In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the ex...In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.展开更多
The random packing of tetrahedral particles is studied by applying the discrete element method （DEM）, which simulates the effects of friction, height ratio, and eccentricity. The model predictions are ana- lyzed in ...The random packing of tetrahedral particles is studied by applying the discrete element method （DEM）, which simulates the effects of friction, height ratio, and eccentricity. The model predictions are ana- lyzed in terms of packing density and coordination number （CN）. It is demonstrated that friction has the maximal effect on packing density and mean CN among the three parameters. The packing den- sity of the regular tetrahedron is 0.71 when extrapolated to a zero friction effect. The shape effects of height ratio and eccentricity show that the regular tetrahedron has the highest packing density in the family of tetrahedra, which is consistent with what has been reported in the literature. Compared with geometry-based packing algorithms, the DEM packing density is much lower. This demonstrates that the inter-particle mechanical forces have a considerable effect on packing. The DEM results agree with the published experimental results, indicating that the polyhedral DEM model is suitable for simulating the random packing of tetrahedral particles.展开更多
A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated b...A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.展开更多
In this article,a family of H^2-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3 D.In the family,the Pl polynomial space is enriched by some high order polynom...In this article,a family of H^2-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3 D.In the family,the Pl polynomial space is enriched by some high order polynomials for all l≥3 and the corresponding finite element solution converges at the order l-1 in H2 norm.Moreover,the result is improved for two low order cases by using P6 and P7 polynomials to enrich P4 and P5 polynomial spaces,respectively.The error estimate is proved.The numerical results are.provided to confirm the theoretical findings.展开更多
A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec elements. The shape functions are classified into several categories with respect to their ...A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec elements. The shape functions are classified into several categories with respect to their topological entities on the reference 3-simplex. The basis functions in each category are constructed to achieve maximum orthogonaiity. The numerical study on the matrix conditioning shows that for the mass and quasi-stiffness matrices, and in a logarithmic scale the condition number grows linearly vs. order of approximation up to order three. For each order of approximation, the condition number of the quasi-stiffness matrix is about one order less than the corresponding one for the mass matrix. Also, up to order six of approximation the conditioning of the mass and quasi- stiffness matrices with the proposed basis is better than the corresponding one with the Ainsworth-Coyle basis Internat. J. Numer. Methods. Engrg., 58：2103-2130, 2003. except for order four with the quasi-stiffness matrix. Moreover, with the new basis the composite matrix μM ＋ S has better conditioning than the Ainsworth-Coyle basis for a wide range of the parameter μ.展开更多
A partition of unity(PU) based four-node tetrahedral element with continuous nodal stress(Tetr4-CNS) was recently proposed for static analysis of three-dimensional solids. By simply using the same mesh as the classica...A partition of unity(PU) based four-node tetrahedral element with continuous nodal stress(Tetr4-CNS) was recently proposed for static analysis of three-dimensional solids. By simply using the same mesh as the classical four-node tetrahedral(Tetr4)element, high order global approximation function in the Tetr4-CNS element can be easily constructed without extra nodes or nodal DOFs. In this paper, the Tetr4-CNS element is further applied in the analysis of three dimensional dynamic problems. A series of free vibration and forced vibration problems are solved using the Tetr4-CNS element. The numerical results show that,for regular meshes, accuracy obtained using the Tetr4-CNS element is superior to that obtained using the Tetr4 and eight-node hexahedral(Hexa8) elements. For distorted meshes, the Tetr4-CNS element has better mesh-distortion tolerance than both the Tetr4 and Hexa8 elements.展开更多
