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numerical solution of the Schrodinger equations via a reliable algorithm

INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2015年第5期6卷 417-424页

作者： Heidari, Mohammad Borzabadi, Akbar Hashemi Damghan Univ Sch Math & Comp Sci Damghan Iran

In this paper, a reliable algorithm for solving Schrodinger equations is established. By second-order central difference scheme, the second-order spatial partial derivative of the Schrodinger equations are reduced to a system of first-order ordinary differential equations, that are solved by an efficient algorithm. The comparison of the numerical solution and the exact solution for some test cases shows that the given algorithm is easy and practical for extracting good approximate solutions of Schrodinger equations.

关键词： Schrodinger equation finite difference method numerical algorithm approximation

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Computing matrix symmetrizers, part 2: New methods using eigendata and linear means;a comparison

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LINEAR ALGEBRA AND ITS APPLICATIONS 2016年 504卷 590-622页

作者： Dopico, Froilan Uhlig, Frank Univ Carlos III Madrid Dept Matemat Avda Univ 30 Leganes 28911 Spain Auburn Univ Dept Math & Stat Auburn AL 36849 USA

Over any field F every square matrix A can be factored into the product of two symmetric matrices as A = S-1 . S-2 with S-i = S-r(T) is an element of F-n,F-n and either factor can be chosen nonsingular;as was discovered by Frobenius in 1910. Frobenius' symmetric matrix factorization has been lying almost dormant for a century. The first successful method for computing matrix symmetrizers, i.e., symmetric matrices S such that SA is symmetric, was inspired by an iterative linear systems algorithm of Huang and Nong (2010) in 2013 [29,30]. The resulting iterative algorithm has solved this computational problem over R and C, but at high computational cost. This paper develops and tests another linear equations solver, as well as eigen- and principal vector or Schur Normal Form based algorithms for solving the matrix symmetrizer problem numerically. Four new eigendata based algorithms use, respectively, SVD based principal vector chain constructions, Gram-Schmidt orthogonalization techniques, the Arnoldi method, or the Schur Normal Form of A in their formulations. They are helped by Datta's 1973 method that symmetrizes unreduced Hessenberg matrices directly. The eigendata based methods work well and quickly for generic matrices A and create well conditioned matrix symmetrizers through eigenvector dyad accumulation. But all of the eigen based methods have differing deficiencies with matrices A that have ill-conditioned or complicated eigen structures with nontrivial Jordan normal forms. Our symmetrizer studies for matrices with ill-conditioned eigensystems lead to two open problems of matrix optimization. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Symmetric matrix factorization Symmetrizer Symmetrizer computation Eigenvalue method Linear equation Principal subspace computation Matrix optimization numerical algorithm MATLAB code

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Coupling 2D thermal and 3D optical model for performance prediction of a parabolic trough solar collector

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SOLAR ENERGY 2016年 139卷 365-380页

作者： Huang, Weidong Xu, Qian Hu, Peng Univ Sci & Technol China Dept Earth & Space Sci 96 Jinzhai Rd Hefei 230026 Anhui Peoples R China Univ Sci & Technol China Dept Thermal Sci & Energy Engn 96 Jinzhai Rd Hefei 230026 Anhui Peoples R China

A 2D thermal model for tube receiver in parabolic trough solar collector is proposed, and a fast numerical algorithm is developed. Comparing to the previous models, we consider the radiation loss from the side plate of the tube receiver and direct transmission of the absorber radiation to the air to construct a physical model and mathematical equations. We also reduce the calculation by simplifying them to algebraic equations for numerical solution without needing iteration after ignoring the axial heat transfer. It is further coupled to the three-dimensional optical model to predict the performance of parabolic trough solar collector. The performances of the overall model and thermal model are tested against experimental measurements from Sandia National Laboratories. In all cases, the simulation results show a good agreement with the experimental results. The models developed in this paper can predict performance of parabolic trough solar collector with parabolic trough reflector and tube receiver accurately and quickly based on the structure and material properties of the system. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Parabolic trough Heat transfer model Thermal radiation analysis Optical model numerical algorithm

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Fractional oscillator equation: analytical solution and algorithm for its approximate computation

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JOURNAL OF VIBRATION AND CONTROL 2016年第8期22卷 2045-2052页

作者： Blaszczyk, Tomasz Ciesielski, Mariusz Czestochowa Tech Univ Inst Math Al Armii Krajowej 21 PL-42201 Czestochowa Poland Czestochowa Tech Univ Inst Comp & Informat Sci PL-42201 Czestochowa Poland

In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order (0,1] is transformed into its corresponding integral form, by using the symbolic calculus method, in which the binomial expansion of the inverse integral operator is used. A new fractional integral operator is introduced. A numerical algorithm to approximate the solution of the considered equation is proposed. In the final part of this paper examples of numerical solutions of this equation are given.

