark)

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

2010-01-01

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

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

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2012-01-01

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

Polynomic nonlinear dynamical systems - A residual sensitivity method for model reduction

Science.gov (United States)

Yurkovich, S.; Bugajski, D.; Sain, M.

1985-01-01

The motivation for using polynomic combinations of system states and inputs to model nonlinear dynamics systems is founded upon the classical theories of analysis and function representation. A feature of such representations is the need to make available all possible monomials in these variables, up to the degree specified, so as to provide for the description of widely varying functions within a broad class. For a particular application, however, certain monomials may be quite superfluous. This paper examines the possibility of removing monomials from the model in accordance with the level of sensitivity displayed by the residuals to their absence. Critical in these studies is the effect of system input excitation, and the effect of discarding monomial terms, upon the model parameter set. Therefore, model reduction is approached iteratively, with inputs redesigned at each iteration to ensure sufficient excitation of remaining monomials for parameter approximation. Examples are reported to illustrate the performance of such model reduction approaches.

Development of new multigrid schemes for the method of characteristics in neutron transport theory

International Nuclear Information System (INIS)

Grassi, G.

2006-01-01

This dissertation is based upon our doctoral research that dealt with the conception and development of new non-linear multigrid techniques for the Method of the Characteristics (MOC) within the TDT code. Here we focus upon a two-level scheme consisting of a fine level on which the neutron transport equation is iteratively solved using the MOC algorithm, and a coarse level defined by a more coarsely discretized phase space on which a low-order problem is considered. The solution of this problem is then used in order to correct the angular flux moments resulting from the previous transport iteration. A flux-volume homogenization procedure is employed to evaluate the coarse-level material properties after each transport iteration. This entails the non-linearity of the methods. According to the Generalised Equivalence Theory (GET), additional degrees of freedom are introduced for the low-order problem so that the convergence of the acceleration scheme can be ensured. We present two classes of non-linear methods: transport-like methods and discussion-like methods. Transport-like methods consider a homogenized low-order transport problem on the coarse level. This problem is iteratively solved using the same MOC algorithm as for the transport problem on the fine level. Discontinuity factors are then employed, per region or per surface, in order to reconstruct the currents evaluated by the low-order operator, which ensure the convergence of the acceleration scheme. On the other hand, discussion-like methods consider a low-order problem inspired by diffusion. We studied the non-linear Coarse Mesh Finite Difference (CMFD) method, already present in literature, in the perspective of integrating it into TDT code. Then, we developed a new non-linear method on the model of CMFD. From the latter, we borrowed the idea to establish a simple relation between currents and fluxes in order to obtain a problem involving only coarse fluxes. Finally, those non-linear methods have been

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

International Nuclear Information System (INIS)

Hong, Ser Gi; Kim, Kang-Seog

2011-01-01

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

A sparse electromagnetic imaging scheme using nonlinear landweber iterations

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

Development and use of electromagnetic inverse scattering techniques for imagining sparse domains have been on the rise following the recent advancements in solving sparse optimization problems. Existing techniques rely on iteratively converting

An iterative method for selecting degenerate multiplex PCR primers.

Science.gov (United States)

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

2007-01-01

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

Iterative approach to effective interactions in nuclei

International Nuclear Information System (INIS)

Heiss, W.D.

1982-01-01

Starting from a non-linear equation for the effective interaction in a model space, various iteration procedures converge to a correct solution irrespective of the presence of intruder states. The physical significance of the procedures and the respective solution is discussed

Homogenized description and retrieval method of nonlinear metasurfaces

Science.gov (United States)

Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

2018-03-01

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

Energy Technology Data Exchange (ETDEWEB)

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Salgado, Abner J., E-mail: asalgad1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Wang, Cheng, E-mail: cwang1@umassd.edu [Department of Mathematics, The University of Massachusetts, North Dartmouth, MA 02747 (United States); Wise, Steven M., E-mail: swise1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States)

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.