In this paper,we construct a tetrahedral element named DST20 for the three dimensional Darcy-Stokes problem,which reduces the degrees of velocity in [30].The finite element space Vh for velocity is H(div)-conforming,i...In this paper,we construct a tetrahedral element named DST20 for the three dimensional Darcy-Stokes problem,which reduces the degrees of velocity in [30].The finite element space Vh for velocity is H(div)-conforming,i.e.,the normal component of a function in Vh is continuous across the element boundaries,meanwhile the tangential component of a function in Vh is average continuous across the element boundaries,hence Vh is H^1- average conforming.We prove that this element is uniformly convergent with respect to the perturbation constant s for the Darcy-Stokes problem.At the same time,we give a discrete de Rham complex corresponding to DST20 element.展开更多
针对三维推进波前算法(AFT-Advancing Front Technique)存在的效率与收敛性问题,文中提出了一整套改进方案,给出了基于拓扑连接的网格数据结构和基于Hash表的网格元素的插入、查找、删除算法,提高了整个算法的效率.通过在网格生成过程...针对三维推进波前算法(AFT-Advancing Front Technique)存在的效率与收敛性问题,文中提出了一整套改进方案,给出了基于拓扑连接的网格数据结构和基于Hash表的网格元素的插入、查找、删除算法,提高了整个算法的效率.通过在网格生成过程中动态维护前沿的尺寸信息,提高四面体单元的整体质量.在内核回退求解时通过引入前沿优先因子,改变前沿推进的路径,大大增加了回退求解的成功概率;对于极少数不能回退求解的内核采用基于线性规划的插点方法加以解决,这样就基本保证了整个算法的收敛.在网格生成以后,通过删除不必要的内部节点、合并相关四面体单元以及对所有内部节点进行基于角度的优化,从而进一步有效提高了网格质量.数值算例表明,文中提出的改进算法具有接近线性的时间复杂度,生成网格质量好.该算法已经得到工程应用.展开更多
对生成三维非结构化网格的D e launay方法进行了分析,给出四面体网格生成的基本步骤.改进判断非结构化网格质量的方法,提出采用四面体单元无量纲棱长的标准差对网格质量进行评价.对于已经生成的初始化网格,在棱长标准差最大的四面体单...对生成三维非结构化网格的D e launay方法进行了分析,给出四面体网格生成的基本步骤.改进判断非结构化网格质量的方法,提出采用四面体单元无量纲棱长的标准差对网格质量进行评价.对于已经生成的初始化网格,在棱长标准差最大的四面体单元内加入新点重新构造网格,反复进行迭代直到所有的标准差小于设定值.该方法比较灵活且易于实现.通过不同的算例对网格生成及改进方法进行了验证,获得了理想的结果.展开更多
基金the Boya postdoctoral fellowship from Peking University and the support fromthe China Postdoctoral Science Foundation(No.2023M740107)the Natural Science Starting Project of SWPU(No.2024QHZ030)+2 种基金the support from The Science and Technology Development Fund,Macao SAR(No.0068/2024/RIA1)National Natural Science Foundation of China(No.11922120)MYRG of University of Macao(No.MYRG-CRG2024-00042-FST).
文摘In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.
文摘The random packing of tetrahedral particles is studied by applying the discrete element method （DEM）, which simulates the effects of friction, height ratio, and eccentricity. The model predictions are ana- lyzed in terms of packing density and coordination number （CN）. It is demonstrated that friction has the maximal effect on packing density and mean CN among the three parameters. The packing den- sity of the regular tetrahedron is 0.71 when extrapolated to a zero friction effect. The shape effects of height ratio and eccentricity show that the regular tetrahedron has the highest packing density in the family of tetrahedra, which is consistent with what has been reported in the literature. Compared with geometry-based packing algorithms, the DEM packing density is much lower. This demonstrates that the inter-particle mechanical forces have a considerable effect on packing. The DEM results agree with the published experimental results, indicating that the polyhedral DEM model is suitable for simulating the random packing of tetrahedral particles.
基金supported by National Natural Science Foundation of China(Grant Nos.11271035,91430213 and 11421101)
文摘A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.
基金supported by National Natural Science Foundation of China(Grant Nos.11625101 and 11421101)。
文摘In this article,a family of H^2-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3 D.In the family,the Pl polynomial space is enriched by some high order polynomials for all l≥3 and the corresponding finite element solution converges at the order l-1 in H2 norm.Moreover,the result is improved for two low order cases by using P6 and P7 polynomials to enrich P4 and P5 polynomial spaces,respectively.The error estimate is proved.The numerical results are.provided to confirm the theoretical findings.
