Hyperbolic systems of conservation laws in multiple spatial dimensions display features absent in the one-dimensional case,such as involutions and non-trivial stationary states.These features need to be captured by nu...Hyperbolic systems of conservation laws in multiple spatial dimensions display features absent in the one-dimensional case,such as involutions and non-trivial stationary states.These features need to be captured by numerical methods without excessive grid refine-ment.The active flux method is an extension of the finite volume scheme with additional point values distributed along the cell boundary.For the equations of linear acoustics,an exact evolution operator can be used for the update of these point values.It incorporates all multi-dimensional information.The active flux method is stationarity preserving,i.e.,it discretizes all the stationary states of the PDE.This paper demonstrates the experimental evidence for the discrete stationary states of the active flux method and shows the evolution of setups towards a discrete stationary state.展开更多
To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array (SPS-ALPHA) solar receiver, the symplectic Runge-Kutta method is used to simulate the si...To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array (SPS-ALPHA) solar receiver, the symplectic Runge-Kutta method is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method. First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.展开更多
Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a ...Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.展开更多
In this paper, a fundamental fact that Nambu mechanics is source free was proved. Based on this property, and via the idea of prolongation, finite dimensional Nambu system was prolonged to difference jet bundle. Struc...In this paper, a fundamental fact that Nambu mechanics is source free was proved. Based on this property, and via the idea of prolongation, finite dimensional Nambu system was prolonged to difference jet bundle. Structure preserving numerical methods of Nambu equations were established. Numerical experiments were presented at last to demonstrate advantages of the structure preserving schemes.展开更多
The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating...The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices.In particular,some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems(such as generalized Lotka-Volterra systems,Robbins equations and so on).展开更多
文摘Hyperbolic systems of conservation laws in multiple spatial dimensions display features absent in the one-dimensional case,such as involutions and non-trivial stationary states.These features need to be captured by numerical methods without excessive grid refine-ment.The active flux method is an extension of the finite volume scheme with additional point values distributed along the cell boundary.For the equations of linear acoustics,an exact evolution operator can be used for the update of these point values.It incorporates all multi-dimensional information.The active flux method is stationarity preserving,i.e.,it discretizes all the stationary states of the PDE.This paper demonstrates the experimental evidence for the discrete stationary states of the active flux method and shows the evolution of setups towards a discrete stationary state.
基金supported by the National Natural Science Foundation of China(Nos.11432010,11672241,and 11502202)the Open Foundation of the State Key Laboratory of Structural Analysis of Industrial Equipment of China(No.GZ1605)
文摘To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array (SPS-ALPHA) solar receiver, the symplectic Runge-Kutta method is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method. First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.
基金Supported by the National Natural Science Foundation of China Youth Fund(No.61807029)Natural Science Foundation of Hebei Province(No.F2019203427).
文摘Texture smoothing is a fundamental tool in various applications. In this work, a new image texture smoothing method is proposed by defining a novel objective function, which is optimized by L0-norm minimization and a modified relative total variation measure. In addition, the gradient constraint is adopted in objective function to eliminate the staircase effect, which can preserve the structure edges of small gradients. The experimental results show that compared with the state-of-the-art methods, especially the L0 gradient minimization method and the relative total variation method, the proposed method achieves better results in image texture smoothing and significant structure preserving.
文摘In this paper, a fundamental fact that Nambu mechanics is source free was proved. Based on this property, and via the idea of prolongation, finite dimensional Nambu system was prolonged to difference jet bundle. Structure preserving numerical methods of Nambu equations were established. Numerical experiments were presented at last to demonstrate advantages of the structure preserving schemes.
基金projects NSF of China(11271311)Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)the Aid Program for Science and Technology,Innovative Research Team in Higher Educational Institutions of Hunan Province of China,and Hunan Province Innovation Foundation for Postgraduate(CX2011B245).
文摘The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices.In particular,some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems(such as generalized Lotka-Volterra systems,Robbins equations and so on).