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On the numerical solutions of two-dimensional scattering problems for an open arc

BOUNDARY VALUE PROBLEMS 2020年第1期2020卷 1-15页

作者： Li, Hu Huang, Jin Zeng, Guang Chengdu Normal Univ Sch Math Chengdu 611130 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China East China Univ Technol Sch Sci Nanchang 330013 Jiangxi Peoples R China

For the scattering problems of acoustic wave for an open arc in two dimensions, we give a uniqueness and existence analysis via the single layer potential approach leading to a system of integral equations that contains a weakly singular operator. For its numerical solutions, we describe an O(h(3)) order quadrature method based on the specific integral formula including convergence and stability analysis. Moreover, the asymptotic expansion of errors with odd power O(h(3)) is got and the Richardson extrapolation algorithm (EA) is used to improve the accuracy of numerical solutions. The efficiency of the method is illustrated by a numerical example.

关键词： Quadrature method extrapolation algorithm Scattering problems Smooth open arc

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Modified Model Predictive Controlfor the Aerospace PWM Rectifiers 28

Modified Model Predictive Controlfor the Aerospace PWM Recti...

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28th IEEE International Symposium on Industrial Electronics (IEEE-ISIE)

作者： Lei, Tao Kong, Delin Min, Zhihao Northwestern Polytech Univ Automat Sch Elect Engn Dept Xian Shaanxi Peoples R China Minist Ind & Informat Technol China Key Lab Aircraft Elect Prop Technol Xian Shaanxi Peoples R China

ISBN: (纸本)9781728136660

This paper proposes a modified finite control set model predictive control method (FCS-MPC) for three-phase PWM aerospace rectifiers. According to the operating conditions in aircraft variable frequency alternating current (VFAC) electrical power system, the power flow in ac side is analyzed. The proposed control method is based on the discrete-time model of rectifiers and does not require additional PWM modulators. It is noticed that the controlling performance of MPC is affected seriously by the number of points in each sampling period duo to the variation of main frequency, which is changed from 360-800Hz in the aircraft electrical power system, to solve the problem, the linear extrapolation method is derived with the traditional FCS-MPC. Based on this method, the controlling time sequences must be chosen properly. The derived points from the extrapolation algorithm can be used to calculate the predictive power of MPC. So the performance of MPC can be improved by adding the predictive points during one cycle. The simulation and experimental results show that under balanced three-phase aeronautical alternating power supply, the accurate tracking function for the reference of the output voltage and reactive power can be achieved with the proposed MPC method.

关键词： extrapolation algorithm finite set model predictive control direct power control aircraft variable frequency system

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The Calculation Methods for Solving a Kind of Boundary Value Problems in Elasticity

The Calculation Methods for Solving a Kind of Boundary Value...

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2017 International Conference on Mathematics, Modelling and Simulation Technologies and Applications（MMSTA 2017)

作者： Pan CHENG School of Mathematics and Statistics Chongqing Jiaotong University

This paper will study the numerical solutions for equations with a kind of boundary value *** equations will be converted into nonlinear boundary integral equations by the potential theory,in which logarithmic singularity and Cauchy singularity are calculated *** quadrature methods(MQMs) are presented to solve the nonlinear equations that the accuracy of the solutions are three *** to the asymptotical compact convergence theory,the errors with an odd powers asymptotic expansion is *** results are shown regarding these approximations for problems by the numerical example.

关键词： Nonlinear boundary value condition Elasticity extrapolation algorithm Mechanical quadrature methods Boundary integral equations

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Unified approach to extrapolation of bandlimited signals in linear canonical transform domain

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SIGNAL PROCESSING 2014年 101卷 65-73页

作者： Zhao, Hui Wang, Ruyan Song, Daiping Zhang, Tianqi Liu, Yuanni Chongqing Univ Posts & Telecommun Sch Commun & Informat Engn Chongqing 400065 Peoples R China Chongqing Key Lab Signal & Informat Proc Chongqing 400065 Peoples R China Chongqing Univ Coll Mech Engn Chongqing 400044 Peoples R China

The linear canonical transform (LCT) has been shown to be a powerful tool for signal processing and optics. Several extrapolation strategies for bandlimited signals in LCT domain have been proposed. The purpose of this paper is to present an approach that unifies a number of different algorithms for the extrapolation of bandlimited signals in LCT domain. This unification is achieved through integral equation and Hilbert space theories. First, the following existing techniques are unified: (1) a continuous signal extrapolation algorithm based on series expansion in terms of generalized prolate spheroidal functions;(2) a generalized Papoulis-Gerchberg iterative algorithm;(3) a two-step extrapolation algorithm for continuous signal from finite samples;and (4) an iterative extrapolation algorithm based on error energy reduction procedure for continuous signal from finite samples. Then, two extrapolation algorithms for discrete bandlimited signals in LCT domain are proposed, which also belongs to the unified framework. (C) 2014 Elsevier B.V. All rights reserved.

关键词： extrapolation algorithm Bandlimited signal Linear canonical transform Hilbert space

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extrapolation methods to compute hypersingular integral in boundary element methods

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Science China Mathematics 2013年第8期56卷 1647-1660页

作者： LI Jin ZHANG XiaoPing YU DeHao School of Science Shandong Jianzhu University School of Mathematics and Statistics Wuhan University School of Mathematical Sciences Xiamen University LSEC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing

The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.

