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Geometric Conversion Approach for the Numerical Evaluation of Hypersin gular and Nearly Hypersingular Boundary Integrals over Curved Surface Boundary Elements
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作者 马杭 《Journal of Shanghai University(English Edition)》 CAS 2002年第2期101-110,共10页
With the aid of the properties of the hypersingular kernels, a geometric conversion approach was presented in this paper. The conversion leads to a general approach for the accurate and reliable numerical evaluation o... With the aid of the properties of the hypersingular kernels, a geometric conversion approach was presented in this paper. The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary integrals encountered in a variety of applications with boundary element method. Based on the conversion, the hypersingularity in the boundary integrals could be lowered by one order, resulting in the simplification of the computer code. Moreover, an integral transformation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar coordinate system for the nearly hypersingular case. The approach is simple to use, which can be inserted readily to computer code, thus getting rid of the dull routine deduction of formulae before the numerical implementations, as the expressions of these kernels are in general complicated. The numerical examples were given in three dimensional elasticity, verifying the effectiveness of the proposed approach, which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernels across the boundary. 展开更多
关键词 boundary element method numerical evaluation hypersingular boundary integral nearly hypersingular boundary integral geometric conversion.
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A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials 被引量:1
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作者 X.WANG W.T.ANG H.FAN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第2期193-206,共14页
The current work models a weak(soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system ... The current work models a weak(soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes. 展开更多
关键词 MICROMECHANICAL modeling micro-crazed interface effective STIFFNESS COEFFICIENT hypersingular integro-differential equation
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Examination of Extraordinary Transmission of Waves Propagation through Gaps of Vertical Thin Barriers in Channels by A Hypersingular Boundary Element Method
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作者 TENG Bin HUANG Jin 《China Ocean Engineering》 SCIE EI CSCD 2019年第5期509-521,共13页
The extraordinary transmission (ET) phenomenon is examined for waves propagating through gaps of vertical thin barriers in channels with a hypersingular boundary element method model on the linear potential theory, an... The extraordinary transmission (ET) phenomenon is examined for waves propagating through gaps of vertical thin barriers in channels with a hypersingular boundary element method model on the linear potential theory, and an estimate formula based on small gap approximation for predicting the number of ET frequencies is proposed. Numerical computations are carried out to examine the influences of barrier number, barrier interval, gap size, gap position and barrier arrangement on extraordinary transmission and wave height in the channel. It shows that all of those factors evidently affect the extraordinary transmission frequencies. The contours of wave amplitude show that very high waves can be excited in the basins between barriers at the extraordinary transmission frequencies. Proper arrangement of barriers in a channel can avoid the occurrence of ET phenomenon and reduce wave height in the channel. 展开更多
关键词 extraordinary TRANSMISSION reflection and TRANSMISSION COEFFICIENTS wave height in CHANNELS hypersingular BEM
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A multiscale Galerkin method for the hypersingular integral equation reduced by the harmonic equation
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作者 LI Song-hua XIAN Jun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第1期75-89,共15页
The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersi... The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot(θ/2). Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j+1 × 2j+1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular. 展开更多
关键词 Trigonometric wavelet multiscale Galerkin method matrix decomposition FFT hypersingular integral equation harmonic equation.
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Approximate Formulation and Numerical Solution for Hypersingular Boundary Integral Equations in Plane Elasticity
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作者 马杭 黄兴 《Journal of Shanghai University(English Edition)》 CAS 2003年第2期124-130,共7页
Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general app... Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations. 展开更多
关键词 hypersingular boundary integral equation numerical solution approximate formulation splitting distance.
