In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dim...In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dimensional partially symmetric tensors.Then,we obtain several sufficient conditions for rank-one positive definiteness of fourth-order three dimensional partially symmetric tensors.展开更多
NITE(nano-infiltration and transient eutectic)工艺作为一种制备碳化硅纤维增强碳化硅基(SiCf/SiC)复合材料的新方法,具备周期短、工艺简单、生产成本低等优点,制备出的复合材料基体致密、孔隙率低、不含残余硅,适用于1400℃及以上...NITE(nano-infiltration and transient eutectic)工艺作为一种制备碳化硅纤维增强碳化硅基(SiCf/SiC)复合材料的新方法,具备周期短、工艺简单、生产成本低等优点,制备出的复合材料基体致密、孔隙率低、不含残余硅,适用于1400℃及以上高温长时服役环境应用。目前,日本、美国等国家基于其成熟的第三代碳化硅纤维,对该技术开展了较为深入的研究,并在核能工业热交换器、航空发动机燃烧室衬套等领域进行了应用验证。本文针对NITE工艺从基本概念、工艺流程、制备的SiCf/SiC复合材料和构件考核验证及前景展望四方面进行综合阐述,以期为国内该工艺的发展及应用提供一定程度的参考。展开更多
Based on the quantile regression,we extend Koenker and Xiao(2004)and Ling and McAleer(2004)'s works from nite-variance innovations to in nite-variance innovations.A robust t-ratio statistic to test for unit-root a...Based on the quantile regression,we extend Koenker and Xiao(2004)and Ling and McAleer(2004)'s works from nite-variance innovations to in nite-variance innovations.A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper.It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge.The nite sample studies show that the proposed t-ratio test always performs signi cantly better than the conventional unit-root tests based on least squares procedure,such as the Augmented Dick Fuller(ADF)and Philliphs-Perron(PP)test,in the sense of power and size when in nitevariance disturbances exist.Also,quantile Kolmogorov-Smirnov(QKS)statistic and quantile Cramer-von Mises(QCM)statistic are considered,but the nite sample studies show that they perform poor in power and size,respectively.An application to the Consumer Price Index for nine countries is also presented.展开更多
A coal seam is thin compared to the wavelength of seismic waves and usually shows strong anisotropy.It may form special geological formations,such as goafs and collapses,in coal mines.The existence of these formations...A coal seam is thin compared to the wavelength of seismic waves and usually shows strong anisotropy.It may form special geological formations,such as goafs and collapses,in coal mines.The existence of these formations may lead to instability in numerical simulations of the goaf area in a coal seam.The calculation speed of simulations is always a factor that restricts the development of simulation techniques.To improve the accuracy and effi ciency of seismic numerical simulations of goaf areas,an improved vacuum method has been incorporated into a rotated staggered grid scheme and calculations implemented by combining parallel computing and task parallelism.This ensures that the proposed numerical simulation method can be utilized in a geological model with large differences in elastic parameters among layers and improve the performance of a parallel application by enabling the full use of processor resources to expedite the calculations.We set up anisotropic coal seam models and then analyze numerically the characteristics of synthetic seismograms and snapshots of diff erent goaf areas with or without collapse.The results show that the proposed method can accurately simulate the goaf area and the calculation method can run with a high speed and parallel efficiency.The research will further advance the technology of anisotropic seismic exploration in coal fi elds,provide data for seismic inversion and build a theoretical support for coal mine disaster prediction.展开更多
Wavefield extrapolation is critical in reverse time migration(RTM).The finite diff erence method is primarily used to achieve wavefi eld extrapolation in case of the RTM imaging of tunnels.However,complex tunnel model...Wavefield extrapolation is critical in reverse time migration(RTM).The finite diff erence method is primarily used to achieve wavefi eld extrapolation in case of the RTM imaging of tunnels.However,complex tunnel models,including those for karsts and fault fracture zones,are constructed using regular grids with straight curves,which can cause numerical dispersion and reduce the imaging accuracy.In this study,wavefi eld extrapolation was conducted for tunnel RTM using the finite element method,wherein an unstructured mesh was considered to be the body-fi tted partition in a complex model.Further,a Poynting vector calculation equation suitable for the unstructured mesh considered in the fi nite element method was established to suppress the interference owing to low-frequency noise.The tunnel space was considered during wavefi eld extrapolation to suppress the mirror artifacts based on the fl exibility of mesh generation.Finally,the infl uence of the survey layouts(one and two sidewalls)on the tunnel imaging results was investigated.The RTM results obtained for a simple tunnel model with an inclined interface demonstrate that the method based on unstructured meshes can effectively suppress the low-frequency noise and mirror artifacts,obtaining clear imaging results.Furthermore,the two-sidewall tunnel survey layout can be used to accurately obtain the real position of the inclined interface ahead of the tunnel face.The complex tunnel numerical modeling and actual data migration results denote the eff ectiveness of the fi nite element method in which an unstructured mesh is used.展开更多