Methods of stability analysis in nonlinear mechanics

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.

1989-01-01

We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs

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

International Nuclear Information System (INIS)

Cao, A.

1981-07-01

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

Method for conducting nonlinear electrochemical impedance spectroscopy

Science.gov (United States)

Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.

2015-06-02

A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.

An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers

Directory of Open Access Journals (Sweden)

Vasyl Chekurin

2017-01-01

Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.

Plasma flow to a surface using the iterative Monte Carlo method

International Nuclear Information System (INIS)

Pitcher, C.S.

1994-01-01

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

Detailed Design and Fabrication Method of the ITER Vacuum Vessel Ports

International Nuclear Information System (INIS)

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

2006-01-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

An efficient flexible-order model for 3D nonlinear water waves

Science.gov (United States)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

An efficient flexible-order model for 3D nonlinear water waves

International Nuclear Information System (INIS)

Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.

2009-01-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature

Iterative methods for photoacoustic tomography in attenuating acoustic media

Science.gov (United States)

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

2017-11-01

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

Direct application of Padé approximant for solving nonlinear differential equations.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

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

Science.gov (United States)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

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

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

Science.gov (United States)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Iterative and variational homogenization methods for filled elastomers

Science.gov (United States)

Goudarzi, Taha

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents --- i.e., the elastomeric matrix and the filler particles --- and their microstructure --- i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly

Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1994-05-01

Let E=L p , p≥2 and let T:E→ E be a Lipschitzian and strongly accretive mapping. Let S:E → E be defined by Sx=f-Tx+x. It is proved that under suitable conditions on the real sequences {α n } ∞ n=0 and {β n } ∞ n=0 , the iteration process, x 0 is an element of E, x n+1 =(1-α n ) x n +α n S[(1-β n ) x n +β n Sx n ], n≥0, converges strongly to the unique solution of Tx=f. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our results gives an affirmative answer to a problem posed by one of the authors in 1990. (J. Math. Anal. Appl. 151, 2 (1990) p. 460). (author). 36 refs

Computation of saddle-type slow manifolds using iterative methods

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall

2015-01-01

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

Nonlinear Maps and their Applications 2011 International Workshop

CERN Document Server

Fournier-Prunaret, Daniele; Ueta, Tetsushi; Nishio, Yoshifumi

2014-01-01

In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics, biology, or can also be obtained via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists. This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in Évora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramount importance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well as researchers in the field.

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

Science.gov (United States)

Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.

Analysis of Nonlinear Dynamics by Square Matrix Method

Energy Technology Data Exchange (ETDEWEB)

Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II

2016-07-25

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

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

Energy Technology Data Exchange (ETDEWEB)

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

2001-11-01

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

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

International Nuclear Information System (INIS)

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

2001-01-01

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

Bifurcation methods of dynamical systems for handling nonlinear ...

Indian Academy of Sciences (India)

physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

S.H. Chen

1996-01-01

Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Interactive Nonlinear Multiobjective Optimization Methods

OpenAIRE

Miettinen, Kaisa; Hakanen, Jussi; Podkopaev, Dmitry

2016-01-01

An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the...

ROTAX: a nonlinear optimization program by axes rotation method

International Nuclear Information System (INIS)

Suzuki, Tadakazu

1977-09-01

A nonlinear optimization program employing the axes rotation method has been developed for solving nonlinear problems subject to nonlinear inequality constraints and its stability and convergence efficiency were examined. The axes rotation method is a direct search of the optimum point by rotating the orthogonal coordinate system in a direction giving the minimum objective. The searching direction is rotated freely in multi-dimensional space, so the method is effective for the problems represented with the contours having deep curved valleys. In application of the axes rotation method to the optimization problems subject to nonlinear inequality constraints, an improved version of R.R. Allran and S.E.J. Johnsen's method is used, which deals with a new objective function composed of the original objective and a penalty term to consider the inequality constraints. The program is incorporated in optimization code system SCOOP. (auth.)