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APPLICATION OF THE HYPERSINGULAR INTEGRAL EQUATIONS METHOD TO THE INTERACTION BETWEEN TWO PARALLEL PLANAR CRACKS IN 3-D ELASTICITY
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作者 Qin Taiyan, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. ChinaYue Jinchao Tang Renji, Dept. of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, P. R. China 《Acta Mechanica Solida Sinica》 SCIE EI 1995年第1期64-74,共11页
By using the analytic theory of hypersingular integral equations in three- dimensional fracture mechanics, the interactions between two parallel planar cracks under arbitrary loads are investigated. According to the c... By using the analytic theory of hypersingular integral equations in three- dimensional fracture mechanics, the interactions between two parallel planar cracks under arbitrary loads are investigated. According to the concepts and method of finite- part integrals, a set of hypersingular integral equations is derived, in which the unknown functions are the displacement discontinuities of the crack surfaces. Then its numerical method is proposed by combining the finite-part integral method with the boundary element method. Based on the above results, the method for calculating the stress intensity factors with the displacement discontinuities of the crack surfaces is presented. Finally, several typical examples are calculated and the numerical results are satisfactory. 展开更多
关键词 interaction hypersingular integral equation two parallel planar cracks stress intensity factor
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ROUGH HYPERSINGULAR INTEGRAL OPERATORS WITH AN OSCILLATING FACTOR
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作者 陈杰诚 尤英 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第2期179-190,共12页
The singular integral operator FΩ.a, and the Marcinkiewicz integral operator μ^-Ω.a are studied. The kernels of the operators behave like |y|^-n-a(a〉0) near the origin, and contain an oscillating factor e^i|y... The singular integral operator FΩ.a, and the Marcinkiewicz integral operator μ^-Ω.a are studied. The kernels of the operators behave like |y|^-n-a(a〉0) near the origin, and contain an oscillating factor e^i|y|^-β(β〉0) and a distribution Ω on the unit sphere S^n-1. It is proved that, if Ω is in the Hardy space H^r(S^n-1) with 0〈r=(n-1)/(n-1+y)(r〉0), and satisfies certain eancellation condition,then FΩ.a and μ^-Ω.a extend the bounded operator from Sobolev space L^pr to Lebesgue space L^p for some p. The result improves and extends some known results. 展开更多
关键词 rough hypersingular integral operator Marcinkiewicz integral operator rough kernel Sobolev space.
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A ROUGH HYPERSINGULAR INTEGRAL OPERATOR WITH AN OSCILLATING FACTOR ON FUNCTION SPACE
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作者 Ye Xiaofeng Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China Dept.of Math.,East China JiaoTong Univ.,Nanchang 330013,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第4期449-452,共4页
The singular integral operatorTα,βf(x)=p.v.∫R^n[e^i|y|^-βΩ(y’)]/[|y|^n+α]f(x-y)dy,defined for all test functions f is studied, where Ω(y') is a distribution on the unit sphere S^n-1 satisfying ce... The singular integral operatorTα,βf(x)=p.v.∫R^n[e^i|y|^-βΩ(y’)]/[|y|^n+α]f(x-y)dy,defined for all test functions f is studied, where Ω(y') is a distribution on the unit sphere S^n-1 satisfying certain cancellation condition. It is proved that Tα,β is a bounded operator from the Triebel-Lizorkin space Fp^s,q to the Triebel-Lizorkin space Fp^s+γ,q, provided that Ω(y') is a distribution in the Hardy space H^r(S^n-1) with r = (n - 1)/(n - 1 + γ). 展开更多
关键词 Hardy space hypersingular integral.
