A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is refo...A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.展开更多
The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions ...The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method （MDBEM） is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.展开更多
This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a...This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.展开更多
We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu ...We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.展开更多
We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materialsusing the integral equation method (IEM).Based on the superposition principle, we use Hertz vector formula...We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materialsusing the integral equation method (IEM).Based on the superposition principle, we use Hertz vector formulations ofradiated fields to study the interaction of wave with matter.We derive in a new way the dispersion relation, Snell's lawand reflection/transmission coefficients by self-consistent analyses.Moreover, we find two new forms of the generalizedextinction theorem.Applying the IEM, we investigate the wave propagation through a slab and disclose the underlyingphysics, which are further verified by numerical simulations.The results lead to a unified framework of the IEM for thepropagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.展开更多
We study the well-posedness of the second order degenerate integro-differential equations （P2）： （Mu）t＇（t） ＋ a（Mu）＇（t） = Au（t） ＋ ft_c~ a（t - s）Au（s）ds ＋ f（t）, 0 ≤ t ≤ 27r, with periodic bounda...We study the well-posedness of the second order degenerate integro-differential equations （P2）： （Mu）t＇（t） ＋ a（Mu）＇（t） = Au（t） ＋ ft_c~ a（t - s）Au（s）ds ＋ f（t）, 0 ≤ t ≤ 27r, with periodic boundary conditions Mu（O） = Mu（27r）, （Mu）＇（O） = （Mu）＇（2π）, in periodic Lebesgue-Bochner spaces LP（T,X）, periodic Besov spaces BBp,q（T, X） and periodic Triebel-Lizorkin spaces F~,q（＇F, X）, where A and M are closed linear operators on a Banach space X satisfying D（A） C D（M）, a C LI（R＋） and a is a scalar number. Using known operator- valued Fourier multiplier theorems, we completely characterize the well-posedness of （P2） in the above three function spaces.展开更多
In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by ...In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach. The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number. Furthermore, the critical magnetic Reynolds number is more sensi- tive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall. For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment, when the relative electrical conductivity of the side wall or the rel- ative magnetic permeability of the end wall is less than some critical value, the m=l （m is the azimuthal wave number） mag- netic mode is the dominant mode, otherwise the m=0 mode predominates the excited magnetic field. Therefore, by changing the material of the walls of the cylindrical vessel, one can select the magnetic mode excited by the anisotropic dynamo.展开更多
A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis i...A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.展开更多
基金Supported by the National Natural Science Foundation of China(No.50969007)the Youth Science Foundation of Jiangxi Provincial Department of Education(No.GJJ09367)the Students’ Scientific Research Training Plan of Nanchang Institute of Technology~~
基金The Scientific Research Foundation of Nanjing University of Posts and Telecommunications(No.NY210049)
文摘A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.
文摘The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method （MDBEM） is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.
文摘This study presents the determination of the stress intensity factors （SIFs） at the edges of the cracks in an elastic strip weakened by N-collinear cracks. The problem of an orthotropic elastic strip is reduced to a system of Cauchy type singular integral equations. The system of singular integral equations is approached by a Quadrature technique. Under two different loading conditions, the results are obtained for the different cases of crack numbers. The resistance of the strip is examined by considering the orthotropic properties of the strip material. Finally, the crack interactions are clarified during the analysis.
文摘We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10847121,10804029,and 10904036
文摘We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materialsusing the integral equation method (IEM).Based on the superposition principle, we use Hertz vector formulations ofradiated fields to study the interaction of wave with matter.We derive in a new way the dispersion relation, Snell's lawand reflection/transmission coefficients by self-consistent analyses.Moreover, we find two new forms of the generalizedextinction theorem.Applying the IEM, we investigate the wave propagation through a slab and disclose the underlyingphysics, which are further verified by numerical simulations.The results lead to a unified framework of the IEM for thepropagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.
基金supported by National Natural Science Foundation of China(Grant No.11171172)
文摘We study the well-posedness of the second order degenerate integro-differential equations （P2）： （Mu）t＇（t） ＋ a（Mu）＇（t） = Au（t） ＋ ft_c~ a（t - s）Au（s）ds ＋ f（t）, 0 ≤ t ≤ 27r, with periodic boundary conditions Mu（O） = Mu（27r）, （Mu）＇（O） = （Mu）＇（2π）, in periodic Lebesgue-Bochner spaces LP（T,X）, periodic Besov spaces BBp,q（T, X） and periodic Triebel-Lizorkin spaces F~,q（＇F, X）, where A and M are closed linear operators on a Banach space X satisfying D（A） C D（M）, a C LI（R＋） and a is a scalar number. Using known operator- valued Fourier multiplier theorems, we completely characterize the well-posedness of （P2） in the above three function spaces.
基金supported by the National Natural Science Foundation of China(Grant No.11272187)
文摘In this paper, based on the mean field dynamo theory, the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach. The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number. Furthermore, the critical magnetic Reynolds number is more sensi- tive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall. For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment, when the relative electrical conductivity of the side wall or the rel- ative magnetic permeability of the end wall is less than some critical value, the m=l （m is the azimuthal wave number） mag- netic mode is the dominant mode, otherwise the m=0 mode predominates the excited magnetic field. Therefore, by changing the material of the walls of the cylindrical vessel, one can select the magnetic mode excited by the anisotropic dynamo.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10671184 and 10971203.
文摘A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.
