In this paper, we propose an optical burst network architecture supporting the ge- netic mesh topology. The intermediate node architecture of the mesh network can be the same with current wavelength switching Wave- le...In this paper, we propose an optical burst network architecture supporting the ge- netic mesh topology. The intermediate node architecture of the mesh network can be the same with current wavelength switching Wave- length Division Multiplexing （WDM） net- works, and thus can reuse existing deployed infrastructure. We employ a novel Optical Time Slot Interchange （OTSI） at the source nodes for the first time to mitigate the burst conten- tion and to increase the bandwidth utilization. Time- and wavelength-domain reuse in the OTSI significantly saves optical components and red- uces blocking probability.展开更多
To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified f...To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified for essential boundary condition, can make the trail function pass through these nodes. And then, the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM. The MLS method is adopted to validate this method, and it is proved that this method is eostless and robust in most of mesh-less methods.展开更多
In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In ...In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.展开更多
Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committe...Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.展开更多
文摘In this paper, we propose an optical burst network architecture supporting the ge- netic mesh topology. The intermediate node architecture of the mesh network can be the same with current wavelength switching Wave- length Division Multiplexing （WDM） net- works, and thus can reuse existing deployed infrastructure. We employ a novel Optical Time Slot Interchange （OTSI） at the source nodes for the first time to mitigate the burst conten- tion and to increase the bandwidth utilization. Time- and wavelength-domain reuse in the OTSI significantly saves optical components and red- uces blocking probability.
文摘To improve the treatment efficiency of essential boundary condition in mesh-less methods, a simple and robust method is proposed in this paper. Rising weight of nodes in the construction of trail function, specified for essential boundary condition, can make the trail function pass through these nodes. And then, the trail function can satisfy the essential boundary condition previously by setting diagonal element to 1 or multiplying diagonal element by a big number in FEM. The MLS method is adopted to validate this method, and it is proved that this method is eostless and robust in most of mesh-less methods.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100)the National Natural Science Foundation of China(Grant Nos.11572009&51538001)
文摘In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.
文摘Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.