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Numerical Quadratures for Hadamard Hypersingular Integrals 被引量:1
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作者 Youjian Shen 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2006年第1期50-59,共10页
In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate th... In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions. 展开更多
关键词 数值积分 有限部分 规格化正交多项式 求积公式
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QUASI-INTERPOLATING OPERATORS AND THEIR APPLICATIONS IN HYPERSINGULAR INTEGRALS 被引量:7
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作者 Wong, RH Lu, Y 《Journal of Computational Mathematics》 SCIE EI CSCD 1998年第4期337-344,共8页
The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space S-1/2(Delta(mn)(2*)) on non-uniform type-2 triangulation. Based on the operators, we construct cu... The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space S-1/2(Delta(mn)(2*)) on non-uniform type-2 triangulation. Based on the operators, we construct cubature formula for two-dimensional hypersingular integrals. Some computing work have been done and the results are quite satisfactory. 展开更多
关键词 hypersingular integral finite-part integral quasi-interpolating operator non-uniform type-2 triangulation
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Extrapolation methods to compute hypersingular integral in boundary element methods 被引量:6
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作者 LI Jin ZHANG XiaoPing YU DeHao 《Science China Mathematics》 SCIE 2013年第8期1647-1660,共14页
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... 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. 展开更多
关键词 hypersingular integrals trapezoidal rule asymptotic error expansion extrapolation algorithm
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APPROXIMATIONS OF HYPERSINGULAR INTEGRALS FOR NEGATIVE FRACTIONAL EXPONENT 被引量:1
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作者 Chaolang Hu Tao Lu 《Journal of Computational Mathematics》 SCIE CSCD 2018年第5期627-643,共17页
This article presents approximations of the hypersingular integrals fa^b g(x)(x- t)^adx and fa^b g(x)|x- t|dx with arbitrary singular point t C (a, b) and negative fraction number 〈 -1. These general expan... This article presents approximations of the hypersingular integrals fa^b g(x)(x- t)^adx and fa^b g(x)|x- t|dx with arbitrary singular point t C (a, b) and negative fraction number 〈 -1. These general expansions are applicable to a large range of hypersingular inte- grals, including both popular hypersingular integrals discussed in the literature and other important ones which have not been addressed yet. The corresponding mid-rectangular formulas and extrapolations, which can be calculated in fairly straightforward ways, are investigated. Numerical examples are provided to illustrate the features of the numerical methods and verify the theoretical conclusions. 展开更多
关键词 hypersingular integral Negative fractional exponent Mid-rectangular quadrature formula Extrapolation.
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The boundedness for commutators of maximal hypersingular integrals with rough kernels 被引量:1
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作者 CHEN YanPing DING Yong LI Ran 《Science China Mathematics》 SCIE 2013年第4期707-728,共22页
In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an exte... In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an extension of some known results. 展开更多
关键词 COMMUTATOR maximal hypersingular integrals rough kernel BMO sobolev space
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Weil配对求解椭圆曲线离散对数的实施分析
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作者 胡建军 《新疆大学学报(自然科学版中英文)》 CAS 2024年第3期329-335,343,共8页
Weil配对广泛应用于加密、解密、签名、密码交换和密码体制安全分析中.1993年,Menezes等利用Weil配对有效地将超奇异椭圆曲线的离散对数约减到有限域上的离散对数,基于Weil配对的椭圆曲线密码体制遭受严峻挑战,然而,基于Weil配对的椭圆... Weil配对广泛应用于加密、解密、签名、密码交换和密码体制安全分析中.1993年,Menezes等利用Weil配对有效地将超奇异椭圆曲线的离散对数约减到有限域上的离散对数,基于Weil配对的椭圆曲线密码体制遭受严峻挑战,然而,基于Weil配对的椭圆曲线密码体制的应用并未止步.为此,分析了适合Weil配对椭圆曲线的特征,指出适合Weil配对的椭圆曲线是具有二元循环群结构的曲线,一元群结构的超奇异椭圆曲线通过嵌入度的方式能够构造出二元群结构的超奇异椭圆曲线.同时,为了方便理解Weil配对的实施,列出了适合Weil配对安全的常见椭圆曲线.最后,聚焦了MOV攻击嵌入度为偶数的超奇异椭圆的实施过程,利用PARI软件验证了分析结论,指出了PARI和SageMath软件在设计上存在的缺陷. 展开更多
关键词 有限域 超奇异椭圆曲线 扭曲群 离散对数 WEIL配对
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Hypersingular integral-partial differential equations for a planar interface crack in bimaterial
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作者 乐金朝 汤任基 《Chinese Science Bulletin》 SCIE EI CAS 1996年第14期1225-1228,共4页
With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, ... With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, many researches on this subject have been taken. However, they are usually applied to two-dimensional cases. For the three-dimensional ones, very few analyses have been done because of the great complexity on mathematics and mechanics. In this study, based on the point-force solutions for two perfectly 展开更多
关键词 hypersingular integral-partial diflerential EQUATIONS PLANAR INTERFACE CRACK halfspaces.
