Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v...Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.展开更多
Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent fl...Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent flow controlled by large eddy,in which the effect of small eddy could be negligible as an approximation.The grid dimension could easily satisfy the resolution requirement to describe the characteristics of a large eddy flow.Therefore,direct numerical simulation of N-S equations to obtain the turbulent flow field on the coarse grid could be realized.Numerical simulation of a two-dimensional flow over a backward-facing step at a Reynolds number Re=44000 was conducted using Euler-Lagrange finite element scheme based on the efficient operator-splitting method(OSFEM).The flow field was descretized by triangle meshes with 16669 nodes.The overall computational time only took 150 min on a PC.Both the characteristics of time-averaged and instantaneous turbulent flow were simultaneously obtained.The analysis showed that the calculated results were in good agreement with the test data.Hence,the DNS approach could become the reality to solve the complex turbulent flow with high Reynolds numbers in practical engineering.展开更多
We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a...We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.展开更多
Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-...Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible(ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties(angle and area)of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.展开更多
Immersed boundary method is a crucial method to deal with particle suspension flow.Particle shapes involved in such flow are usually simple geometry,such as sphere and ellipsoid,which can be conveniently represented b...Immersed boundary method is a crucial method to deal with particle suspension flow.Particle shapes involved in such flow are usually simple geometry,such as sphere and ellipsoid,which can be conveniently represented by the triangular surface grid.When the number of particles and resolution of the surface grid increase,calculating the hydrodynamic force on the particle surface through integration can be time-consuming.Hence,the present paper establishes a fast mapping method to evaluate immersed boundary hydrodynamic force.Firstly,the particle surface grid is generated by an initial triangular element grid.Subsequently,the initial surface grid is refined by bisection refinement to the desired resolution.The final step is to find the triangular element index on the particle triangular surface grid,which contains the projective point.Test cases show that the present mapping algorithm has good accuracy and efficiency for calculating hydrodynamic forces of particles.展开更多
This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test f...This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.展开更多
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
文摘Given a graph G and a positive integer d, an L( d, 1) -labeling of G is afunction / that assigns to each vertex of G a non-negative integer such that |f(u)-f (v) | >=d ifd_c(u, v) =1;|f(u)-f(v) | >=1 if d_c(u, v) =2. The L(d, 1)-labeling number of G, lambda_d(G) is theminimum range span of labels over all such labelings, which is motivated by the channel assignmentproblem. We consider the question of finding the minimum edge span beta_d( G) of this labeling.Several classes of graphs such as cycles, trees, complete k-partite graphs, chordal graphs includingtriangular lattice and square lattice which are important to a telecommunication problem arestudied, and exact values are given.
基金supported by the Major National Science and Technology Projects of China (Grant No. 2012ZX07506003)the Public Research and Development Project for Water Resource (Grant No. 201001030)
文摘Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent flow controlled by large eddy,in which the effect of small eddy could be negligible as an approximation.The grid dimension could easily satisfy the resolution requirement to describe the characteristics of a large eddy flow.Therefore,direct numerical simulation of N-S equations to obtain the turbulent flow field on the coarse grid could be realized.Numerical simulation of a two-dimensional flow over a backward-facing step at a Reynolds number Re=44000 was conducted using Euler-Lagrange finite element scheme based on the efficient operator-splitting method(OSFEM).The flow field was descretized by triangle meshes with 16669 nodes.The overall computational time only took 150 min on a PC.Both the characteristics of time-averaged and instantaneous turbulent flow were simultaneously obtained.The analysis showed that the calculated results were in good agreement with the test data.Hence,the DNS approach could become the reality to solve the complex turbulent flow with high Reynolds numbers in practical engineering.
基金supported by the National Natural Science Foundation of China (No. 60773179)the National Basic Research Program (973) of China (No. 2004CB318000)
文摘We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.
基金supported by the National Natural Science Foundation of China(Nos.61432003,61572105,11171052,and 61328206)
文摘Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible(ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties(angle and area)of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51636009 and 52006212)Chinese Academy of Sciences(Grant Nos.ZDBS-LY-JSC033 and XDB22040201).
文摘Immersed boundary method is a crucial method to deal with particle suspension flow.Particle shapes involved in such flow are usually simple geometry,such as sphere and ellipsoid,which can be conveniently represented by the triangular surface grid.When the number of particles and resolution of the surface grid increase,calculating the hydrodynamic force on the particle surface through integration can be time-consuming.Hence,the present paper establishes a fast mapping method to evaluate immersed boundary hydrodynamic force.Firstly,the particle surface grid is generated by an initial triangular element grid.Subsequently,the initial surface grid is refined by bisection refinement to the desired resolution.The final step is to find the triangular element index on the particle triangular surface grid,which contains the projective point.Test cases show that the present mapping algorithm has good accuracy and efficiency for calculating hydrodynamic forces of particles.
基金This research is supported by the ＇985＇ programme of Jilin University, the National Natural Science Foundation of China under Grant Nos. 10971082 and 11076014.
文摘This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
