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Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments
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作者 Yujing Ma Zhongwang Wang +2 位作者 Jieyuan Zhang Ruijin Huo Xiaohui Yuan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第8期2079-2102,共24页
In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is a... In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets. 展开更多
关键词 Adaptive polynomial chaos expansion method method of moments radar cross section electromagnetic scattering
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Impact of surface-reflected seismic waves on the seismic isolation performance of circular tunnel isolation layers
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作者 LU Jiahui LUO Junjie +3 位作者 HUANG Xiangyun HONG Junliang HE YanXin ZHOU Fulin 《Journal of Mountain Science》 SCIE CSCD 2024年第3期901-917,共17页
Seismic isolation is an effective strategy to mitigate the risk of seismic damage in tunnels.However,the impact of surface-reflected seismic waves on the effectiveness of tunnel isolation layers remains under explored... Seismic isolation is an effective strategy to mitigate the risk of seismic damage in tunnels.However,the impact of surface-reflected seismic waves on the effectiveness of tunnel isolation layers remains under explored.In this study,we employ the wave function expansion method to provide analytical solutions for the dynamic responses of linings in an elastic half-space and an infinite elastic space.By comparing the results of the two models,we investigate the seismic isolation effect of tunnel isolation layers induced by reflected seismic waves.Our findings reveal significant differences in the dynamic responses of the lining in the elastic half-space and the infinitely elastic space.Specifically,the dynamic stress concentration factor(DSCF)of the lining in the elastic half-space exhibits periodic fluctuations,influenced by the incident wave frequency and tunnel depth,while the DSCF in the infinitely elastic space remain stable.Overall,the seismic isolation application of the tunnel isolation layer is found to be less affected by surface-reflected seismic waves.Our results provide valuable insights for the design and assessment of the seismic isolation effect of tunnel isolation layers. 展开更多
关键词 Circular tunnel seismic isolation Surface reflection Response of liners Wave-function expansion method
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Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model
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作者 国伟华 黄永箴 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2002年第6期577-581,共5页
The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of pla... The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range. 展开更多
关键词 semiconductor optical amplifier strained quantum well plane wave expansion method POLARIZATION
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Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates 被引量:7
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作者 WANG Hua Alatancang HUANG Jun-Jie 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第12期1087-1092,共6页
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia... The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method. 展开更多
关键词 free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution
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New Exact Solutions for Konopelchenko-Dubrovsky Equation Using an Extended Riccati Equation Rational Expansion Method 被引量:5
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作者 SONG Li-Na ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5期I0003-I0003,770-776,共8页
Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by u... Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations. 展开更多
关键词 Konopelchenko-Dubrovsky equation extended Riccati equation rational expansion method nonlinear partial differential equation or equations
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A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model 被引量:3
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作者 潘军廷 龚伦训 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期399-402,共4页
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper... Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations. 展开更多
关键词 nonlinear evolution equations new expansion method mBBM model exact solutions
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A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation 被引量:3
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作者 赵银龙 柳银萍 李志斌 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期41-46,共6页
Recently the (G′/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G′/G)-expansion method is a special form of the truncated Pain... Recently the (G′/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G′/G)-expansion method is a special form of the truncated Painlev'e expansion method by introducing an intermediate expansion method. Then the generalized (G′/G)-(G/G′) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev'e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the ( G′/ G)-expansion method. 展开更多
关键词 (G′/G)-expansion method truncated Painlev'e expansion method mKdV equation trav-eling wave solutions
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Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations 被引量:2
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作者 WANG Mei-Jiao WANG Qi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5期785-789,共5页
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly const... In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations. 展开更多
关键词 extended Riccati equation rational expansion method nonlinear stochastic evolution equation stochastic mKdV equation soliton-like solutions
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A polynomial Expansion Method and New General Solitary Wave Solutions to KS Equation 被引量:2
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作者 PENGYan-Ze 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第6期641-642,共2页
Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolu... Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation. 展开更多
关键词 KS equation solitary wave solution polynomial expansion method
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Application of Boundary Collocation Method to Two-Dimensional Wave Propagation 被引量:1
