Study on Coordinated Development of Regions Based on the Construction of Enterprise Value Network

Under the background of constructing harmonious economic society, how to realize the coordinated development of regions in the course of region integration is a key problem. According to the relevant theory of enterprise gene reconfiguration and enterprise value network construction, we analyzed the problems in the merging course between the value network construction and region economic growth. Finally, we put forward the basic path of coordinated development of regions.

Mesh Deformation Method Based on Mean Value Coordinates Interpolation

Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.

Robust Mesh Smoothing

This paper proposes a vertex-estimation-based, feature-preserving smoothingtechnique for meshes. A robust mesh smoothing operator called mean value coordinates flow isintroduced to modify mean curvature flow and make it more stable. Also the paper proposes athree-pass vertex estimation based on bilateral filtering of local neighbors which is transferredfrom image processing settings and a Quasi-Laplacian operation, derived from the standard Laplacianoperator, is performed to increase the smoothness order of the mesh rapidly whilst denoising meshesefficiently, preventing volume shrinkage as well as preserving sharp features of the mesh. Comparedwith previous algorithms, the result shows it is simple, efficient and robust.

Rigidity Constraints for Large Mesh Deformation

It is a challenging problem of surface-based deformation to avoid apparent volumetric distortions around largely deformed areas. In this paper, we propose a new rigidity constraint for gradient domain mesh deformation to address this problem. Intuitively the proposed constraint can be regarded as several small cubes defined by the mesh vertices through mean value coordinates. The user interactively specifies the cubes in the regions which are prone to volumetric distortions, and the rigidity constraints could make the mesh behave like a solid object during deformation. The experimental results demonstrate that our constraint is intuitive, easy to use and very effective.

Rational Quasi-Interpolation Approximation of Scattered Data in R^(3)

This paper is concerned with a piecewise smooth rational quasi-interpolation with algebraic accuracy of degree(n+1)to approximate the scattered data in R 3.We firstly use the modified Taylor expansion to expand the mean value coordinates interpolation with algebraic accuracy of degree one to one with algebraic accuracy of degree(n+1).Then,based on the triangulation of the scattered nodes in R^(2),on each triangle a rational quasi-interpolation function is constructed.The constructed rational quasi-interpolation is a linear combination of three different expanded mean value coordinates interpolations and it has algebraic accuracy of degree(n+1).By comparing accuracy,stability,and efficiency with the C^(1)-Tri-interpolation method of Goodman[16]and the MQ Shepard method,it is observed that our method has some computational advantages.

An h-adaptive numerical manifold method for solid mechanics problems

The numerical manifold method(NMM) features its dual cover systems, namely the mathematical cover and physical cover,which provide a unified framework for mechanics problems involving continuum and discontinuum deformation. Uniform finite element meshes can be and are usually used to construct the mathematical cover. Though this strategy can handle different kinds of problems in a unified way, it is not economical for cases with steep deformation gradients or singularities. In this paper, using the recovery-based error estimator, an h-adaptive NMM on quadtree meshes is proposed to deal with such cases. The quadtree meshes serve as the mathematical meshes, on which the local refinement is carried out. When the quadtree meshes are refined,the corresponding mathematical cover, physical cover and manifold elements are updated accordingly. To handle the hanging nodes in the quadtree meshes, we resort to mean value coordinates. Comparing to the refinement based on manifold elements,the proposed strategy guarantees consistent structured meshes throughout the adaptive process, thus retaining the unique feature of original NMM. In contrast with polygonal finite element method, an advantage of the proposed method is that the meshes do not need to conform to the crack face and material boundary, which means the adaptive NMM is very suitable for problems with complex geometric boundary. Several representative mechanics problems, including crack problems, are analyzed to investigate the effectiveness of the proposed method. It is demonstrated that the proposed adaptive NMM has higher accuracy and better performance comparing to uniform refinement strategy.