基于非结构自适应网格的复合有限体积法

利用文献[1]中将Lax-Wendroff格式和Lax-Friedrichs格式整体复合作用构成二维无结构网格上的复合型有限体积法,同时利用Delaunay方法,根据流场流动特性变化的梯度值为指示器对网格进行加密和粗化,实现自适应,并将此方法应用到二维浅水波方程的求解上,进行了二维部分溃坝,倾斜水跃的数值实验.结果表明,该方法是一个计算稳定、能适应复杂的求解域、能很好地捕捉激波、且计算速度快的算法.     

Nther-type theorem of piecewise algebraic curves on triangulation

The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space.In this paper,using the properties of bivariate splines,the Nther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.     

快速三维散乱数据点重建算法

提出了一种快速三维散乱数据点重建算法.我们对包围盒算法进行了改进,减少了建立散乱点近邻关系所需的计算量;同时针对位置相对平坦的数据点,结合最小二乘法给出了一种计算法矢的混合方法.实例表明,该算法是有效的.     

On the sizes of Delaunay meshes

Let be a polyhedral domain occupying a convex volume. We prove that the size of a graded mesh of with bounded vertex degree is within a factor of the size of any Delaunay mesh of with bounded radius-edge ratio. The term depends on the geometry of and it is likely a small constant when the boundaries of are fine triangular meshes. There are several consequences. First, among all Delaunay meshes with bounded radius-edge ratio, those returned by Delaunay refinement algorithms have asymptotically optimal sizes. This is another advantage of meshing with Delaunay refinement algorithms. Second, if no input angle is acute, the minimum Delaunay mesh with bounded radius-edge ratio is not much smaller than any minimum mesh with aspect ratio bounded by a particular constant.     

Minimal triangulations of graphs: A survey

Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph. In this paper we study minimal triangulations, which are the result of adding an inclusion minimal set of edges to produce a triangulation. This topic was first studied from the standpoint of sparse matrices and vertex elimination in graphs. Today we know that minimal triangulations are closely related to minimal separators of the input graph. Since the first papers presenting minimal triangulation algorithms appeared in 1976, several characterizations of minimal triangulations have been proved, and a variety of algorithms exist for computing minimal triangulations of both general and restricted graph classes. This survey presents and ties together these results in a unified modern notation, keeping an emphasis on the algorithms.     

Non-manifold surface reconstruction from high-dimensional point cloud data

We present an algorithm capable of reconstructing a non-manifold surface embedded as a point cloud in a high-dimensional space. Our algorithm extends a previously developed incremental method and produces a non-optimal triangulation, but will work for non-orientable surfaces, and for surfaces with certain types of self-intersection. The self-intersections must be ordinary double curves and are fitted locally by intersecting planes using a degenerate quadratic surface. We present the algorithm in detail and provide many examples, including a dataset describing molecular conformations of cyclo-octane.     

Coloring-flow duality of embedded graphs

Let be a directed graph embedded in a surface. A map is a tension if for every circuit , the sum of on the forward edges of is equal to the sum of on the backward edges of . If this condition is satisfied for every circuit of which is a contractible curve in the surface, then is a local tension. If holds for every , we say that is a (local) -tension. We define the circular chromatic number and the local circular chromatic number of by and , respectively. The invariant is a refinement of the usual chromatic number, whereas is closely related to Tutte's flow index and Bouchet's biflow index of the surface dual .

From the definitions we have . The main result of this paper is a far-reaching generalization of Tutte's coloring-flow duality in planar graphs. It is proved that for every surface and every 0$">, there exists an integer so that holds for every graph embedded in with edge-width at least , where the edge-width is the length of a shortest noncontractible circuit in .

In 1996, Youngs discovered that every quadrangulation of the projective plane has chromatic number 2 or 4, but never 3. As an application of the main result we show that such `bimodal' behavior can be observed in , and thus in for two generic classes of embedded graphs: those that are triangulations and those whose face boundaries all have even length. In particular, if is embedded in some surface with large edge-width and all its faces have even length , then . Similarly, if is a triangulation with large edge-width, then . It is also shown that there exist Eulerian triangulations of arbitrarily large edge-width on nonorientable surfaces whose circular chromatic number is equal to 5.

     

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The IPSP algorithm is an efficient algorithm for computing maximum likelihood estimation of Gaussian graphical models. It first divides clique marginals of graphical models into several groups, and then it adjusts clique marginals in each group locally. This paper uses the IIPS algorithm on junction tree to replace local adjustment on each group in the IPSP algorithm and propose a resulting algorithm called IPSP-JT to reduce the complexity of the IPSP algorithm. Moreover, we give a graph with minimum edges used by IIPS to adjust locally, and we prove its existence and uniqueness and construct a local junction tree. Numerical experiments show that the IPSP-JT algorithm runs faster than the IPSP algorithm for large Gaussian graphical models.