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numerical integration Method in Analysis of Wire Antennas

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Wuhan University Journal of Natural Sciences 1998年第3期3卷 55-60页

作者： Yang, Shaolin Ke, Hengyu Hou, Jiechang

The numerical evaluation of an integral is a frequently encountered problem in antenna analysis. A special Gauss Christoffel quadrature formula for nonclassical weight function is constructed for solving the pseudo singular integration problem arising from the analysis of thin wire antennas. High integration accuracy is obtained at comparable low computation cost by the quadrature formula constructed. This integration method can be also used in other electromagnetic integral equation problems.

关键词： antenna analysis numerical integration singularity Gauss quadratrue

CASCADIC MULTIGRID METHOD FOR ISOPARAMETRIC FINITE ELEMENT WITH numerical integration

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Journal of Computational Mathematics 2004年第1期22卷 123-136页

作者： Chun-jiaBi Li-kangLi DepartmentofMathematics YantaiUniversityYantai264005China DepartmentofMathematics FudanUniversityShanghai200433China

The purpose of this paper is to study the cascadic multigrid method for the secondorder elliptic problems with curved boundary in two-dimension which are discretized by the isoparametric finite element method with numerical integration. We show that the CCG method is accurate with optimal complexity and traditional multigrid smoother (likesymmetric Gauss-Seidel, SSOR or damped Jacobi iteration) is accurate with suboptimal complexity.

关键词： Cascadic multigrid method Isoparametric element numerical integration

Comparison study of several numerical integration schemes used in calculations of density functional theory

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Chinese Journal of Chemistry 1996年第4期14卷 289-296页

作者： Hong, GY Li, LM BEIJING UNIV COLL CHEM & MOL ENGNSTATE KEY LAB RARE EARTH MAT CHEM & APPLICATBEIJING 100871PEOPLES R CHINA

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition [function proposed by Becke with the scaled generalized Gauss‐Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.

关键词： density functional theory partition function numerical integration Gaussian quadrature numerical error

The numerical integration of Discrete Functions on a Triangular Element

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Journal of Modern Transportation 2001年第1期18卷 50-42,51-58页

作者：陆宏轮仇文革关宝树 Department of Applied Mechanics and Engineering Southwest Jiaotong University School of Civil Engineering Southwest Jiaotong University

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re... 详细信息

关键词： numerical integration discrete functions finite element method base function triangular element

Online Calculation Model of Rolling Force for Cold Rolling Mill Based on numerical integration

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Online Calculation Model of Rolling Force for Cold Rolling M...

THEORETICAL ANALYSIS OF THE REPRODUCING KERNEL GRADIENT SMOOTHING integration TECHNIQUE IN GALERKIN MESHLESS METHODS

第24届中国控制与决策会议

作者： Chen Shu-zong 1 , Zhang Dian-hua 1 , Sun Jie 1 , Wang Jun-sheng 2 , Song Jun 2 1. The State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, Liaoning, 110819, China2. Technology Center of Angang Steel Company Limited, Anshan, Liaoning, 114009, China

Based on comprehensive consideration of elastic and plastic deformation of both strip and work roll, an online rolling force model for tandem cold rolling mill has been developed by numerical integration method in this paper. According to the load equilibrium equation and the boundary condition, the vertical stress of every unit can be obtained. The rolling force in the plastic deformation zone can be calculated via the sum of vertical stress of every unit, and the total rolling force can be obtained by summing rolling force of elastic and plastic deformation zones. In addition, the suitable mathematic models of friction coefficient and strip deformation resistance were also established. In accordance with the coupling problem between the flatten roll radius and rolling force, the iterative procedure by computer was built. This rolling force model has been applied to a 5-stand tandem cold mill and the relative error of rolling force prediction is within ±4.1%, which proves the model is accurate and meets the requirement of online process control.

关键词： tandem cold rolling rolling force model numerical integration roll flattening friction coefficient deformation resistance

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Journal of Computational Mathematics 2023年第3期41卷 501-524页

作者： Xiaolin Li School of Mathematical Sciences Chongqing Normal UniversityChongqing 400047China

numerical integration poses greater challenges in Galerkin meshless methods than finite element methods owing to the non-polynomial feature of meshless shape functions.The reproducing kernel gradient smoothing integration(RKGSI)is one of the optimal numerical integration techniques in Galerkin meshless methods with minimum integration points.In this paper,properties,quadrature rules and the effect of the RKGSI on meshless methods are analyzed.The existence,uniqueness and error estimates of the solution of Galerkin meshless methods under numerical integration with the RKGSI are established.A procedure on how to choose quadrature rules to recover the optimal convergence rate is presented.