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作者 曹雪玲 游亚戈 +2 位作者 盛松伟 彭雯 叶寅 《China Ocean Engineering》 SCIE EI CSCD 2015年第4期579-587,共9页
Boundary Collocation Method (BCM) based on Eigenfunction Expansion Method (EEM), a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of b... Boundary Collocation Method (BCM) based on Eigenfunction Expansion Method (EEM), a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of beaches with different geometries are solved, and the errors of the method are analyzed. The calculation firmly confirms that the results will be more precise if we choose more rational points on the beach. The application of BCM, available for the problems with irregular domains and arbitrary boundary conditions, can effectively avoid complex calculation and programming. It can be widely used in ocean engineering. 展开更多
关键词 boundary collocation method eigenfunction expansion method wave propagation BEACH
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TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS 被引量:1
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作者 何银年 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期522-529,共8页
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while t... A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely, the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution. 展开更多
关键词 nonlinear evolution equation Navier_Stokes equation Taylor expansion method convergence rate
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Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation 被引量:1
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作者 黄俊杰 阿拉坦仓 王华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第8期1039-1048,共10页
This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe... This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method. 展开更多
关键词 eigenfunction expansion method two-dimensional (2D) elasticity problem upper triangular differential system general solution
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A New Generalized Riccati Equation Rational Expansion Method to Generalized Burgers-Fisher Equation with Nonlinear Terms of Any Order 被引量:1
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作者 ZHANG Xiao-Ling WANG Jing ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期779-786,共8页
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution eq... In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 展开更多
关键词 generalized Riccati equation rational expansion method generalized Burgers-Fisher equation with nonlinear terms of any order symbolic computation
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Exact Traveling Wave Solutions for Generalized Camassa-Holm Equation by Polynomial Expansion Methods 被引量:1
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作者 Junliang Lu Xiaochun Hong 《Applied Mathematics》 2016年第14期1599-1611,共13页
We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the gener... We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions. 展开更多
关键词 Camassa-Holm Equation Partial Differential Equation Polynomial Expansion methods Traveling Wave Solutions
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NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS
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作者 张解放 刘宇陆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第11期1259-1263,共5页
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef... The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated. 展开更多
关键词 variable coefficient nonlinear evolution equation soliton-like solution truncated expansion method
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Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation Using an Extended sinh-Gordon Equation Expansion Method
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作者 YANG Xian-Lin TANG Jia-Shi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第11期1047-1051,共5页
The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konop... The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics. 展开更多
关键词 extended sinh-Gordon equation expansion method exact solutions nonlinear evolution equations Konopelchenko-Dubrovsky equation
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Application of Rational Expansion Method for Differential-Difference Equation
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作者 王琪 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第12期981-986,共6页
In this paper, we applied the rational formal expansion method to construct a series of sofiton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the ... In this paper, we applied the rational formal expansion method to construct a series of sofiton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice. 展开更多
关键词 rational expansion method Toda lattice Ablowitz-Ladik lattice
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THE CONVERGENCE FOR NODAL EXPANSION METHOD
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作者 黄艾香 张波 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1993年第2期135-149,共15页
In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
关键词 Nodal Expansion method CONVERGENCE Error Estimate. Primal Hybrid Finite Element method.
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Application of Fourier Series Expansion Method with PMLs to the Microcavities on Two-Dimensional Photonic Crystals
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作者 Dan Zhang Hong-Ting Jia 《Journal of Electronic Science and Technology》 CAS 2010年第2期122-125,共4页
By using a Fourier series expansion method combined with Chew's perfectly matched layers (PMLs), we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Comp... By using a Fourier series expansion method combined with Chew's perfectly matched layers (PMLs), we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain (FDTD) based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity. 展开更多
关键词 Index Terms---Fourier series expansion method MICROCAVITIES photonic crystals.
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Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation
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作者 额布日力吐 阿拉坦仓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第2期223-232,共10页
This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem... This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example. 展开更多
关键词 eigenfunction expansion method two-dimensional (2D) elasticity problem upper triangular operator matrix general solution
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