Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort...Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.展开更多
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious...Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.展开更多
This paper relates to the deep research on the Splinc Model Method of KED analysis. With the use of cubic B-splinc function as a link’s transverse deflection interpolation function, the principle of virtual displacem...This paper relates to the deep research on the Splinc Model Method of KED analysis. With the use of cubic B-splinc function as a link’s transverse deflection interpolation function, the principle of virtual displacement is presented as a basic theory for the general formulation of the equations of motion, and thus abandoned the kinematic assumption and the instantaneous structure assumption which arc used in the Spline Model Method. In thc same time, the nonlinear terms sue as coupling terms between thc rigid body motion and elastic deformation arc included. New member’s spline models are established. Mass matrix, Coriolis mass matrix, normal and tangential mass matrix, linear stiffness matrix, nonlinear stiffness matrix and rotation matrix arc derived. The kinematic differential equations of a member and system are deduced in the end. The Newmark direct integration method is used as the solution scheme of the kinematic differential equations to get the periodic response.展开更多
We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The ac...We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions.展开更多
The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific com...The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.展开更多
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of ord...We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline method is formulated as an approximation solution. We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions. Resulting in low absolute errors shows that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.展开更多
This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear comb...This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.展开更多
Wavelet collocation method is used to solve an elliptic singularly perturbed problem with two parameters. The B-spline function is used as a single mother wavelet, which leads to a tri-diagonal linear system. The accu...Wavelet collocation method is used to solve an elliptic singularly perturbed problem with two parameters. The B-spline function is used as a single mother wavelet, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problem and the result shows the reliability and efficiency of the method.展开更多
The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the ...The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method （FEM） as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline （TPS） radial basis functions.展开更多
A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization tech...A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques.展开更多
功能梯度材料是一种特殊的复合材料,在高温下能很好地缓解热应力.由于其材料结构和物理力学性质的特殊性,热冲击下功能梯度梁呈现出较为复杂的热力学行为.B样条物质点法作为一种物质点法的改进算法,已在各类复杂问题中展现了强大的求解...功能梯度材料是一种特殊的复合材料,在高温下能很好地缓解热应力.由于其材料结构和物理力学性质的特殊性,热冲击下功能梯度梁呈现出较为复杂的热力学行为.B样条物质点法作为一种物质点法的改进算法,已在各类复杂问题中展现了强大的求解能力.本文基于傅里叶热传导理论与BSMPM(B-spline Material Point Method)的框架提出了热力耦合方程的离散格式,分析了SiC-Al功能梯度梁的自由振动以及温度荷载作用下的动力响应;同时,基于快速傅里叶变换,研究了SiC-Al功能梯度梁横向振动固有频率随梯度幂律指数的变化规律,并分别与传统物质点法、有限元法和理论解进行了比较分析.结果表明:相较于传统物质点法,B样条物质点法有效改善了应力振荡以及能量耗散.热冲击作用下,B样条物质点法所得功能梯度梁内温度分布与有限元结果吻合较好;B样条物质点法能有效求得一阶横向振动固有频率;随着梯度幂律指数的增加,功能梯度梁固有频率随幂函数变化减小,与理论结果吻合较好.本文验证了热力耦合B样条物质点法的有效性,拓展了B样条物质点法的工程应用,为功能梯度材料在热力耦合作用下的动力响应研究提供了新的计算思路.展开更多
This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis fu...This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.展开更多
基金theNationalNaturalScienceFoundationofChina (No .50 40 90 0 8)
文摘Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.
文摘Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.
文摘This paper relates to the deep research on the Splinc Model Method of KED analysis. With the use of cubic B-splinc function as a link’s transverse deflection interpolation function, the principle of virtual displacement is presented as a basic theory for the general formulation of the equations of motion, and thus abandoned the kinematic assumption and the instantaneous structure assumption which arc used in the Spline Model Method. In thc same time, the nonlinear terms sue as coupling terms between thc rigid body motion and elastic deformation arc included. New member’s spline models are established. Mass matrix, Coriolis mass matrix, normal and tangential mass matrix, linear stiffness matrix, nonlinear stiffness matrix and rotation matrix arc derived. The kinematic differential equations of a member and system are deduced in the end. The Newmark direct integration method is used as the solution scheme of the kinematic differential equations to get the periodic response.
文摘We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions.
文摘The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.
文摘We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline method is formulated as an approximation solution. We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions. Resulting in low absolute errors shows that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.
文摘This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.
文摘Wavelet collocation method is used to solve an elliptic singularly perturbed problem with two parameters. The B-spline function is used as a single mother wavelet, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problem and the result shows the reliability and efficiency of the method.
基金supported by the Key Program of the National Natural Science Foundation of China (Grand No. 51138001)the China-German Cooperation Project (Grand No. GZ566)+1 种基金the Innovative Research Groups Funded by the National Natural Science Foundation of China (Grand No. 51121005)the Special Funds for the Basic Scientific Research Expenses for the Central University (Grant No. DUT13LK16)
文摘The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method （FEM） as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline （TPS） radial basis functions.
文摘A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques.
文摘功能梯度材料是一种特殊的复合材料,在高温下能很好地缓解热应力.由于其材料结构和物理力学性质的特殊性,热冲击下功能梯度梁呈现出较为复杂的热力学行为.B样条物质点法作为一种物质点法的改进算法,已在各类复杂问题中展现了强大的求解能力.本文基于傅里叶热传导理论与BSMPM(B-spline Material Point Method)的框架提出了热力耦合方程的离散格式,分析了SiC-Al功能梯度梁的自由振动以及温度荷载作用下的动力响应;同时,基于快速傅里叶变换,研究了SiC-Al功能梯度梁横向振动固有频率随梯度幂律指数的变化规律,并分别与传统物质点法、有限元法和理论解进行了比较分析.结果表明:相较于传统物质点法,B样条物质点法有效改善了应力振荡以及能量耗散.热冲击作用下,B样条物质点法所得功能梯度梁内温度分布与有限元结果吻合较好;B样条物质点法能有效求得一阶横向振动固有频率;随着梯度幂律指数的增加,功能梯度梁固有频率随幂函数变化减小,与理论结果吻合较好.本文验证了热力耦合B样条物质点法的有效性,拓展了B样条物质点法的工程应用,为功能梯度材料在热力耦合作用下的动力响应研究提供了新的计算思路.
文摘This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.
