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base functions and discrete constitutive relations for staggered polyhedral grids

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2009年第9-12期198卷 1117-1123页

作者： Codecasa, Lorenzo Specogna, Ruben Trevisan, Francesco Univ Udine I-33100 Udine Italy Politecn Milan I-20133 Milan Italy

An electromagnetic problem can be discretized on a pair of interlocked primal-dual grids according to discrete geometric approaches like the Finite Integration Technique (FIT) or the Coll Method (CM). The critical aspect is however the construction of the discrete Counterparts Of the Constitutive relations assuring stability and consistency of the overall discrete system of algebraic equations. Initially only orthogonal Cartesian grids where considered: more recently primal grids of tetrahedra and oblique prisms with triangular base can be handled. With this paper a novel set of edge and face vector functions I'm general polyhedral primal grids is presented, complying with precise specifications which allow to construct stable and consistent discrete constitutive equations in the framework of an energetic approach. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Finite Integration Technique base functions Discrete constitutive equations Non-orthogonal polyhedral dual grids

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On solitary *** 2 A unified perturbation theory for higher-order waves

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Acta Mechanica Sinica 2005年第6期21卷 515-530页

作者： Theodore Yaotsu Wu Xinlong Wang Wendong Qu California Institute of Technology Pasadena CA 91125 U.S.A. Fellow Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China State Key Laboratory of Modern Acoustics and Institute of Acoustics Nanjing University Nanjing 210093 China California Institute of Technology Pasadena CA 91125 U.S.A PIMCO Newport Beach CA 92660 U.S.A.

A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n）（the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.

关键词： Solitary waves on water Unified perturbation theory base functions base parameters Asymptotic representation

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High-order nonlinear Volterra-Fredholm-Hammerstein integro-differential equations and their effective computation

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APPLIED MATHEMATICS AND COMPUTATION 2014年 247卷 410-416页

作者： Turkyilmazoglu, M. Hacettepe Univ Dept Math TR-06532 Ankara Turkey

In a recent study (Turkyilmazoglu, 2014) high-order linear Fredholm integro-differential equations were solved by means of an elegant and accurate effective technique. This approach is extended here to obtain exact and analytic approximate solutions of high-order nonlinear Volterra-Fredholm-Hammerstein integro-differential equations. Difference from the earlier work is that the method involves solution of nonlinear algebraic equations in place of linear ones. High accuracy of the introduced technique is also observed for the nonlinear equations via comparisons with some of the available methods. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Nonlinear equations Volterra-Fredholm-Hammerstein equations Analytic solution Galerkin method base functions

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An efficient method for solving a class of nonlocal boundary value problems and error estimate

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APPLIED MATHEMATICS LETTERS 2017年 72卷 42-49页

作者： Hao, T. C. Cong, F. Z. Aviat Univ Air Force Dept Basic Sci Changchun 130022 Peoples R China

In this paper, we propose an efficient method for solving a class of BVPs with nonlocal boundary conditions. The main idea of our method is to obtain the approximate solutions by series representation via suitable base functions. We prove the convergence of the proposed method and give the error estimate. The proposed method is applied to solve two BVPs. The numerical results show that our algorithm is better as compared to the existing ones. Furthermore, our method can deal with linear and nonlinear problems both efficiently. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： BVPs Nonlocal boundary conditions Approximate solutions base functions

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Adaptive predictive functional control of a class of nonlinear systems

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ISA TRANSACTIONS 2006年第2期45卷 175-183页

作者： Zhang, B Zhang, WD Shanghai Jiao Tong Univ Dept Automat Shanghai 200030 Peoples R China

This paper describes the use of pseudo-partial derivative (PPD) to dynamically linearize a nonlinear system, and aggregation is applied to the predicted PPD, resulting in a model-free adaptive predictive control algorithm for a nonlinear system. The algorithm design is only based on the PPD derived online from the input/output data of the controlled process, however it does provide bounded input/output sequence and setpoint tracking without steady-state error. A detailed discussion on parameter selection is also provided. To show the capability of the algorithm, simulations of a time-delay plant and a pH neutralization process show that the proposed method is effective for system parameter perturbation and external disturbance rejection. (c) 2006 ISA-The Instrumentation, Systems, and Automation Society.

关键词： predictive functional control nonlinear system aggregation dynamic linearization base functions

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The homotopy analysis method for multiple solutions of nonlinear boundary value problems

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2009年第9-10期14卷 3530-3536页

作者： Abbasbandy, S. Magyari, E. Shivanian, E. Imam Khomeini Int Univ Dept Math Ghazvin *** Iran ETH Inst Hochbautech CH-8093 Zurich Switzerland

This paper investigates two basic steps of the homotopy analysis method (HAM) when applied to nonlinear boundary value problems of the chemical reaction kinetics, namely (I) the prediction and (2) the effective calculation of multiple solutions. To be specific, the approach is applied to the dual solutions of an exactly solvable reaction-diffusion model for porous catalysts with apparent reaction order n = -1. It is shown that (i) the auxiliary parameter h which controls the convergence of the HAM solutions in general plays a basic role also in the prediction of dual solutions, and (ii) the dual solutions can be calculated by starting the HAM-algorithm with one and the same initial guess. It is conjectured that the features (1) and (2) hold generally in use of HAM to identify and to determine the multiple solutions of nonlinear boundary value problems. (C) 2009 Published by Elsevier B.V.

