In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique ...In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.展开更多
A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh si...A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.展开更多
In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p <...In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.展开更多
Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid...Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.展开更多
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to des...Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
Cold atmospheric plasmas(CAPs)have attracted considerable interest in the field of plasma medicine.Generated reactive species such as hydroxyl(OH)species play an important role in applications of CAPs.Transportation o...Cold atmospheric plasmas(CAPs)have attracted considerable interest in the field of plasma medicine.Generated reactive species such as hydroxyl(OH)species play an important role in applications of CAPs.Transportation of OH species towards the target and distribution of these OH species in the plasma plume play an important role in the applications of plasma medicine.In the present work,a computational model was built to simulate the transportation and distribution of OH species in CAP discharges,which was based on the level set method to dynamically track the propagation of plasma carrier gas in air.A reaction term was incorporated for the OH species.The OH species tended to diffuse around the main stream of the carrier gas,and thus covered larger radial and axial distances.A CAP discharge onto a skin layer led to the largest accumulation of OH species at the central part of the exposed area.The distribution of OH species on the skin was asymmetric,which agreed with experiments.The computational model itself and the obtained results would be useful for future development of plasma medicine.展开更多
At the late stage of continuous casting（CC）ladle teeming,sink vortex can suck the liquid slag into tundish,and cause negative influences on the cleanliness of molten steel.To address this issue,a twophase fluid mech...At the late stage of continuous casting（CC）ladle teeming,sink vortex can suck the liquid slag into tundish,and cause negative influences on the cleanliness of molten steel.To address this issue,a twophase fluid mechanical modeling method for ladle teeming was proposed.Firstly,a dynamic model for vortex suction process was built,and the profiles of vortex flow field were acquired.Then,based on the level set method（LSM）,a two-phase 3Dinterface coupling model for slag entrapment was built.Finally,in combination with high-order essentially non-oscillatory（ENO）and total variation diminishing（TVD）methods,a LSM-based numerical solution method was proposed to obtain the 3Dcoupling evolution regularities in vortex suction process.Numerical results show that the vortex with higher kinetic energy can form an expanded sandglass-shape region with larger slag fraction and lower rotating velocity;there is a pressure oscillation phenomenon at the vortex penetration state,which is caused by the energy shock of two-phase vortex penetration coupling.展开更多
A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method...A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implementation in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy are generated subsequently, via one step Newton or monidifed Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.展开更多
A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on ...A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector(eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problemsfor the case of eigenvalue approximation of nonsymmetric problems). The improved solution has theasymptotic accuracy of the Galerkin discretization solution. The link between the method and theiterated Galerkin method is established. Error estimates for the general nonsymmetric case arederived.展开更多
文摘In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.10901131,10971166, and 10961024)the National High Technology Research and Development Program of China (No.2009AA01A135)the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No.2010211B04)
文摘A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.
基金the National Natural Science Foundation of China(Nos.6136200161365013 and 51165033)+3 种基金the Natural Science Foundation of Jiangxi Province(Nos.20132BAB211030 and 20122BAB211015)the Technology Foundation of Department of Education in Jiangxi Province(Nos.GJJ 13061 and GJJ14196)the National Postdoctoral Research Funds(No.2014M551867)the Jiangxi Advanced Projects for Postdoctoral Research Funds(No.2014KY02)
文摘In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.
文摘Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金National High Technology Research and Development Program of China (863program) (2006AA04Z140)National Natural Science Foundation of China (NSFC) (50605024)
文摘Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
基金funded by National Natural Science Foundation of China (Nos. U1632145, 81573093 and 81227902)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Jiangsu Provincial Key Laboratory of Radiation Medicine and Protection, China Postdoctoral Science Foundation (No. 2016M592584)Strategic Research Grant 7004641 from City University of Hong Kong
文摘Cold atmospheric plasmas(CAPs)have attracted considerable interest in the field of plasma medicine.Generated reactive species such as hydroxyl(OH)species play an important role in applications of CAPs.Transportation of OH species towards the target and distribution of these OH species in the plasma plume play an important role in the applications of plasma medicine.In the present work,a computational model was built to simulate the transportation and distribution of OH species in CAP discharges,which was based on the level set method to dynamically track the propagation of plasma carrier gas in air.A reaction term was incorporated for the OH species.The OH species tended to diffuse around the main stream of the carrier gas,and thus covered larger radial and axial distances.A CAP discharge onto a skin layer led to the largest accumulation of OH species at the central part of the exposed area.The distribution of OH species on the skin was asymmetric,which agreed with experiments.The computational model itself and the obtained results would be useful for future development of plasma medicine.
基金supported by NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization(U1509212)National Natural Science Foundation of China(51375446)Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists(LR16E050001)
文摘At the late stage of continuous casting（CC）ladle teeming,sink vortex can suck the liquid slag into tundish,and cause negative influences on the cleanliness of molten steel.To address this issue,a twophase fluid mechanical modeling method for ladle teeming was proposed.Firstly,a dynamic model for vortex suction process was built,and the profiles of vortex flow field were acquired.Then,based on the level set method（LSM）,a two-phase 3Dinterface coupling model for slag entrapment was built.Finally,in combination with high-order essentially non-oscillatory（ENO）and total variation diminishing（TVD）methods,a LSM-based numerical solution method was proposed to obtain the 3Dcoupling evolution regularities in vortex suction process.Numerical results show that the vortex with higher kinetic energy can form an expanded sandglass-shape region with larger slag fraction and lower rotating velocity;there is a pressure oscillation phenomenon at the vortex penetration state,which is caused by the energy shock of two-phase vortex penetration coupling.
文摘A novel two level spline method is proposed for semi-linear elliptic equations, where the two level iteration is implemented between a pair of hierarchical spline spaces with different orders. The new two level method is implementation in a manner of p-adaptivity. A coarse solution is obtained from solving the model problem in the low order spline space, and the solution with higher accuracy are generated subsequently, via one step Newton or monidifed Newton iteration in the high order spline space. We also derive the optimal error estimations for the proposed two level schemes. At last, the illustrated numerical results confirm our error estimations and further research topics are commented.
文摘A two-level discretization method for eigenvalue problems is studied.Compared to the standard Galerkin finite element discretization technique performed on a fine gridthis method discretizes the eigenvalue problem on a coarse grid and obtains an improved eigenvector(eigenvalue) approximation by solving only a linear problem on the fine grid (or two linear problemsfor the case of eigenvalue approximation of nonsymmetric problems). The improved solution has theasymptotic accuracy of the Galerkin discretization solution. The link between the method and theiterated Galerkin method is established. Error estimates for the general nonsymmetric case arederived.
