A surface edge element method is proposed and implemented in the study ofelectromagnetic scattering fields of general targets. The basis functions for surfaces of arbitraryshape are derived according to the geometrica...A surface edge element method is proposed and implemented in the study ofelectromagnetic scattering fields of general targets. The basis functions for surfaces of arbitraryshape are derived according to the geometrical properties of each triangular patch. The proposedbasis functions are 3-D linear functions and the tangential components of the vectors are continuousas the traditional edge element method. Combined field integral equations (CFIE) that include bothelectrical field and magnetic field integral equations are used to model the electromagneticscattering of general dielectric targets. Special treatment for singularity is presented to enhancethe quality of numerical solutions. The proposed method is used to compute the scattering fieldsfrom various targets. Numerical results obtained by the proposed method are validated by resultsfrom other numerical methods.展开更多
We present an equivalent form of the expres- sions first obtained by Tada （Geophys J Int 164：653-669, 2006. doi： 10.1111/j. 1365-246X.2006.03868.x）, which rep- resents the transient stress response of an infinite,...We present an equivalent form of the expres- sions first obtained by Tada （Geophys J Int 164：653-669, 2006. doi： 10.1111/j. 1365-246X.2006.03868.x）, which rep- resents the transient stress response of an infinite, homo- geneous and isotropic medium to a constant slip rate on a triangular fault that continues perpetually after the slip onset. Our results are simpler than Tada＇s, and the corre- sponding codes have a higher running speed.展开更多
The primary purpose of this paper is to present the Volterra integral equa- tion of the two-variable Hermite matrix polynomials. Moreover, a new representation of these matrix polynomials are established here.
The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material propert...The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material properties depend only on the coordinate y (alongthe thickness direcion). In the analysis, the elastic region isdivided into a number of plies of infinite length. The materialproperties are taken to be constants for each ply. By utilizing theLaplace transform and Fourier transform technique, the generalsolutions for plies are derived.展开更多
This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 20...This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233：938 950], the error analysis for this approach is carried out for 0 〈 μ 〈 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i.e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-ype but also establish the error estimates under a more general regularity assumption on the exact solution.展开更多
In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. Th...In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonM Haar basis functions which leads to sparse matrices causes the convergence and com- putational efficiency. Some illustrative results show the reliability and accuracy of the presented method.展开更多
文摘A surface edge element method is proposed and implemented in the study ofelectromagnetic scattering fields of general targets. The basis functions for surfaces of arbitraryshape are derived according to the geometrical properties of each triangular patch. The proposedbasis functions are 3-D linear functions and the tangential components of the vectors are continuousas the traditional edge element method. Combined field integral equations (CFIE) that include bothelectrical field and magnetic field integral equations are used to model the electromagneticscattering of general dielectric targets. Special treatment for singularity is presented to enhancethe quality of numerical solutions. The proposed method is used to compute the scattering fieldsfrom various targets. Numerical results obtained by the proposed method are validated by resultsfrom other numerical methods.
基金supported by the National Natural Science Foundation of China (Grant No. 41674050)MOST Grant (2012CB417301)
文摘We present an equivalent form of the expres- sions first obtained by Tada （Geophys J Int 164：653-669, 2006. doi： 10.1111/j. 1365-246X.2006.03868.x）, which rep- resents the transient stress response of an infinite, homo- geneous and isotropic medium to a constant slip rate on a triangular fault that continues perpetually after the slip onset. Our results are simpler than Tada＇s, and the corre- sponding codes have a higher running speed.
文摘The primary purpose of this paper is to present the Volterra integral equa- tion of the two-variable Hermite matrix polynomials. Moreover, a new representation of these matrix polynomials are established here.
文摘The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material properties depend only on the coordinate y (alongthe thickness direcion). In the analysis, the elastic region isdivided into a number of plies of infinite length. The materialproperties are taken to be constants for each ply. By utilizing theLaplace transform and Fourier transform technique, the generalsolutions for plies are derived.
文摘This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel p（t, s） = （t - s）^-μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233：938 950], the error analysis for this approach is carried out for 0 〈 μ 〈 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i.e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-ype but also establish the error estimates under a more general regularity assumption on the exact solution.
文摘In this study, Haar wavelet method is implemented for solving the nonlinear age- structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonM Haar basis functions which leads to sparse matrices causes the convergence and com- putational efficiency. Some illustrative results show the reliability and accuracy of the presented method.