关键词： Reaction-diffusion model Dual solutions Homotopy analysis method base functions Auxiliary parameter Initial approximation

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Effective computation of exact and analytic approximate solutions to singular nonlinear equations of Lane-Emden-Fowler type

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APPLIED MATHEMATICAL MODELLING 2013年第14-15期37卷 7539-7548页

作者： Turkyilmazoglu, M. Hacettepe Univ Dept Math TR-06532 Ankara Turkey

The particular motivation of this work is to develop a computational method to calculate exact and analytic approximate solutions to singular strongly nonlinear initial or boundary value problems of Lane-Emden-Fowler type which model many phenomena in mathematical physics and astrophysics. A powerful algorithm is proposed based on the series representation of the solution via suitable base functions. The utilization of such functions converts the solution of a given nonlinear differential equation to the solution of algebraic equations. Error analysis and convergence of the method is presented. Comparisons with the other methods reveal validity, applicability and great potential of the method. Several physical problems are treated to illustrative the good performance and high accuracy of the technique. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Nonlinear singular boundary value problems Lane-Emden equation Emden-Fowler equation Analytic approximate methods base functions

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An efficient method for solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions and error estimate

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JOURNAL OF MATHEMATICAL CHEMISTRY 2018年第9期56卷 2691-2706页

作者： Hao, Tian-Chu Cong, Fu-Zhong Shang, Yu-Feng Aviat Univ Air Force Dept Basic Sci Changchun 130022 Jilin Peoples R China

In this paper, we propose an efficient method for solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions. The target is to obtain approximations of coupled Lane-Emden boundary value problems via series representation. Convergence and an error estimate are presented. Finally, two BVPs are solved to illustrative high accuracy of our method. Furthermore, our algorithm is easy to implement.

关键词： Approximate solutions Coupled Lane-Emden equations BVPs Series representation Error estimate base functions 34B15 34B16

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Predictive functional control （PFC） and its application in chlorinated polyethylene process

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Journal of Zhejiang University Science 2003年第3期4卷 300-304页

作者：李鸿亮苏宏业刘军褚健 NationalKeyLaboratoryofIndustrialControlTechnology InstituteofAdvancedProcessControl MaterialandChemicalengineeringInstitute ZhejiangUniversityHongzhou310027China）

The main principle and the characteristic of Predictive Functional Control (PFC) strategy are presented in this paper and the corresponding control system aid design software APC-PFC is also introduced. For a chlorinated polyethylene (CPE) process, a design scheme of cascade predictive functional control system is described and the control performance is improved obviously.

关键词： Predictive control Predictive functional control (PFC) base functions Chlorinated Polyethylene (CPE)

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Optimization of model wavefront-sensorless adaptive optics system based on eigenmodes of deformable mirror

Optimization of model wavefront-sensorless adaptive optics s...

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Annual Conference of the Chinese-Society-of-Optical-Engineering (CSOE) on Optical Sensing and Imaging Technology (AOPC)

作者： Wu, Yang Yang, Haibo Xu, Qi Yang, Huizhen Jangsu Ocean Univ Lianyungang 222005 Jiangsu Peoples R China Sci & Technol Electroopt Informat Secur Control L Tianjin 300308 Peoples R China China Univ Min & Technol Xuzhou 221116 Jiangsu Peoples R China Jangsu Marine Resources Dev Res Inst Lianyungang 222005 Jiangsu Peoples R China

ISBN: (数字)9781510634497

ISBN: (纸本)9781510634497

It is important for the convergence of model wavefront-sensorless (WFSless) adaptive optics (AO) system that how to generate base functions and their numbers of order. The convergence speed of model WFSless AO system depends on the number of eigenmodes when eigenmodes of deformable mirrors (DM) are used as base functions of model WFSless AO system. In practice, lower order aberrations occupy the majority. In order to accelerate the convergence rate of model WFSless AO system, this paper uses partial low-order modes of eigenmodes as base functions of the system to analyze its convergence speed and correction capability. Simulation results demonstrate that the convergence speed of the system is improved to a certain extent regardless of the intensity of turbulence when the correction effect reaches 80% of all-order modes of eigenmodes. For the same wavefront aberration, the more the number of actuators is, the bigger the optimization of the convergence rate of the model WFSless AO system is.

关键词： adaptive optics system wavefront-sensorless base functions eigenmodes optimization

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