In this paper, we analyze a compact finite difference scheme for computing a coupled nonlinear SchrSdinger equation. The proposed scheme not only conserves the totM mass and energy in the discrete level but also is de...In this paper, we analyze a compact finite difference scheme for computing a coupled nonlinear SchrSdinger equation. The proposed scheme not only conserves the totM mass and energy in the discrete level but also is decoupled and linearized in practical computa- tion. Due to the difficulty caused by compact difference on the nonlinear term, it is very hard to obtain the optimal error estimate without any restriction on the grid ratio. In order to overcome the difficulty, we transform the compact difference scheme into a special and equivalent vector form, then use the energy method and some important lemmas to obtain the optimal convergent rate, without any restriction on the grid ratio, at the order of O（h4 ＋r2） in the discrete L∞ -norm with time step - and mesh size h. Finally, numerical results are reported to test our theoretical results of the proposed scheme.展开更多
This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local Holder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated...This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local Holder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated;then we provide a linear wavelet estimate to obtain the optimal convergence rate,which means that the convergence rate coincides with the lower bound.The non-linear wavelet estimator is introduced for adaptivity,although it is nearly-optimal.However,the non-linear wavelet one depends on an upper bound of the smoothness index of unknown functions,we finally discuss a data driven version without any assumptions on the estimated functions.展开更多
This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-b...This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-based topology optimization approaches,this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain.To be specific,the density design variable points can be freely positioned,independently of the field points used for discretization of the displacement field.By this means,a material interface description of relatively high quality can be achieved,even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain.Numerical examples,regarding the minimum static compliance design and the maximum fundamental eigen-frequency design,are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques.It is shown that this method is free of numerical difficulties such as checkerboard patterns and the“islanding”phenomenon.展开更多
To compare finite element analysis(FEA)predictions and stereovision digital image correlation(StereoDIC)strain measurements at the same spatial positions throughout a region of interest,a field comparison procedure is...To compare finite element analysis(FEA)predictions and stereovision digital image correlation(StereoDIC)strain measurements at the same spatial positions throughout a region of interest,a field comparison procedure is developed.The procedure includes(a)conversion of the finite element data into a triangular mesh,(b)selection of a common coordinate system,(c)determination of the rigid body transformation to place both measurements and FEA data in the same system and(d)interpolation of the FEA nodal information to the same spatial locations as the StereoDIC measurements using barycentric coordinates.For an aluminum Al-6061 double edge notched tensile specimen,FEA results are obtained using both the von Mises isotropic yield criterion and Hill’s quadratic anisotropic yield criterion,with the unknown Hill model parameters determined using full-field specimen strain measurements for the nominally plane stress specimen.Using Hill’s quadratic anisotropic yield criterion,the point-by-point comparison of experimentally based full-field strains and stresses to finite element predictions are shown to be in excellent agreement,confirming the effectiveness of the field comparison process.展开更多
The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and ...The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.展开更多
文摘In this paper, we analyze a compact finite difference scheme for computing a coupled nonlinear SchrSdinger equation. The proposed scheme not only conserves the totM mass and energy in the discrete level but also is decoupled and linearized in practical computa- tion. Due to the difficulty caused by compact difference on the nonlinear term, it is very hard to obtain the optimal error estimate without any restriction on the grid ratio. In order to overcome the difficulty, we transform the compact difference scheme into a special and equivalent vector form, then use the energy method and some important lemmas to obtain the optimal convergent rate, without any restriction on the grid ratio, at the order of O（h4 ＋r2） in the discrete L∞ -norm with time step - and mesh size h. Finally, numerical results are reported to test our theoretical results of the proposed scheme.
基金supported by the National Natural Science Foundation of China(No.11901019)the Science and Technology Program of Beijing Municipal Commission of Education(No.KM202010005025).
文摘This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local Holder condition by wavelet methods.A point-wise lower bound estimation of that model is first investigated;then we provide a linear wavelet estimate to obtain the optimal convergence rate,which means that the convergence rate coincides with the lower bound.The non-linear wavelet estimator is introduced for adaptivity,although it is nearly-optimal.However,the non-linear wavelet one depends on an upper bound of the smoothness index of unknown functions,we finally discuss a data driven version without any assumptions on the estimated functions.
基金The financial support of the National Natural Science Foundation of China(11425207,U1508209)is gratefully acknowledged.
文摘This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-based topology optimization approaches,this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain.To be specific,the density design variable points can be freely positioned,independently of the field points used for discretization of the displacement field.By this means,a material interface description of relatively high quality can be achieved,even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain.Numerical examples,regarding the minimum static compliance design and the maximum fundamental eigen-frequency design,are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques.It is shown that this method is free of numerical difficulties such as checkerboard patterns and the“islanding”phenomenon.
基金Financial support provided by Correlated Solutions Incorporated to perform StereoDIC experimentsthe Department of Mechanical Engineering at the University of South Carolina for simulation studies is deeply appreciated.
文摘To compare finite element analysis(FEA)predictions and stereovision digital image correlation(StereoDIC)strain measurements at the same spatial positions throughout a region of interest,a field comparison procedure is developed.The procedure includes(a)conversion of the finite element data into a triangular mesh,(b)selection of a common coordinate system,(c)determination of the rigid body transformation to place both measurements and FEA data in the same system and(d)interpolation of the FEA nodal information to the same spatial locations as the StereoDIC measurements using barycentric coordinates.For an aluminum Al-6061 double edge notched tensile specimen,FEA results are obtained using both the von Mises isotropic yield criterion and Hill’s quadratic anisotropic yield criterion,with the unknown Hill model parameters determined using full-field specimen strain measurements for the nominally plane stress specimen.Using Hill’s quadratic anisotropic yield criterion,the point-by-point comparison of experimentally based full-field strains and stresses to finite element predictions are shown to be in excellent agreement,confirming the effectiveness of the field comparison process.
文摘The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.