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

International Nuclear Information System (INIS)

Gao, H

2016-01-01

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

A non-iterative method for fitting decay curves with background

International Nuclear Information System (INIS)

Mukoyama, T.

1982-01-01

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

Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties

DEFF Research Database (Denmark)

Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto

2017-01-01

discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...

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

New nonlinear methods for linear transport calculations

International Nuclear Information System (INIS)

Adams, M.L.

1993-01-01

We present a new family of methods for the numerical solution of the linear transport equation. With these methods an iteration consists of an 'S N sweep' followed by an 'S 2 -like' calculation. We show, by analysis as well as numerical results, that iterative convergence is always rapid. We show that this rapid convergence does not depend on a consistent discretization of the S 2 -like equations - they can be discretized independently from the S N equations. We show further that independent discretizations can offer significant advantages over consistent ones. In particular, we find that in a wide range of problems, an accurate discretization of the S 2 -like equation can be combined with a crude discretization of the S N equations to produce an accurate S N answer. We demonstrate this by analysis as well as numerical results. (orig.)

Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

Directory of Open Access Journals (Sweden)

Jun Yan

2013-01-01

Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Nonlinear Motion Tracking by Deep Learning Architecture

Science.gov (United States)

Verma, Arnav; Samaiya, Devesh; Gupta, Karunesh K.

2018-03-01

In the world of Artificial Intelligence, object motion tracking is one of the major problems. The extensive research is being carried out to track people in crowd. This paper presents a unique technique for nonlinear motion tracking in the absence of prior knowledge of nature of nonlinear path that the object being tracked may follow. We achieve this by first obtaining the centroid of the object and then using the centroid as the current example for a recurrent neural network trained using real-time recurrent learning. We have tweaked the standard algorithm slightly and have accumulated the gradient for few previous iterations instead of using just the current iteration as is the norm. We show that for a single object, such a recurrent neural network is highly capable of approximating the nonlinearity of its path.

Nonlinear programming analysis and methods

CERN Document Server

Avriel, Mordecai

2012-01-01

This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.

Aerodynamic Modeling of NREL 5-MW Wind Turbine for Nonlinear Control System Design: A Case Study Based on Real-Time Nonlinear Receding Horizon Control

Directory of Open Access Journals (Sweden)

Pedro A. Galvani

2016-08-01

Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

Science.gov (United States)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

Directory of Open Access Journals (Sweden)

Markou A.A.

2018-03-01

Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

GHM method for obtaining rationalsolutions of nonlinear differential equations.

Science.gov (United States)

Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

2015-01-01

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

A Multiple Iterated Integral Inequality and Applications

Directory of Open Access Journals (Sweden)

Zongyi Hou

2014-01-01

Full Text Available We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite function w(u(s of the unknown function u with nonlinear function w in integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities. Nonlinear Anal. 69 (2008 393–407] is changed into the composite functions w1(u(s,w2(u(s,…, wn (u(s of the unknown function u with different nonlinear functions w1,w2,…,wn, respectively. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.

A theoretical study on a convergence problem of nodal methods

Energy Technology Data Exchange (ETDEWEB)

Shaohong, Z.; Ziyong, L. [Shanghai Jiao Tong Univ., 1954 Hua Shan Road, Shanghai, 200030 (China); Chao, Y. A. [Westinghouse Electric Company, P. O. Box 355, Pittsburgh, PA 15230-0355 (United States)

2006-07-01

The effectiveness of modern nodal methods is largely due to its use of the information from the analytical flux solution inside a homogeneous node. As a result, the nodal coupling coefficients depend explicitly or implicitly on the evolving Eigen-value of a problem during its solution iteration process. This poses an inherently non-linear matrix Eigen-value iteration problem. This paper points out analytically that, whenever the half wave length of an evolving node interior analytic solution becomes smaller than the size of that node, this non-linear iteration problem can become inherently unstable and theoretically can always be non-convergent or converge to higher order harmonics. This phenomenon is confirmed, demonstrated and analyzed via the simplest 1-D problem solved by the simplest analytic nodal method, the Analytic Coarse Mesh Finite Difference (ACMFD, [1]) method. (authors)

