农牧业气象情报自动化处理系统

叙述了农牧业气象情报业务自动化的基础工作一信息接收与处理自动化的设计思想，在三角形网格等值线方法的基础上，提出了多边形网格的概念，系统介绍了多边形网格文件生成的过程，完成了线条对不规则边界的识别算法设计。

Edge span of L(d,1)-labeling on some graphs

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.

Positioning of grid points in wave front construction

In view of the relative positioning problem between non-regular quadrilateral grids and regular rectangle grid nodes in the wave front construction method, concrete realization problems with four grid positioning methods （vector cross product judgment, angle sum, intersection-point, and signs comparison algorithms） in wave front construction which are commonly used in computer graphics are compared and analyzed in this paper. Based on the stability analysis of the location method, the calculation examples show that the vector cross product judgment method is faster and more accurate than other methods in the realization of the relative positioning between non-regular quadrilateral grids and regular rectangle grid nodes in wave front construction. It provides precise grid point attribute values for the next steps of migration and demigration.

3D Engineering Model Retrieval Based on Enhanced Shape Distributions

To reuse and share the valuable knowledge embedded in repositories of engineering models for accelerating the design process, improving product quality, and reducing costs, it is crucial to devise search engines capable of matching 3D models efficiently and effectively. In this paper, an enhanced shape distributions-based technique of using geometrical and topological information to search 3D engineering models represented by polygonal meshes was presented. A simplification method of polygonal meshes was used to simplify engineering model as the pretreatment for generation of sample points. The method of sampling points was improved and a pair of functions that was more sensitive to shape was employed to construct a 2D shape distribution. Experiments were conducted to evaluate the proposed algorithm utilizing the Engineering Shape Benchmark (ESB) database. The experiential results suggest that the search effectiveness is significantly improved by enforcing the simplification and enhanced shape distributions to engineering model retrieval.

Equality Testing for Soil Grid Unit Resolutions to Polygon Unit Scales with DNDC Modeling of Regional SOC Pools

Matching soil grid unit resolutions with polygon unit map scales is important to minimize the uncertainty of regional soil organic carbon(SOC) pool simulation due to their strong influences on the modeling.A series of soil grid units at varying cell sizes was derived from soil polygon units at six map scales,namely,1:50 000(C5),1:200 000(D2),1:500 000(P5),1:1 000 000(N1),1:4 000 000(N4) and 1:14 000 000(N14),in the Taihu Region of China.Both soil unit formats were used for regional SOC pool simulation with a De Nitrification-DeC omposition(DNDC) process-based model,which spans the time period from 1982 to 2000 at the six map scales.Four indices,namely,soil type number(STN),area(AREA),average SOC density(ASOCD) and total SOC stocks(SOCS) of surface paddy soils that were simulated by the DNDC,were distinguished from all these soil polygon and grid units.Subjecting to the four index values(IV) from the parent polygon units,the variations in an index value(VIV,%) from the grid units were used to assess its dataset accuracy and redundancy,which reflects the uncertainty in the simulation of SOC pools.Optimal soil grid unit resolutions were generated and suggested for the DNDC simulation of regional SOC pools,matching their respective soil polygon unit map scales.With these optimal raster resolutions,the soil grid units datasets can have the same accuracy as their parent polygon units datasets without any redundancy,when VIV < 1% was assumed to be a criterion for all four indices.A quadratic curve regression model,namely,y = – 0.80 × 10^(–6)x^2 + 0.0228 x + 0.0211(R^2 = 0.9994,P < 0.05),and a power function model R? = 10.394?^(0.2153)(R^2 = 0.9759,P < 0.05) were revealed,which describe the relationship between the optimal soil grid unit resolution(y,km) and soil polygon unit map scale(1:10 000x),the ratio(R?,%) of the optimal soil grid size to average polygon patch size(?,km^2) and the ?,with the highest R^2 among different mathematical regressions,respectively.This knowledge may facilitate the grid partitioning of regions during the investigation and simulation of SOC pool dynamics at a certain map scale,and be referenced to other landscape polygon patches' mesh partition.

EQ_1^(rot) nonconforming finite element approximation to Signorini problem

Abstract In this paper, we apply EQ1^rot nonconforming finite element to approximate Signorini problem. If 5 the exact solution u EQ1^rot, the error estimate of order O（h） about the broken energy norm is obtained for quadrilateral meshes satisfying regularity assumption and bi-section condition. Furthermore, the superconver- gence results of order EQ1^rot are derived for rectangular meshes. Numerical results are presented to confirm the considered theory.

ＱＵＡＤＲＩＬＡＴＥＲＡＬ ＭＥＳＨ

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.

Numerical study on the evolution of the shock-accelerated SF_6 interface:Influence of the interface shape

The early phases of the shock interaction process on two-dimensional interfaces with different shapes are numerically investigated in this study,which are closely related to the shock refraction and reflection,vorticity production and transport.The numerical method employs an adaptive unstructured quadrilateral mesh,which can capture the wave pattern and interface evolution very well.Simulations are carried out under the conditions of an incident shock Mach number of 1.2 and the light/heavy (air/SF 6) interface.Five different shapes are considered in the simulations:rectangle,ellipse,diamond and two kinds of triangle.The results show that the interfacial shapes can influence the wave patterns particularly on the shape and evolution of refracted shock waves.The generation and the distribution of vorticity on the interfaces with five different shapes also have dissimilarities.The circulation deposition on five interfaces is quantitatively investigated and compared with theoretical model.A good agreement is found between the numerical results and the predictions by the theoretical model.Some characteristic scales of the interface are tracked.Under the influence of nonlinear-acoustic effect and vorticity effect,the interfaces present different evolution modes.

Nonconforming finite element methods on quadrilateral meshes

It is well known that it is comparatively difficult to design nonconforming finite elements on quadri- lateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these de- grees of freedom associated with these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes. Degrees of freedom are given for these elements, which are proved to be well-defined for their corresponding shape function spaces in a unifying way. These elements generalize three lower order nonconforming finite elements on quadri- laterals to any order. In addition, these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before.

SUPERCONVERGENCE OF MIXED COVOLUME METHOD ON QUADRILATERAL GRIDS FOR ELLIPTIC PROBLEMS

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h^2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L^2 norm.Numerical experiments illustrating the theoretical results are provided.