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Normal moveout for long offset in isotropic media using the Padé approximation

2002 3rd International Conference on Microwave and Millimeter Wave Technology

作者： Wenliang Dai Zhengfan Li Fuhua Li Department of Electronic Engineering Shanghai Jiaotong University

ISBN: (纸本)078037486X

＜正＞the dielectric image Green’s function method with point matching is used to analyze and calculate the capacitance and conductance of the coplanar transmission lines on semiconducting substrate as operating frequency changes from 0 to 20 *** order to improve the computation efficiency,the pade approximation is applied to deal with infinite series of complex dielectric image Green’s *** validity of the method is proved by comparison with experiment data gained from chip measurement and the results obtained from SDA and quasi-analytical analysis.

关键词： coplanar transmission lines transmission line theory Green's function methods series (mathematics) dielectric image Green's function broadband properties coplanar transmission line semiconducting substrate pade approximation infinite series point matching capacitance conductance 0 to 20 GHz

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Applied Geophysics 2016年第4期13卷 658-666,738,739页

作者： Song Han-Jie Zhang Jin-Hai Yao Zhen-Xing Key Laboratory of Earth and Planetary Physics Institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China University of Chinese Academy of Sciences Beijing 100049 China

The nomaal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the pade approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order pade approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum oft＇set-to-depth ratio for the [3, 3]-order pade approximation is typically double of those in typical methods. The [7, 7]-order pade approximation performs better than the [3.3]-order pade armroximation.

关键词： pade approximation long offset normal moveout isotropic medium

Magnetic interface forward and inversion method based on Padé approximation

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Applied Geophysics 2016年第4期13卷 712-720,740页

作者： Zhang Chong Huang Da-Nian Zhang Kai Pu Yi-Tao Yu Ping College of Geo-Exploration Science and Technology Jilin University Changchun 130026 China Mathematics School and Institute Jilin University Changchun 130026 China Bureau of Geophysical Prospecting INC. China National Petroleum Corporation Korla 841001 China

The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on pade approximation instead of the Taylor series expansion. Compared with the Taylor series, pade＇s expansion＇s convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of pade approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained.

关键词： pade approximation magnetic interface fand inversion method Taylor seriesexpansion

基于函数值Pad逼近的[1/n]阶迭代算法

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高等学校计算数学学报 2015年第3期37卷 234-243页

作者：郭巧檀结庆合肥工业大学数学学院

1引言一般的,我们在求解非线性方程的根时,利用最多的是迭代法,其迭代效果也各不一样[1-4].通常,我们在构造非线性方程求根的迭代方法有Newton迭代算法、Halley迭代算法和割线法等,而Newton迭代格式构造简单且收敛速度较快,又被认为是... 详细信息

1引言一般的,我们在求解非线性方程的根时,利用最多的是迭代法,其迭代效果也各不一样[1-4].通常,我们在构造非线性方程求根的迭代方法有Newton迭代算法、Halley迭代算法和割线法等,而Newton迭代格式构造简单且收敛速度较快,又被认为是求解一般非线性方程根的最常用方法.在:Newton迭代公式的推导过程中,利用最多的是泰勒展开式法、切线法、积分法[5].本文基于函数值Pad6逼近的行列式表示[6-7],构造出[1/0]、[1/1]、[1/2]阶pade逼近

关键词： pade approximation Taylor series expansion Convergence Iterative algorithm

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

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Earthquake Engineering and Engineering Vibration 2010年第3期9卷 425-438页

作者： Chi Fudong Wang Jinting Jin Feng State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

关键词： real-time dynamic hybrid testing root locus analysis delay-dependent stability pade approximation added damping

NUMERICAL SIMULATION FOR SOLITARY WAVES OF RLW EQUATION

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Journal of Hydrodynamics 2004年第2期16卷 130-135页

作者： XUZhen-li LIURu-xun DepartmentofMathematics UniversityofScienceandTechnologyofChinaHefei230026Chinae-mail.xuzl@ustcedu

A high order finite difference scheme for solving the Regularised Long Wave(RLW) equation, based on the high order pade approximation and Lax-Wendroff type timediscretization, was developed in this paper. Some numerical examples, including the propagation of asingle soliton, the interaction of double solitary waves and the temporal evolution of a Maxwellianinitial pulse, were studied to test the accuracy, efficiency and conservation property of thescheme. Compared with the results based on finite element methods, the scheme is proven successful.