A novel iterative energy calibration method for composite germanium detectors

International Nuclear Information System (INIS)

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

2004-01-01

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

A novel iterative energy calibration method for composite germanium detectors

Energy Technology Data Exchange (ETDEWEB)

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

2004-07-01

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

Adaptive Iterated Extended Kalman Filter and Its Application to Autonomous Integrated Navigation for Indoor Robot

Directory of Open Access Journals (Sweden)

Yuan Xu

2014-01-01

Full Text Available As the core of the integrated navigation system, the data fusion algorithm should be designed seriously. In order to improve the accuracy of data fusion, this work proposed an adaptive iterated extended Kalman (AIEKF which used the noise statistics estimator in the iterated extended Kalman (IEKF, and then AIEKF is used to deal with the nonlinear problem in the inertial navigation systems (INS/wireless sensors networks (WSNs-integrated navigation system. Practical test has been done to evaluate the performance of the proposed method. The results show that the proposed method is effective to reduce the mean root-mean-square error (RMSE of position by about 92.53%, 67.93%, 55.97%, and 30.09% compared with the INS only, WSN, EKF, and IEKF.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc

2011-05-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

2011-01-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Dynamics of a new family of iterative processes for quadratic polynomials

Science.gov (United States)

Gutiérrez, J. M.; Hernández, M. A.; Romero, N.

2010-03-01

In this work we show the presence of the well-known Catalan numbers in the study of the convergence and the dynamical behavior of a family of iterative methods for solving nonlinear equations. In fact, we introduce a family of methods, depending on a parameter . These methods reach the order of convergence m+2 when they are applied to quadratic polynomials with different roots. Newton's and Chebyshev's methods appear as particular choices of the family appear for m=0 and m=1, respectively. We make both analytical and graphical studies of these methods, which give rise to rational functions defined in the extended complex plane. Firstly, we prove that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers. Secondly, we make an incursion into its dynamical behavior. In fact, we show that the rational maps related to these methods can be written in terms of the entries of the Catalan triangle. Next we analyze its general convergence, by including some computer plots showing the intricate structure of the Universal Julia sets associated with the methods.

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

Indian Academy of Sciences (India)

Shwetabh Srivastava

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

Fitting method of pseudo-polynomial for solving nonlinear parametric adjustment

Institute of Scientific and Technical Information of China (English)

陶华学; 宫秀军; 郭金运

2001-01-01

The optimal condition and its geometrical characters of the least-square adjustment were proposed. Then the relation between the transformed surface and least-squares was discussed. Based on the above, a non-iterative method, called the fitting method of pseudo-polynomial, was derived in detail. The final least-squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor's series. The example verifies the correctness and validness of the method.

Note: interpreting iterative methods convergence with diffusion point of view

OpenAIRE

Hong, Dohy

2013-01-01

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

The nonlinear dynamics of the Oklo natural reactor

International Nuclear Information System (INIS)

Bilanovic, Z.; Harms, A.A.

1985-01-01

An analysis of the Oklo natural reactor, a self-sustaining and self-regulating critical assembly that existed some 2 billion years ago in Gabon, Africa, is presented. Nonlinear continuous dif ferential and nonlinear discrete iterative formulations are established and selected parameter characterizations identified. Conceivable power oscillations are calculated and discussed. Some implications of nonlinear mappings for nuclear simulation are suggested

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.

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

Directory of Open Access Journals (Sweden)

Jen-Yuan Chen

2014-01-01

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

Iterative-Transform Phase Retrieval Using Adaptive Diversity

Science.gov (United States)

Dean, Bruce H.

