Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the p...Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to <em>X</em>. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.展开更多
Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmi...Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.展开更多
Identifying vital nodes is a basic problem in social network research.The existing theoretical framework mainly focuses on the lowerorder structure of node-based and edge-based relations and often ignores important fa...Identifying vital nodes is a basic problem in social network research.The existing theoretical framework mainly focuses on the lowerorder structure of node-based and edge-based relations and often ignores important factors such as interactivity and transitivity between multiple nodes.To identify the vital nodes more accurately,a high-order structure,named as the motif,is introduced in this paper as the basic unit to evaluate the similarity among the node in the complex network.It proposes a notion of high-order degree of nodes in complex network and fused the effect of the high-order structure and the lower-order structure of nodes,using evidence theory to determine the vital nodes more efficiently and accurately.The algorithm was evaluated from the function of network structure.And the SIR model was adopted to examine the spreading influence of the nodes ranked.The results of experiments in different datasets demonstrate that the algorithm designed can identify vital nodes in the social network accurately.展开更多
文摘Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to <em>X</em>. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.
文摘Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.
基金the Natural Science Foundation of China(No.61662066,61163010).
文摘Identifying vital nodes is a basic problem in social network research.The existing theoretical framework mainly focuses on the lowerorder structure of node-based and edge-based relations and often ignores important factors such as interactivity and transitivity between multiple nodes.To identify the vital nodes more accurately,a high-order structure,named as the motif,is introduced in this paper as the basic unit to evaluate the similarity among the node in the complex network.It proposes a notion of high-order degree of nodes in complex network and fused the effect of the high-order structure and the lower-order structure of nodes,using evidence theory to determine the vital nodes more efficiently and accurately.The algorithm was evaluated from the function of network structure.And the SIR model was adopted to examine the spreading influence of the nodes ranked.The results of experiments in different datasets demonstrate that the algorithm designed can identify vital nodes in the social network accurately.