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Commutator of Hypersingular Integral with Rough Kernels on Sobolev Spaces
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作者 Yan Ping CHEN Yong DING Xin Xia WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第6期1043-1054,共12页
In this paper, the authors give the boundedness of the commutator of hypersingular integral T γ from the homogeneous Sobolev space Lpγ (Rn) to the Lebesgue space Lp(Rn) for 1
关键词 hypersingular integral paraproduct COMMUTATOR Sobolev space
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A SPLINE METHOD FOR SOLVING TWO-DIMENSIONAL FREDHOLM INTEGRAL EQUATION OF SECOND KIND WITH THE HYPERSINGULAR KERNEL
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作者 Wang, RH Lu, Y 《Journal of Computational Mathematics》 SCIE EI CSCD 2001年第3期225-230,共6页
Provides information on a study which proposed a spline method for solving two-dimensional Fredholm Integral Equations of second kind space with hypersingular kernels. Details on the quasi-interpolating operators; Inf... Provides information on a study which proposed a spline method for solving two-dimensional Fredholm Integral Equations of second kind space with hypersingular kernels. Details on the quasi-interpolating operators; Information on the cubature formulas; Formulas of the approximation method. 展开更多
关键词 hypersingular integral finite-part integral quasi-interpolating operator nonuniform type-2 triangulation
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Antiplane shear crack in a prestressed elastic medium based on the couple stress theory
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作者 Jian CHEN Yawei WANG Xianfang LI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第4期583-602,共20页
A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value p... A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF. 展开更多
关键词 couple stress theory(CST) initial stress antiplane shear crack SINGULARITY hypersingular integral equation
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一类高振荡超奇异积分的分析与计算 被引量:1
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作者 王箬夏 康洪朝 《杭州电子科技大学学报(自然科学版)》 2023年第4期66-71,共6页
运用复积分方法计算一类高振荡超奇异积分∫b a f(x)/(x-σ)v+1 e iωx d x,其中a<σ<b,ω是较大的实数,v是正整数,i是虚数单位,f(x)在包含[a,b]的足够大的复区域内是解析的。首先,将∫b a f(x)(x-σ)v+1 e iωx d x看作高振荡柯... 运用复积分方法计算一类高振荡超奇异积分∫b a f(x)/(x-σ)v+1 e iωx d x,其中a<σ<b,ω是较大的实数,v是正整数,i是虚数单位,f(x)在包含[a,b]的足够大的复区域内是解析的。首先,将∫b a f(x)(x-σ)v+1 e iωx d x看作高振荡柯西主值奇异积分∫b a f(x)/x-σe iωx d x的v阶导数形式;然后,根据解析延拓,将其转化为2个无穷积分,因获得的无穷积分的被积函数是非振荡且指数快速衰减的,故使用高斯拉盖尔积分法则进行高效计算;最后,针对ω负次幂的误差展开分析,并通过数值实验验证了复积分方法的高效性和精确性。 展开更多
关键词 高振荡积分 超奇异 复积分法 高斯拉盖尔积分法则
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一类强奇异积分方程的数值求解方法 被引量:7
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作者 陈一鸣 赵所所 +2 位作者 徐增辉 王乾 武永兵 《辽宁工程技术大学学报(自然科学版)》 CAS 北大核心 2011年第1期157-160,共4页
为了改进边界元方法中的强奇异积分方程的数值算法,通过对奇异积分大量文献的研究,提出了一种强奇异积分方程的数值解法,该方法通过Chebyshev多项式展开和方程奇异性的降低,有效的改进了强奇异方程的数值求解方法,并将算法推广至求解更... 为了改进边界元方法中的强奇异积分方程的数值算法,通过对奇异积分大量文献的研究,提出了一种强奇异积分方程的数值解法,该方法通过Chebyshev多项式展开和方程奇异性的降低,有效的改进了强奇异方程的数值求解方法,并将算法推广至求解更一般的强奇异积分方程。结果表明:该方法在计算量和误差方面有了明显的改进。通过算例说明方法的可行性、有效性。 展开更多
关键词 积分方程 强奇异积分 Cauchy主值积分
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