2007-01-01

A phase-diverse iterative-transform phase-retrieval algorithm enables high spatial-frequency, high-dynamic-range, image-based wavefront sensing. [The terms phase-diverse, phase retrieval, image-based, and wavefront sensing are defined in the first of the two immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] As described below, no prior phase-retrieval algorithm has offered both high dynamic range and the capability to recover high spatial-frequency components. Each of the previously developed image-based phase-retrieval techniques can be classified into one of two categories: iterative transform or parametric. Among the modifications of the original iterative-transform approach has been the introduction of a defocus diversity function (also defined in the cited companion article). Modifications of the original parametric approach have included minimizing alternative objective functions as well as implementing a variety of nonlinear optimization methods. The iterative-transform approach offers the advantage of ability to recover low, middle, and high spatial frequencies, but has disadvantage of having a limited dynamic range to one wavelength or less. In contrast, parametric phase retrieval offers the advantage of high dynamic range, but is poorly suited for recovering higher spatial frequency aberrations. The present phase-diverse iterative transform phase-retrieval algorithm offers both the high-spatial-frequency capability of the iterative-transform approach and the high dynamic range of parametric phase-recovery techniques. In implementation, this is a focus-diverse iterative-transform phaseretrieval algorithm that incorporates an adaptive diversity function, which makes it possible to avoid phase unwrapping while preserving high-spatial-frequency recovery. The algorithm includes an inner and an outer loop (see figure). An initial estimate of phase is used to start the algorithm on the inner loop, wherein

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

Science.gov (United States)

Novak, Roman; Vencelj, Matja¿

2009-12-01

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

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)

Multigrid Reduction in Time for Nonlinear Parabolic Problems

Energy Technology Data Exchange (ETDEWEB)

Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-01-04

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

Iterative methods for nonlinear set-valued operators of the monotone type with applications to operator equations

International Nuclear Information System (INIS)

Chidume, C.E.

1989-06-01

The fixed points of set-valued operators satisfying a condition of monotonicity type in real Banach spaces with uniformly convex dual spaces are approximated by recursive averaging processes. Applications to important classes of linear and nonlinear operator equations are also presented. (author). 33 refs

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

International Nuclear Information System (INIS)

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

1982-01-01

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

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2014-01-01

Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

Science.gov (United States)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Digital-Control-Based Approximation of Optimal Wave Disturbances Attenuation for Nonlinear Offshore Platforms

Directory of Open Access Journals (Sweden)

Xiao-Fang Zhong

2017-12-01

Full Text Available The irregular wave disturbance attenuation problem for jacket-type offshore platforms involving the nonlinear characteristics is studied. The main contribution is that a digital-control-based approximation of optimal wave disturbances attenuation controller (AOWDAC is proposed based on iteration control theory, which consists of a feedback item of offshore state, a feedforward item of wave force and a nonlinear compensated component with iterative sequences. More specifically, by discussing the discrete model of nonlinear offshore platform subject to wave forces generated from the Joint North Sea Wave Project (JONSWAP wave spectrum and linearized wave theory, the original wave disturbances attenuation problem is formulated as the nonlinear two-point-boundary-value (TPBV problem. By introducing two vector sequences of system states and nonlinear compensated item, the solution of introduced nonlinear TPBV problem is obtained. Then, a numerical algorithm is designed to realize the feasibility of AOWDAC based on the deviation of performance index between the adjacent iteration processes. Finally, applied the proposed AOWDAC to a jacket-type offshore platform in Bohai Bay, the vibration amplitudes of the displacement and the velocity, and the required energy consumption can be reduced significantly.

Convergence of hybrid methods for solving non-linear partial ...

African Journals Online (AJOL)

This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour

DEFF Research Database (Denmark)

Ottosen, N. Saabye; Gunneskov, O.

1985-01-01

to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...