关键词： Fractional oscillator equation fractional Euler-Lagrange equation fractional integral equation numerical algorithm

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The effects of different parameters of pyramidal textured silicon surface on the optical reflectance

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SOLAR ENERGY 2016年 134卷 392-398页

作者： Yang, Shengyao Ge, Peiqi Zhang, Lei Shandong Univ Sch Mech Engn Jinan 250061 Peoples R China Shandong Univ Minist Educ Key Lab High Efficiency & Clean Mech Manufacture Jinan 250061 Peoples R China

The effects of different light trapping structure, as formed on the surface of silicon solar cells to increase the light trapping efficiency, are different on the optical reflectance and absorptance. The aim of this paper is to study the effects of the incident angle and pyramidal textured surface formed mechanically on the light trapping efficiency. The base angle size can be controlled mechanically to break through the limitation of crystal structure, and a fillet on the included angle between neighboring pyramidal structures was obtained unavoidable. A numerical algorithm was developed to calculate the weighted reflectance of different structure in this work. Every light transmission process was tracked and the weighted reflectance was calculated numerically. Then the light trapping efficiency of the pyramid texture with different parameters was obtained and analyzed. The weighted reflectance in changed conditions was calculated respectively. By analyzing the values, the optimized parameters of the pyramid texture were proposed, and the best incident angle was obtained. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Silicon solar cells Light trapping structure numerical algorithm Weighted reflectance

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Method of change of the subspace of control parameters and its application to problems of synthesis of nonlinearly deformable axisymmetric thin-walled structures

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MECHANICS OF SOLIDS 2016年第3期51卷 339-348页

作者： Gavryushin, S. S. Nikolaeva, A. S. Bauman Moscow State Tech Univ Ul 2 Ya Baumanskaya 5 Moscow 105005 Russia

The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes of nonlinear deformation of thin-walled axisymmetric shells by the solution parametric continuation method is generalized to solving the practical problem of design of mechanical actuators of discrete action. The synthesis algorithm is based on the method of changing the subspace of control parameters, which is supplemented with the procedure of smooth transition in changing the subspaces. The efficiency of the proposed algorithm is illustrated by an example of synthesis of a thermobimetallic actuator of discrete action. The procedure of determining an isolated solution, whose existencewas predicted byV. I. Feodosiev, is considered in the framework of studying the process of nonlinear deformation of a corrugated membrane loaded by an external pressure.

关键词： nonlinear deformation synthesis problem thin-walled axisymmetric shell actuator postbuckling behavior discrete switching numerical algorithm parametric continuation changing the subspace of parameters smooth transition procedure

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A NONSTATIONARY DYNAMIC PROBLEM ON THE EFFECTS OF SURFACE LOADS ON A HALF-SPACE WITH A NANOSIZED STRUCTURE WITHIN THE FRAMEWORK OF THE COSSERAT MEDIUM MODEL

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NANOSCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL 2016年第1期7卷 61-75页

作者： Okonechnikov, A. S. Rabinskiy, L. N. Tarlakovskii, D. V. Fedotenkov, G. V. Natl Res Univ Moscow Aviat Inst 4 Volokolamskoe Highway Moscow 125993 Russia

A method for solving plane nonstationary problems on the effect of surface loads on a half-space filled with a nanosized micropolar material structure, whose model is the Cosserat continuum, is developed. The approach suggested is based on the principle of superposition in combination with the small parameter method, with the small parameter being represented by one of the micropolar material constants. A boundary resolving integral representation, whose nucleus is the surface function of the effect of the half-space filled with a micropolar medium, is built. A numerical algorithm for computation of normal displacements of the half-space surface, which is based on the method of weight coefficients, has been developed and implemented. Examples of computations are given.

关键词： a nanosized micropolar material Cosserat continuum nonstationary problems half-space surface loads small parameter method Green function method boundary integral representation numerical algorithm

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An algorithm for conditional multidimensional parameter identification with asymmetric and correlated losses of under- and overestimations

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2016年第5期86卷 1032-1055页

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods PL-01447 Warsaw Poland AGH Univ Sci & Technol Fac Phys & Appl Comp Sci Div Informat Technol & Biometr PL-30059 Krakow Poland Catholic Univ Lublin Inst Math & Comp Sci Lublin Poland

Many of today's specialized applicational tasks are obliged to consider the influence of inevitable errors in the identification of parameters appearing in a model. Favourable results can also be achieved through measuring, and then accounting for definite (e.g. current) values of factors which show a significant reaction to the values of those parameters. This paper is dedicated to the problem of the estimation of a vector of parameters, where losses resulting from their under- and overestimation are asymmetric and mutually correlated. The issue is considered from a supplementary conditional aspect, where particular coordinates of conditioning variables may be continuous, discrete, multivalued (in particular binary) or categorized (ordered and unordered). The final result is a ready-to-use algorithm for calculating the value of an estimator, optimal in the sense of minimum expectation of losses using a multidimensional asymmetric quadratic function, for practically any distributions of describing and conditioning variables.

关键词： identification of vector of parameters conditioning factors Bayes approach asymmetrical loss function nonparametric estimation distribution free method numerical algorithm

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Chipot's method for a one-dimensional Kirchhoff static equation

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numerical algorithmS 2016年第4期73卷 1091-1106页

作者： Kachakhidze, N. Khomeriki, N. Peradze, J. Tsiklauri, Z. Georgian Tech Univ Dept Math Tbilisi 0175 Georgia Tbilisi State Univ Dept Math Tbilisi 0177 Georgia

The paper deals with a method of solution of a nonlinear integro-differential static string equation. The accuracy of the method is discussed. The numerical examples are given.

关键词： Kirchhoff string equation Chipot's method numerical algorithm Error estimate

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Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第10期56卷 1743-1757页

作者： Zubov, V. I. Russian Acad Sci Dorodnicyn Comp Ctr Fed Res Ctr Comp Sci & Control Moscow 119333 Russia Moscow Inst Phys & Technol Dolgoprudnyi 141700 Moscow Oblast Russia

The problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the initial-boundary value problem for the one-dimensional unsteady heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the experimental data on the left boundary of the domain is used as the objective functional. An analytical expression for the gradient of the objective functional is obtained. An algorithm for the numerical solution of the problem based on the modern fast automatic differentiation technique is proposed. Examples of solving the problem are discussed.

关键词： heat conduction inverse coefficient problems gradient heat equation adjoint equations numerical algorithm

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