关键词： RLW equation pade approximation soli-ton lax-wendroff scheme

Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure

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Theoretical & Applied Mechanics Letters 2023年第5期13卷 394-398页

作者： Pang Gang Zheng Zijun School of Mathematical Sciences Beihang UniversityBeijing 100191China College of Mechanical Engineering Chongqing University of TechnologyChongqing 400054China

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded ***,the equation is considered as the axial wave prop-agation in a bar supported on a spring *** numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical *** effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using pade *** each term,a corresponding substructure composed of dampers and masses is ***,the equivalent mechan-ical structure is obtained by parallelly connecting these *** proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper *** examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.

关键词： Artificial boundary condition pade approximation Dispersive wave Spring-damper-mass system Klein-Gordon equation

Solving multi-object radar cross section based on wide-angle parabolic equation method

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Journal of Systems Engineering and Electronics 2006年第4期17卷 722-724页

作者： Huang Zhixiang Wu Qiong Wu Xianliang The Key Lab of Ministry of Education of Intelligent Computing & Signal Processing Anhui Univ. Hefei 230039 P. R. China

Based on a pade approximation, a wide-angle parabolic equation method is introduced for computing the multiobject radar cross section （RCS） for the first time. The method is a paraxial version of the scalar wave equation, which solves the field by marching them along the paraxial direction. Numerical results show that a single wide-angle parabofic equation run can compute multi-object RCS efficiently for angles up to 45 ° . The method provides anew and efficient numerical method for computation electromagnetics.

关键词： parabolic equation method pade approximation radar cross section paraxial direction.

A New Form of Boussineq Equation with Improved Linear Dispersion Characteristics

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China Ocean Engineering 1999年第1期14卷 11-20页

作者： Zhang, YG Li, YC Dalian Naval Acad Dept Navigat Dalian 116018 Peoples R China Dalian Univ Technol Natl Key Lab Coastal & Offshore Engn Dalian 116023 Peoples R China

It has been shown that Boussinesq type equations, which include the lowest order effects of nonlinearity and frequency dispersion, can provide an accurate description of wave evolution in coastal regions. But different linear dispersion characteristics of the equation can be obtained by different integrating method. In this paper, a new form of the Boussinesq equation is derived by use of two different layer horizontal velocity variables instead of the commonly used depth-averaged velocity or an arbitrary layer velocity. This significantly improves the linear dispersion properties of the Boussinesq equation and enables it to be applied to a wider range of water depth.

关键词： Boussinesq equation Airy wave pade approximation numerical simulation irregular wave

Robust Control of Time Delay Systems

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Computer Technology and Application 2012年第1期3卷 69-75页

作者： Farhati Samia Bel Hadj All Naoui Saloua Abdelkrim Mohamed Naceur Modeling Analysis and Control of Systems National Engineering School of Gabes Street lbn E1 Khatab Zrig 6029 Gabes Tunisia

This study presents the design of both H∞ Loop Shaping Control （HLSC） and Internal Model Control （IMC） strategies for linear time delay systems. For first order time delay system, a systematic approach for weight selection based on the sensitivity function was proposed, then compared to the internal model control strategy. For both methods, the synthesis was based on the pade approximation. Two cases are considered for time delay： upper or lower than system time constant. Simulation results for the proposed approaches are acceptable ever in presence of disturbances and model mismatches.

关键词： H∞ loop shaping control internal model control sensitivity function constant delay pade approximation model mismatches.