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

Directory of Open Access Journals (Sweden)

Duygu KOÇAK

2017-11-01

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

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

International Nuclear Information System (INIS)

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

2004-01-01

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

A multigrid Newton-Krylov method for flux-limited radiation diffusion

International Nuclear Information System (INIS)

Rider, W.J.; Knoll, D.A.; Olson, G.L.

1998-01-01

The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques

Fermat's principle and nonlinear traveltime tomography

International Nuclear Information System (INIS)

Berryman, J.G.; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012)

1989-01-01

Fermat's principle shows that a definite convex set of feasible slowness models, depending only on the traveltime data, exists for the fully nonlinear traveltime inversion problem. In a new iterative reconstruction algorithm, the minimum number of nonfeasible ray paths is used as a figure of merit to determine the optimum size of the model correction at each step. The numerical results show that the new algorithm is robust, stable, and produces very good reconstructions even for high contrast materials where standard methods tend to diverge

Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

Science.gov (United States)

Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

2018-03-01

Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

Electromagnetic imaging of multiple-scattering small objects: non-iterative analytical approach

International Nuclear Information System (INIS)

Chen, X; Zhong, Y

2008-01-01

Multiple signal classification (MUSIC) imaging method and the least squares method are applied to solve the electromagnetic inverse scattering problem of determining the locations and polarization tensors of a collection of small objects embedded in a known background medium. Based on the analysis of induced electric and magnetic dipoles, the proposed MUSIC method is able to deal with some special scenarios, due to the shapes and materials of objects, to which the standard MUSIC doesn't apply. After the locations of objects are obtained, the nonlinear inverse problem of determining the polarization tensors of objects accounting for multiple scattering between objects is solved by a non-iterative analytical approach based on the least squares method

Statistical methods in nonlinear dynamics

Indian Academy of Sciences (India)

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical ...

Improved algorithm for solving nonlinear parabolized stability equations

International Nuclear Information System (INIS)

Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

2016-01-01

Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

A finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

OpenAIRE

Choe, Hui-Chol; Kang, Yong-Suk

2013-01-01

We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

Solution of the fully fuzzy linear systems using iterative techniques

International Nuclear Information System (INIS)

Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi

2007-01-01

This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes

ITER radio frequency systems

International Nuclear Information System (INIS)

Bosia, G.

1998-01-01

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

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.

Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

International Nuclear Information System (INIS)

Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.

2009-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.

The spectral cell method in nonlinear earthquake modeling

Science.gov (United States)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Nonlinear dynamic analysis of piping systems using the pseudo force method

International Nuclear Information System (INIS)

Prachuktam, S.; Bezler, P.; Hartzman, M.

1979-01-01

Simple piping systems are composed of linear elastic elements and can be analyzed using conventional linear methods. The introduction of constraint springs separated from the pipe with clearance gaps to such systems to cope with the pipe whip or other extreme excitation conditions introduces nonlinearities to the system, the nonlinearities being associated with the gaps. Since these spring-damper constraints are usually limited in number, descretely located, and produce only weak nonlinearities, the analysis of linear systems including these nonlinearities can be carried out by using modified linear methods. In particular, the application of pseudo force methods wherein the nonlinearities are treated as displacement dependent forcing functions acting on the linear system were investigated. The nonlinearities induced by the constraints are taken into account as generalized pseudo forces on the right-hand side of the governing dynamic equilibrium equations. Then an existing linear elastic finite element piping code, EPIPE, was modified to permit application of the procedure. This option was inserted such that the analyses could be performed using either the direct integration method or via a modal superposition method, the Newmark-Beta integration procedure being employed in both methods. The modified code was proof tested against several problems taken from the literature or developed with the nonlinear dynamics code OSCIL. The problems included a simple pipe loop, cantilever beam, and lumped mass system subjected to pulsed and periodic forcing functions. The problems were selected to gage the overall accuracy of the method and to insure that it properly predicted the jump phenomena associated with nonlinear systems. (orig.)

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations