The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre spectral scheme is proposed. It possesses the accuracy of second order in time and higher order in space. The nume...The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre spectral scheme is proposed. It possesses the accuracy of second order in time and higher order in space. The numerical experiments show the high accuracy of this approach.展开更多
The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in ...The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.展开更多
To solve nonlinear complementarity problems （NCP）, at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal （LQP） method solves a system ...To solve nonlinear complementarity problems （NCP）, at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal （LQP） method solves a system of nonlinear equations （LQP system）. This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate （the corrector） is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.展开更多
In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating dire...In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating direction method of multipliers,the last two subproblems in the prediction step are solved parallelly,and a correction step is employed in the method to correct the dual variable and two blocks of the primal variables.The step size adapted in the correction step allows for major contribution from the latest solution point to the iteration point.Some numerical results are reported to show the effectiveness of the presented method.展开更多
The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It ...The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.展开更多
Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages ...Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages of precisely predicting the boundary configuration of the deformed material, and of efficiently avoiding hexahedron remeshing processes. The key idea of the prediction-correction ALE FEM is elaborated in detail. Accordingly, the strategy of mesh quality control, one of the key enabling techniques for the 3D bulk forming process numerical simulation by the prediction-correction ALE FEM is carefully investigated, and the algorithm for hexahedral element refinement is formulated based on the mesh distortion energy.展开更多
It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studie...It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.展开更多
This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method ...This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework.Convergence results are established without additional assumptions.And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.展开更多
In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite v...In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormack prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.展开更多
基金This work was supported in part by the Natural Science Foundation of China
文摘The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre spectral scheme is proposed. It possesses the accuracy of second order in time and higher order in space. The numerical experiments show the high accuracy of this approach.
文摘The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.
文摘To solve nonlinear complementarity problems （NCP）, at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal （LQP） method solves a system of nonlinear equations （LQP system）. This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate （the corrector） is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
文摘In this paper,we propose a partially parallel prediction-correction splitting method for solving block-separable linearly constrained convex optimization problems with three blocks.Unlike the extended alternating direction method of multipliers,the last two subproblems in the prediction step are solved parallelly,and a correction step is employed in the method to correct the dual variable and two blocks of the primal variables.The step size adapted in the correction step allows for major contribution from the latest solution point to the iteration point.Some numerical results are reported to show the effectiveness of the presented method.
文摘The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.
基金the National Natural Science Foundation of China(No.50275094).
文摘Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages of precisely predicting the boundary configuration of the deformed material, and of efficiently avoiding hexahedron remeshing processes. The key idea of the prediction-correction ALE FEM is elaborated in detail. Accordingly, the strategy of mesh quality control, one of the key enabling techniques for the 3D bulk forming process numerical simulation by the prediction-correction ALE FEM is carefully investigated, and the algorithm for hexahedral element refinement is formulated based on the mesh distortion energy.
基金supported by Jiangsu Province NSF BK2008255The Cultivation Fund of the Key Scientific and Technical Innovation Project Ministry of Education of China 708044The Doctoral Fund of Ministry of Education of China 20060284001
文摘It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.
基金supported by the National Natural Science Foundation of China(No.61373174).
文摘This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework.Convergence results are established without additional assumptions.And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.
文摘In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormack prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.
