A single step scheme with high accuracy for solving parabolic problem is proposed. It is shown that this scheme possesses good stability and fourth order accuracy with respect to both time and space variables, which a...A single step scheme with high accuracy for solving parabolic problem is proposed. It is shown that this scheme possesses good stability and fourth order accuracy with respect to both time and space variables, which are superconvergent.展开更多
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists...This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.展开更多
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently ...Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently for inviscid flow with large amplitude step motion.Here we propose to consider turbulent Wagner problem for a plate that is initially covered with a mixed laminarboundary layer on both sides and is set into step motion of small or large amplitude and in direction normal to the plate.The evolution of skin friction and transition region in time are examined numerically.It is found that transition region unexpectedly changes direction of movement for small amplitude of step motion while global transition or laminarization exists for large amplitude step motion.The significance of this study is twofold.First,the present study treated a new and interesting problem since it combines two problems of fundamental interests,one is Wagner problem and the other is boundary layer transition.Second,the present study appears to show that the pressure gradient normal to the airfoil and caused by discontinuous step motion may have subtle influence on transition and the mechanism of this influence deserves further studies.展开更多
A self-adaptive precise algorithm in the time domain was employed to solve 2-D nonlinear coupled heat and moisture transfer problems. By expanding variables at a discretized time interval, the variations of variables ...A self-adaptive precise algorithm in the time domain was employed to solve 2-D nonlinear coupled heat and moisture transfer problems. By expanding variables at a discretized time interval, the variations of variables can be described more precisely,and a nonlinear coupled initial and boundary value problem was converted into a series of recurrent linear boundary value problems which are solved by FE technique. In the computation, no additional assumption and the nonlinear iteration are required, and a criterion for self-adaptive computation is proposed to maintain sufficient computing accuracy for the change sizes of time steps. In the numerical comparison, the variations of material properties with temperature, moisture content, and both temperature and moisture content are taken into account, respectively. Satisfactory results have been obtained, indicating that the proposed approach is capable of dealing with complex nonlinear problems.展开更多
In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the ...In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.展开更多
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log...This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log（n /ε））iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.展开更多
基金Supported by The National Natural Science Foundations of China (19871027)
文摘A single step scheme with high accuracy for solving parabolic problem is proposed. It is shown that this scheme possesses good stability and fourth order accuracy with respect to both time and space variables, which are superconvergent.
基金Supported by the National Natural Science Fund Finances Projects(71071119)
文摘This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
基金supported by the Special Foundation of Chinese Postdoctoral Science(No.2019T120082)Chinese Post-doc Science Foundation(No.2018M640119)the Natural National Science Foundation of China(No.11802157).
文摘Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently for inviscid flow with large amplitude step motion.Here we propose to consider turbulent Wagner problem for a plate that is initially covered with a mixed laminarboundary layer on both sides and is set into step motion of small or large amplitude and in direction normal to the plate.The evolution of skin friction and transition region in time are examined numerically.It is found that transition region unexpectedly changes direction of movement for small amplitude of step motion while global transition or laminarization exists for large amplitude step motion.The significance of this study is twofold.First,the present study treated a new and interesting problem since it combines two problems of fundamental interests,one is Wagner problem and the other is boundary layer transition.Second,the present study appears to show that the pressure gradient normal to the airfoil and caused by discontinuous step motion may have subtle influence on transition and the mechanism of this influence deserves further studies.
文摘A self-adaptive precise algorithm in the time domain was employed to solve 2-D nonlinear coupled heat and moisture transfer problems. By expanding variables at a discretized time interval, the variations of variables can be described more precisely,and a nonlinear coupled initial and boundary value problem was converted into a series of recurrent linear boundary value problems which are solved by FE technique. In the computation, no additional assumption and the nonlinear iteration are required, and a criterion for self-adaptive computation is proposed to maintain sufficient computing accuracy for the change sizes of time steps. In the numerical comparison, the variations of material properties with temperature, moisture content, and both temperature and moisture content are taken into account, respectively. Satisfactory results have been obtained, indicating that the proposed approach is capable of dealing with complex nonlinear problems.
文摘In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
基金Supported by the National Natural Science Foundation of China(71071119)
文摘This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log（n /ε））iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.