For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Gr...For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.展开更多
As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of pos...As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.展开更多
In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis,...In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.展开更多
This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hy...This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hypersurfaces are convex and of finite type.As applications,we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrodinger equations.展开更多
This study presents numerical and experimental models for the analysis of the excavation of soft soils by means of a cutting tool.The computational model is constructed using an Updated Lagrangean(UL)velocity-based Fi...This study presents numerical and experimental models for the analysis of the excavation of soft soils by means of a cutting tool.The computational model is constructed using an Updated Lagrangean(UL)velocity-based Finite Element approach.A hypoplastic formu-lation is employed to describe the constitutive behavior of soft soils.Large displacements and deformations of the ground resulting from the cutting tool-soil interaction are handled by means of the Particle Finite Element method,characterized by a global re-meshing strat-egy and a boundary identification procedure called a-shape technique.The capabilities and performance of the proposed model are demonstrated through comparative analyses between experiments and simulations of cutting tool-soft soil interactions.The experiments are performed using an excavation device at Ruhr-Universita¨t Bochum(RUB),Germany.The main details concerning the setup and calibration and evolution of the measured draft forces are discussed.Selected computational results characterizing the cutting tool-soft soil interaction including the topology of the free surface,void ratio distribution ahead of the tool,spatio-temporal evolution of the reaction forces and abrasive wear behavior are evaluated.展开更多
The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented,and then a new type of the iteration algorithm is established for the Poisson equatio...The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented,and then a new type of the iteration algorithm is established for the Poisson equation.The new algorithm has not only the obvious property of parallelism,but also faster convergence rate than that of the classical Jacobi iteration.Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision,and the computational velocity increases obviously when the new iterative method,instead of Jacobi method,is applied to polish operation in multi-grid method,furthermore,the polynomial acceleration method is still applicable to the new iterative method.展开更多
We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal d...We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.展开更多
In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,...In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,the two tangent components of the displacement are discretized by using conformingfinite elements(linear element),and the normal component of the displacement is discretized by us-ing conforming Hsieh-Clough-Tocher element(HCT element).Then,the existence,uniqueness,stability,convergence and a priori error estimate of the corresponding analyses are proven and analyzed.Finally,we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.展开更多
Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large...Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large class of exist-ing mixed conformingfinite elements for elasticity in the spatial discretization.In the fully discrete scheme,a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables.Error estimates of the semi-discrete and fully discrete schemes,as well as an unconditional stability result for the fully discrete scheme,are derived.Numerical experiments are provided to verify the theoretical results.展开更多
文摘In this paper,we consider the positive definiteness of fourth-order partially symmetric tensors.First,two analytically sufficient and necessary conditions of positive definiteness are provided for fourth-order two dimensional partially symmetric tensors.Then,we obtain several sufficient conditions for rank-one positive definiteness of fourth-order three dimensional partially symmetric tensors.
