This paper′s aim is to study the numerical method of Fourier eigen transform. The characteristics of eigen bases, the Hermite function are analyzed. And a valuable result of eigen coefficients a n by mean...This paper′s aim is to study the numerical method of Fourier eigen transform. The characteristics of eigen bases, the Hermite function are analyzed. And a valuable result of eigen coefficients a n by means of Gauss Hermite integral is gotten. Through talking about amplitude frequency peculiarities of basic signals, we prove that the method applied in this paper possesses higher precision and smaller computation quantity. Finally, we conducted quasi real time FET analysis in seismicity, tentatively probed into the feasibility of FET in seismic prediction, obtained something of practical value.展开更多
The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary elem...The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.展开更多
In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of （d ＋ 1）! simplices. As two examples, in 2-D and 3-D c...In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of （d ＋ 1）! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform （DFT） and its fast algorithm （FFT） on the super-simplex, as well as generalized sine and cosine transforms （DST, DCT） and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a LaDlacian-like operator over these domains is explored.展开更多
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an ...The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.展开更多
文摘This paper′s aim is to study the numerical method of Fourier eigen transform. The characteristics of eigen bases, the Hermite function are analyzed. And a valuable result of eigen coefficients a n by means of Gauss Hermite integral is gotten. Through talking about amplitude frequency peculiarities of basic signals, we prove that the method applied in this paper possesses higher precision and smaller computation quantity. Finally, we conducted quasi real time FET analysis in seismicity, tentatively probed into the feasibility of FET in seismic prediction, obtained something of practical value.
基金This project is supported by National Natural Science Foundation of China
文摘The numerical methods of Fourier eigen transform FET and its inversion are discussed and applied to the boundary element method for elastodynamics. The program for solving elastodynamic problems with the boundary element method is developed and some examples are given. From the numerical results of the examples, we know the method can increase the computing speed 5 similar to 10 times and the accuracy is guaranteed.
基金This work was partly supported by National Science Foundation of China （No. 10431050 and 60573023）, the Major Basic Project of China （2005CB321702） and by Natural Science Foundation of United States （No. CCF0305666） during the author＇s visit at University of Colorado at Boulder.
文摘In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of （d ＋ 1）! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform （DFT） and its fast algorithm （FFT） on the super-simplex, as well as generalized sine and cosine transforms （DST, DCT） and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a LaDlacian-like operator over these domains is explored.
基金supported by the National Natural Science Foundation of China(Grant No.10571118)the Shanghai Leading Academic Discipline Project(Grant No.Y0103).
文摘The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.