文摘A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec elements. The shape functions are classified into several categories with respect to their topological entities on the reference 3-simplex. The basis functions in each category are constructed to achieve maximum orthogonaiity. The numerical study on the matrix conditioning shows that for the mass and quasi-stiffness matrices, and in a logarithmic scale the condition number grows linearly vs. order of approximation up to order three. For each order of approximation, the condition number of the quasi-stiffness matrix is about one order less than the corresponding one for the mass matrix. Also, up to order six of approximation the conditioning of the mass and quasi- stiffness matrices with the proposed basis is better than the corresponding one with the Ainsworth-Coyle basis Internat. J. Numer. Methods. Engrg., 58：2103-2130, 2003. except for order four with the quasi-stiffness matrix. Moreover, with the new basis the composite matrix μM ＋ S has better conditioning than the Ainsworth-Coyle basis for a wide range of the parameter μ.
基金supported by the National Natural Science Foundation of China(Grant Nos.51609240,11572009,51538001,51579235&41472288)the National Basic Research Program of China(Grant No.2014CB047100)
文摘A partition of unity(PU) based four-node tetrahedral element with continuous nodal stress(Tetr4-CNS) was recently proposed for static analysis of three-dimensional solids. By simply using the same mesh as the classical four-node tetrahedral(Tetr4)element, high order global approximation function in the Tetr4-CNS element can be easily constructed without extra nodes or nodal DOFs. In this paper, the Tetr4-CNS element is further applied in the analysis of three dimensional dynamic problems. A series of free vibration and forced vibration problems are solved using the Tetr4-CNS element. The numerical results show that,for regular meshes, accuracy obtained using the Tetr4-CNS element is superior to that obtained using the Tetr4 and eight-node hexahedral(Hexa8) elements. For distorted meshes, the Tetr4-CNS element has better mesh-distortion tolerance than both the Tetr4 and Hexa8 elements.
基金the National Natural Science Foundation of China (No.11071226).
文摘In this paper,we construct a tetrahedral element named DST20 for the three dimensional Darcy-Stokes problem,which reduces the degrees of velocity in [30].The finite element space Vh for velocity is H(div)-conforming,i.e.,the normal component of a function in Vh is continuous across the element boundaries,meanwhile the tangential component of a function in Vh is average continuous across the element boundaries,hence Vh is H^1- average conforming.We prove that this element is uniformly convergent with respect to the perturbation constant s for the Darcy-Stokes problem.At the same time,we give a discrete de Rham complex corresponding to DST20 element.
文摘针对三维推进波前算法(AFT-Advancing Front Technique)存在的效率与收敛性问题,文中提出了一整套改进方案,给出了基于拓扑连接的网格数据结构和基于Hash表的网格元素的插入、查找、删除算法,提高了整个算法的效率.通过在网格生成过程中动态维护前沿的尺寸信息,提高四面体单元的整体质量.在内核回退求解时通过引入前沿优先因子,改变前沿推进的路径,大大增加了回退求解的成功概率;对于极少数不能回退求解的内核采用基于线性规划的插点方法加以解决,这样就基本保证了整个算法的收敛.在网格生成以后,通过删除不必要的内部节点、合并相关四面体单元以及对所有内部节点进行基于角度的优化,从而进一步有效提高了网格质量.数值算例表明,文中提出的改进算法具有接近线性的时间复杂度,生成网格质量好.该算法已经得到工程应用.
文摘对生成三维非结构化网格的D e launay方法进行了分析,给出四面体网格生成的基本步骤.改进判断非结构化网格质量的方法,提出采用四面体单元无量纲棱长的标准差对网格质量进行评价.对于已经生成的初始化网格,在棱长标准差最大的四面体单元内加入新点重新构造网格,反复进行迭代直到所有的标准差小于设定值.该方法比较灵活且易于实现.通过不同的算例对网格生成及改进方法进行了验证,获得了理想的结果.