文摘NITE(nano-infiltration and transient eutectic)工艺作为一种制备碳化硅纤维增强碳化硅基(SiCf/SiC)复合材料的新方法,具备周期短、工艺简单、生产成本低等优点,制备出的复合材料基体致密、孔隙率低、不含残余硅,适用于1400℃及以上高温长时服役环境应用。目前,日本、美国等国家基于其成熟的第三代碳化硅纤维,对该技术开展了较为深入的研究,并在核能工业热交换器、航空发动机燃烧室衬套等领域进行了应用验证。本文针对NITE工艺从基本概念、工艺流程、制备的SiCf/SiC复合材料和构件考核验证及前景展望四方面进行综合阐述,以期为国内该工艺的发展及应用提供一定程度的参考。
文摘Based on the quantile regression,we extend Koenker and Xiao(2004)and Ling and McAleer(2004)'s works from nite-variance innovations to in nite-variance innovations.A robust t-ratio statistic to test for unit-root and a re-sampling method to approximate the critical values of the t-ratio statistic are proposed in this paper.It is shown that the limit distribution of the statistic is a functional of stable processes and a Brownian bridge.The nite sample studies show that the proposed t-ratio test always performs signi cantly better than the conventional unit-root tests based on least squares procedure,such as the Augmented Dick Fuller(ADF)and Philliphs-Perron(PP)test,in the sense of power and size when in nitevariance disturbances exist.Also,quantile Kolmogorov-Smirnov(QKS)statistic and quantile Cramer-von Mises(QCM)statistic are considered,but the nite sample studies show that they perform poor in power and size,respectively.An application to the Consumer Price Index for nine countries is also presented.
基金This work was supported by the National Natural Science Foundation of China(Nos.41304105 and 41674135)the Natural Science Foundation of Shaanxi province(No.2016JM4010).
文摘A coal seam is thin compared to the wavelength of seismic waves and usually shows strong anisotropy.It may form special geological formations,such as goafs and collapses,in coal mines.The existence of these formations may lead to instability in numerical simulations of the goaf area in a coal seam.The calculation speed of simulations is always a factor that restricts the development of simulation techniques.To improve the accuracy and effi ciency of seismic numerical simulations of goaf areas,an improved vacuum method has been incorporated into a rotated staggered grid scheme and calculations implemented by combining parallel computing and task parallelism.This ensures that the proposed numerical simulation method can be utilized in a geological model with large differences in elastic parameters among layers and improve the performance of a parallel application by enabling the full use of processor resources to expedite the calculations.We set up anisotropic coal seam models and then analyze numerically the characteristics of synthetic seismograms and snapshots of diff erent goaf areas with or without collapse.The results show that the proposed method can accurately simulate the goaf area and the calculation method can run with a high speed and parallel efficiency.The research will further advance the technology of anisotropic seismic exploration in coal fi elds,provide data for seismic inversion and build a theoretical support for coal mine disaster prediction.
基金supported by the National Natural Science Foundation of China (Nos. 41804145, 41704146)Natural Science Foundation of Hebei Province (No. D2018210168)Project of Hebei Province Higher Educational Science and Technology Program (No.QN2019185)。
文摘Wavefield extrapolation is critical in reverse time migration(RTM).The finite diff erence method is primarily used to achieve wavefi eld extrapolation in case of the RTM imaging of tunnels.However,complex tunnel models,including those for karsts and fault fracture zones,are constructed using regular grids with straight curves,which can cause numerical dispersion and reduce the imaging accuracy.In this study,wavefi eld extrapolation was conducted for tunnel RTM using the finite element method,wherein an unstructured mesh was considered to be the body-fi tted partition in a complex model.Further,a Poynting vector calculation equation suitable for the unstructured mesh considered in the fi nite element method was established to suppress the interference owing to low-frequency noise.The tunnel space was considered during wavefi eld extrapolation to suppress the mirror artifacts based on the fl exibility of mesh generation.Finally,the infl uence of the survey layouts(one and two sidewalls)on the tunnel imaging results was investigated.The RTM results obtained for a simple tunnel model with an inclined interface demonstrate that the method based on unstructured meshes can effectively suppress the low-frequency noise and mirror artifacts,obtaining clear imaging results.Furthermore,the two-sidewall tunnel survey layout can be used to accurately obtain the real position of the inclined interface ahead of the tunnel face.The complex tunnel numerical modeling and actual data migration results denote the eff ectiveness of the fi nite element method in which an unstructured mesh is used.