关键词： Galerkin meshless method numerical integration Quadrature rule Error estimates Element-free Galerkin method Degree of precision

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基于无网格移动变形构件的结构拓扑优化方法

Acta Mechanica Sinica 2022年第5期38卷 72-87,I0002页

作者：李林远刘畅杜宗亮张维声郭旭 State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsInternational Research Center for Computational MechanicsDalian University of TechnologyDalian 116023China Ningbo Institute of Dalian University of Technology Ningbo 315016China

传统拓扑优化方法往往需引入人工弱材料来模拟孔洞,以避免整体刚度矩阵的奇异性,并使用固定的有限元网格进行分析和优化.然而,这种处理方法不仅会增加结构分析的计算成本,还会导致不利的数值不稳定性,尤其是当涉及大变形和动力/屈曲行为... 详细信息

传统拓扑优化方法往往需引入人工弱材料来模拟孔洞,以避免整体刚度矩阵的奇异性,并使用固定的有限元网格进行分析和优化.然而,这种处理方法不仅会增加结构分析的计算成本,还会导致不利的数值不稳定性,尤其是当涉及大变形和动力/屈曲行为时.本文提出了一种新的基于无网格的移动可变形组件拓扑优化方法(ML-MMC),该方法只对组件占据的实体区域进行结构分析,并通过自适应构造无网格形函数的影响域来实现离散组件的耦合,可以在不引入人工弱材料的情况下自然地避免拓扑优化过程中刚度矩阵的奇异性问题.与传统拓扑优化方法相比,这种处理方法可以大大减少优化过程中结构分析的自由度(DOFs)数量.一些典型的二维和三维算例说明了该方法的有效性和高效性.

关键词： Topology optimization Moving morphable components(MMCs) Meshless method Influence domain numerical integration

A new integration scheme for application to seismic hybrid simulation

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Earthquake Engineering and Engineering Vibration 2017年第1期16卷 69-81页

作者： Maedeh Zakersalehi Abbas Ali Tasnimi Mehdi Ahmadizadeh Faculty of civil and environmental Engineering Tarbiat Modares University School of civil Engineering Sharif University of Technology

Hybrid simulation is a powerful test method for evaluating the seismic performance of structural systems. This method makes it feasible that only critical components of a structure be experimentally tested. This paper presents a newly proposed integration algorithm for seismic hybrid simulation which is aimed to extend its capabilities to a wide range of systems where existing methods encounter some limitations. In the proposed method, which is termed the variable time step （VTS） integration method, an implicit scheme is employed for hybrid simulation by eliminating the iterative phase on experimental element, the phase which is necessary in regular implicit applications. In order to study the effectiveness of the VTS method, a series of numerical investigations are conducted which show the successfulness of the VTS method in obtaining accurate, stable and converged responses. Then, in a comparative approach, the improved accuracy of the VTS method over commonly used integration methods is demonstrated. The stability of the VTS method is also studied and the results show that it provides conditional stability; however, its stability limit is well beyond the accuracy limit. The effect of time delay on the VTS method results is also investigated and it is shown that the VTS method is quite successful in handling this experimental error.

关键词： seismic hybrid simulation numerical integration accuracy stability error index time delay

Self-adapting radiation control method for RFS in tracking

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Journal of Systems Engineering and Electronics 2018年第2期29卷 244-255页

作者： LIU Hongqiang YU Lei YANG Haiyan ZHOU Zhongliang Aeronautics and Astronautics Engineering College Air Force Engineering University Air Traffic Control and Navigation College Air Force Engineering University

The aim of this paper is to achieve the radio frequency stealth(RFS) during the course of tracking by controlling the radiation energy and the interval of a radar. Firstly, we build the model of probability of interception with the once radiation during the course of tracking. Secondly, we establish the model of the cumulative probability of interception to describe the effect of RFS throughout the tracking process and obtain two solutions that are minimizing the probability of interception and the radiation times to reduce the cumulative probability of interception. Thirdly, we propose a self-adapting radiation energy control method(SARE)to minimize the probability of interception. Fourthly, we propose a self-adapting radiation interval control method(SARI) to minimize radiation times. Fifthly, combining SARE with SARI, we propose a SARE-SARI control method(SAEI) during the course of tracking.Finally, we compare SAEI with two others by simulation, and the results show the effect of RFS of SAEI is better than the other two,but we have to make a trade-off between the ability of RFS and the effect of tracking.

关键词： energy control radiation time intercept probability numerical integration genetic algorithm radio frequency stealth(RFS)