This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint proble...This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.展开更多
In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint...In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.展开更多
The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considere...The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considered, and the error estimation of the twoorder and two-scale approximate solution is derived. The numerical result shows that the presented approximation solution is effective.展开更多
In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is...In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is the same as the heat equation in x-variables and the divergence rate as t→O_(+) is related to the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10761003) the Governor's Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (Grant No.[2005]155)
文摘This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
文摘In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.
基金Project supported by the National Natural Science Foundation of China(No.10590353)the Science Research Project of National University of Defense Technology(No.JC09-02-05)
文摘The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considered, and the error estimation of the twoorder and two-scale approximate solution is derived. The numerical result shows that the presented approximation solution is effective.
文摘In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three.Our result shows that the decay rate as t-→+∞ is the same as the heat equation in x-variables and the divergence rate as t→O_(+) is related to the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.