关键词： hypersingular integrals trapezoidal rule asymptotic error expansion extrapolation algorithm

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Mechanical Quadrature Methods and extrapolation algorithms for Boundary Integral Equations with Linear Boundary Conditions in Elasticity

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JOURNAL OF ELASTICITY 2012年第2期108卷 193-207页

作者： Cheng, Pan Luo, Xin Wang, Zhu Huang, Jin Chongqing Jiaotong Univ Sch Sci Chongqing 400074 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA

By potential theory, elastic problems with linear boundary conditions are converted into boundary integral equations (BIEs) with logarithmic and Cauchy singularity. In this paper, a mechanical quadrature method (MQMs) is presented to deal with the logarithmic and the Cauchy singularity simultaneously for solving the boundary integral equations. The convergence and stability are proved based on Anselone's collective compact and asymptotical compact theory. Furthermore, an asymptotic expansion with odd powers of errors is presented, which possesses high accuracy order O(h (3)). Using h (3)-Richardson extrapolation algorithms (EAs), the accuracy order of the approximation can be greatly improved to O(h (5)), and an a posteriori error estimate can be obtained for constructing a self-adaptive algorithm. The efficiency of the algorithm is illustrated by examples.

关键词： Mechanical quadrature method Asymptotic expansion extrapolation algorithm A posteriori error estimate Elasticity

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The algorithm of Optimal Polynomial extrapolation of Random Processes

The Algorithm of Optimal Polynomial Extrapolation of Random ...

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International Conference of Modeling and Simulation in Engineering, Economics, and Management

作者： Atamanyuk, Igor P. Kondratenko, Volodymyr Y. Kozlov, Oleksiy V. Kondratenko, Yuriy P. Mykolaiv State Agrarian Univ Commune Paris Str 9 UA-54010 Mykolaiv Ukraine Univ Colorado Denver Dept Math & Stat Sci Denver CO 80217 USA Natl Univ Shipbuilding UA-54025 Mykolaiv Ukraine Petro Mohyla Black Sea State Univ UA-54003 Mykolaiv Ukraine

ISBN: (纸本)9783642304330;9783642304323

This work deals with the modelling and prediction of the realizations of random processes in corresponding future time moments. The extrapolation algorithm of nonlinear random process for arbitrary quantity of known significances and random relations used for forecasting has been received on the basis of mathematical instrument of canonical decomposition. The received optimal solutions of the nonlinear extrapolation problem, as well as the canonical decomposition, that was use as a base for optimal solution, does not set any substantional restrictions on the class of investigated random process (liniarity, Markov processes propety, stationarity, monotonicity etc.). Theoretical results, block-diagrams for calculation procedures and the analysis of applied applications, especially for the prediction of economic indexes and parameters of technical devices, are under discussions.

关键词： random process canonical decomposition extrapolation algorithm

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extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods

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NUMERICAL algorithmS 2011年第4期58卷 545-554页

作者： Cheng, Pan Huang, Jin Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China Chongqing Jiaotong Univ Sch Sci Chongqing 400074 Peoples R China

We study the numerical solution procedure for two-dimensional Laplace's equation subjecting to non-linear boundary conditions. Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature methods are presented for solving the equations, which possess high accuracy order O(h(3)) and low computing complexities. Moreover, the algorithms of the mechanical quadrature methods are simple without any integration computation. Harnessing the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with odd powers is shown. Based on the asymptotic expansion, the h(3)-Richardson extrapolation algorithms are used and the accuracy order is improved to O(h(5)). The efficiency of the algorithms is illustrated by numerical examples.

关键词： Laplace's equation Mechanical quadrature method Nonlinear boundary condition extrapolation algorithm

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外推算法在数值三重积分中的应用

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高等学校计算数学学报 2011年第4期33卷 358-370页

作者：孙志忠彭飞潘祝山东南大学数学系淮海工学院计算机科学系

1引言积分的计算是自然科学中的一个基本问题.当积分的精确值不能求出时,数值积分就变得越来越重要了.数值积分的基本思想是直接利用被积函数(及其导数)在若干点处的

关键词： triple integral numerical integration extrapolation algorithm error analysis

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extrapolation algorithmS FOR SOLVING MIXED BOUNDARY INTEGRAL EQUATIONS OF THE HELMHOLTZ EQUATION BY MECHANICAL QUADRATURE METHODS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2009年第6期31卷 4115-4129页

作者： Huang, Jin Wang, Zhu Univ Elect Sci & Technol China Coll Appl Math Chengdu 610054 Peoples R China Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA

This paper presents mechanical quadrature methods with high accuracy for solving mixed boundary integral equations of the Helmholtz equation. By estimating the range of eigenvalues for the discretization matrix of the integral equations and applying the collectively compact convergent theory, we prove the stability and convergence of numerical solutions, which is a challenging task for this method. Moreover, the asymptotic error expansions show the method is of order h(3). Hence, extrapolation algorithms can be introduced to achieve higher approximation accuracy degree (O(h(5))). Meanwhile, an a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

关键词： Helmholtz equation mechanical quadrature method extrapolation algorithm a posteriori estimate

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