基金Supported by Special Projects in Key Fields of Colleges and Universities in Guangdong Province(2022ZDZX3016)Projects of Talents Recruitment of GDUPT.
文摘For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.
基金Supported by the National Natural Science Foundation of China(11671350,11571173,11801043)Natural Science Foundation for Youths of Jiangsu Province(BK20181031).
文摘As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevinsky[7],in this paper,we give a test method of positive definite matrices via the planar networks and the so-called mixing-type sub-cluster algebras respectively,introduced here originally.This work firstly gives a combinatorial realization of all matrices through planar network,and then sets up a test method for positive definite matrices by LDU-decompositions and the horizontal weightings of all lines in their planar networks.On the other hand,mainly the relationship is built between positive definite matrices and mixing-type sub-cluster algebras.
文摘In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.
基金supported by NSFC(No.12471092)the Natural Science Foundation of Hubei Province(No.2023AFB1056)。
文摘This paper studies the H^(p)-H^(q)estimates of a class of oscillatory integrals related to dispersive equations{i■_(t)u_(t,x)=Q(D)(t,x),(t,x)■R×R^(n),u(0,x)=u_(0)(x),x■R,,under the assumption that the level hypersurfaces are convex and of finite type.As applications,we obtain the decay estimates for the solutions of higher order homogeneous and inhomogeneous Schrodinger equations.
文摘This study presents numerical and experimental models for the analysis of the excavation of soft soils by means of a cutting tool.The computational model is constructed using an Updated Lagrangean(UL)velocity-based Finite Element approach.A hypoplastic formu-lation is employed to describe the constitutive behavior of soft soils.Large displacements and deformations of the ground resulting from the cutting tool-soil interaction are handled by means of the Particle Finite Element method,characterized by a global re-meshing strat-egy and a boundary identification procedure called a-shape technique.The capabilities and performance of the proposed model are demonstrated through comparative analyses between experiments and simulations of cutting tool-soft soil interactions.The experiments are performed using an excavation device at Ruhr-Universita¨t Bochum(RUB),Germany.The main details concerning the setup and calibration and evolution of the measured draft forces are discussed.Selected computational results characterizing the cutting tool-soft soil interaction including the topology of the free surface,void ratio distribution ahead of the tool,spatio-temporal evolution of the reaction forces and abrasive wear behavior are evaluated.
文摘The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented,and then a new type of the iteration algorithm is established for the Poisson equation.The new algorithm has not only the obvious property of parallelism,but also faster convergence rate than that of the classical Jacobi iteration.Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision,and the computational velocity increases obviously when the new iterative method,instead of Jacobi method,is applied to polish operation in multi-grid method,furthermore,the polynomial acceleration method is still applicable to the new iterative method.
基金The author gratefully acknowledges valuable support provided by the Department of Mathematics,NIT Calicut and the DST,Government of India,for providing support to carry out this work under the scheme TIST(No.SR/FST/MS-I/2019/40).
文摘We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.
基金supported by the National Natural Science Foundation of China(NSFC Nos.11971379,12071149)the Natural Science Foundation of Shanghai(Grant No.19ZR1414100)。
文摘In this paper,we propose a conformingfinite element method coupling penalty method for the linearly elasticflexural shell to overcome computational dif-ficulties.We start with discretizing the displacement variable,i.e.,the two tangent components of the displacement are discretized by using conformingfinite elements(linear element),and the normal component of the displacement is discretized by us-ing conforming Hsieh-Clough-Tocher element(HCT element).Then,the existence,uniqueness,stability,convergence and a priori error estimate of the corresponding analyses are proven and analyzed.Finally,we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.
基金supported in part by National Natural Science Foundation of China(No.11771312).
文摘Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large class of exist-ing mixed conformingfinite elements for elasticity in the spatial discretization.In the fully discrete scheme,a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables.Error estimates of the semi-discrete and fully discrete schemes,as well as an unconditional stability result for the fully discrete scheme,are derived.Numerical experiments are provided to verify the theoretical results.
