A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guarante...A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guaranteed to converge. Examples are given to illustrate its efficiency.展开更多
A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element nod...A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).展开更多
In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,...During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,road connectivity,展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual...This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual element.The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time.We prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete schemes.After introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and proved.Finally,two numerical examples are investigated to confirm our theoretical analysis.展开更多
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,whic...Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,which controls the error of two discrete finite element solutions based on two nested triangulations.In the error analysis of nonconforming finite element methods,like the Crouzeix-Raviart or Morley finite element schemes,the difference of the piecewise derivatives of discontinuous approximations to the distributional gradients of global Sobolev functions plays a dominant role and is the object of this paper.The nonconforming interpolation operator,which comes natural with the definition of the aforementioned nonconforming finite element in the sense of Ciarlet,allows for stability and approximation properties that enable direct proofs of the reliability for the residual that monitors the equilibrium condition.The novel approach of this paper is the suggestion of a right-inverse of this interpolation operator in conforming piecewise polynomials to design a nonconforming approximation of a given coarse-grid approximation on a refined triangulation.The results of this paper allow for simple proofs of the discrete reliability in any space dimension and multiply connected domains on general shape-regular triangulations beyond newest-vertex bisection of simplices.Particular attention is on optimal constants in some standard discrete estimates listed in the appendices.展开更多
H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximat...H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.展开更多
This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used...This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used to describe the deformation of elastomer. In this paper we consider the 3D models as objects with elasticity. The further demonstrations are provided： the first is intended to give the reader a visual impression of how our measure works in practice; and the second is to give readers a visual impression of how our measure works in evaluating filter algorithms. Our experiments show that our difference estimates are well correlated with human perception of differences. This work has applications in the evaluation of 3D mesh watermarking, 3D mesh compression reconstruction, and 3D mesh filtering.展开更多
Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a pos...Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.展开更多
The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the ...The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.展开更多
In this study,the design,analysis,manufacturing,and testing of a 3D-printed conformal microstrip array antenna for high-temperature environments is presented.3D printing technology is used to fabricate a curved cerami...In this study,the design,analysis,manufacturing,and testing of a 3D-printed conformal microstrip array antenna for high-temperature environments is presented.3D printing technology is used to fabricate a curved ceramic substrate,and laser sintering and microdroplet spraying processes are used to add the conductive metal on the curved substrate.The problems of gain loss,bandwidth reduction,and frequency shift caused by high temperatures are addressed by using a proper antenna design,with parasitic patches,slots,and metal resonant cavities.The antenna prototype is characterized by the curved substrates and the conductive metals for the power dividers,the patch,and the ground plane;its performance is examined up to a temperature of 600℃in a muffle furnace and compared with the results from the numerical analysis.The results show that the antenna can effectively function at 600℃and even higher temperatures.展开更多
Much is said of China’s judicial system and much more remains conspicuously unsaid,but recent changes have seen promising reforms for the state’s beleaguered court system.For starters,the authorities are beginning t...Much is said of China’s judicial system and much more remains conspicuously unsaid,but recent changes have seen promising reforms for the state’s beleaguered court system.For starters,the authorities are beginning to take notice that judges,those on the front lines of dispensing-justice,are underpaid,overworked,and unappreciated.There’s also the rather troubling matter of jurisdiction,but recent changes have provided more provincial展开更多
基金Supported by the Science Technology Development Program of Beijing Municipal Education Commission (KM200510011004)
文摘A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guaranteed to converge. Examples are given to illustrate its efficiency.
文摘A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).
基金The rescarch was supported by the Doctoral Point Foundation of chinese Universities and NSF
文摘In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
文摘During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,road connectivity,
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
基金supported by the NSF of China(Grant Nos.11801527,11701522,11771163,11671160,1191101330)by the China Postdoctoral Science Foundation(Grant No.2018M632791)by the Key Scientific Research Projects of Higher Eduction of Henan(Grant No.19A110034).
文摘This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual element.The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time.We prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete schemes.After introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and proved.Finally,two numerical examples are investigated to confirm our theoretical analysis.
文摘Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,which controls the error of two discrete finite element solutions based on two nested triangulations.In the error analysis of nonconforming finite element methods,like the Crouzeix-Raviart or Morley finite element schemes,the difference of the piecewise derivatives of discontinuous approximations to the distributional gradients of global Sobolev functions plays a dominant role and is the object of this paper.The nonconforming interpolation operator,which comes natural with the definition of the aforementioned nonconforming finite element in the sense of Ciarlet,allows for stability and approximation properties that enable direct proofs of the reliability for the residual that monitors the equilibrium condition.The novel approach of this paper is the suggestion of a right-inverse of this interpolation operator in conforming piecewise polynomials to design a nonconforming approximation of a given coarse-grid approximation on a refined triangulation.The results of this paper allow for simple proofs of the discrete reliability in any space dimension and multiply connected domains on general shape-regular triangulations beyond newest-vertex bisection of simplices.Particular attention is on optimal constants in some standard discrete estimates listed in the appendices.
基金Foundation item： the National Natural Science Foundation of China （Nos. 10671184 10371113）.
文摘H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.
基金supported by the National Basic Research 973 Program of China under Grant No.2006CB303104the National Natural Science Foundation of China under Grant No.60673004an EPSRC Travel Grant.
文摘This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used to describe the deformation of elastomer. In this paper we consider the 3D models as objects with elasticity. The further demonstrations are provided： the first is intended to give the reader a visual impression of how our measure works in practice; and the second is to give readers a visual impression of how our measure works in evaluating filter algorithms. Our experiments show that our difference estimates are well correlated with human perception of differences. This work has applications in the evaluation of 3D mesh watermarking, 3D mesh compression reconstruction, and 3D mesh filtering.
基金supported by National Natural Science Foundation of China(Grant Nos.11201093 and 11161012)
文摘Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.
基金supported by the National Natural Science Foundation of China(Grant Nos.11402015,11872090&11672019)。
文摘The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.
基金National Natural Science Foundation of china(No.U2241205)the Natural Science Basic Research Program of Shaanxi(Nos.2022JC-33,2023-GHZD-35,and 2024JC-ZDXM-25)+1 种基金the Fundamental Research Funds for the Central Universitiesthe National 111 Project to provide fund for conducting experiments。
文摘In this study,the design,analysis,manufacturing,and testing of a 3D-printed conformal microstrip array antenna for high-temperature environments is presented.3D printing technology is used to fabricate a curved ceramic substrate,and laser sintering and microdroplet spraying processes are used to add the conductive metal on the curved substrate.The problems of gain loss,bandwidth reduction,and frequency shift caused by high temperatures are addressed by using a proper antenna design,with parasitic patches,slots,and metal resonant cavities.The antenna prototype is characterized by the curved substrates and the conductive metals for the power dividers,the patch,and the ground plane;its performance is examined up to a temperature of 600℃in a muffle furnace and compared with the results from the numerical analysis.The results show that the antenna can effectively function at 600℃and even higher temperatures.
文摘Much is said of China’s judicial system and much more remains conspicuously unsaid,but recent changes have seen promising reforms for the state’s beleaguered court system.For starters,the authorities are beginning to take notice that judges,those on the front lines of dispensing-justice,are underpaid,overworked,and unappreciated.There’s also the rather troubling matter of jurisdiction,but recent changes have provided more provincial
