Several promising approaches for hexahedral mesh generation work as follows: Given a prescribed quadrilateral surface mesh they first build the combinatorial dual of the hexahedral mesh. This dual mesh is converted into the primal hexahedral mesh, and finally embedded and smoothed into the given domain. Two such approaches, the modified whisker weaving algorithm by Folwell and Mitchell, as well as a method proposed by the author, rely on an iterative elimination of certain dual cycles in the surface mesh. An intuitive interpretation of the latter method is that cycle eliminations correspond to complete sheets of hexahedra in the volume mesh.
Although these methods can be shown to work in principle, the quality of the generated meshes heavily relies on the dual cycle structure of the given surface mesh. In particular, it seems that difficulties in the hexahedral meshing process and poor mesh qualities are often due to self-intersecting dual cycles. Unfortunately, all previous work on quadrilateral surface mesh generation has focused on quality issues of the surface mesh alone but has disregarded its suitability for a high-quality extension to a three-dimensional mesh.
In this paper, we develop a new method to generate quadrilateral surface meshes without self-intersecting dual cycles. This method reuses previous b-matching problem formulations of the quadrilateral mesh refinement problem. The key insight is that the b-matching solution can be decomposed into a collection of simple cycles and paths of multiplicity two, and that these cycles and paths can be consistently embedded into the dual surface mesh.
A second tool uses recursive splitting of components into simpler subcomponents by insertion of internal two-manifolds. We show that such a two-manifold can be meshed with quadrilaterals such that the induced dual cycle structure of each subcomponent is free of self-intersections if the original component satisfies this property. Experiments show that we can achieve hexahedral meshes with a good quality. 相似文献
The element distributions and the magnetic ordering behaviour of compounds RNi10Si2 (R = Tb, Dy, Ho, Er, Tm) have been studied by neutron powder diffraction down to temperatures of 1.6 K. The compounds crystallize
in an ordered variant of the ThMn12 structure type in the tetragonal space group P4/nmm. An ordered 1:1 distribution of Ni and Si on sites 4d and 4e, respectively,
corresponds to a modulation vector [0, 0, 1] with respect to the space group I4/mmm of the ThMn12 structure. TbNi10Si2 orders antiferromagnetically below TN = 4.5 K with a magnetic propagation vector of [0, 0, 1/2]. The magnetic Tb moments, 8.97(2) /Tb atom at 1.6 K, are aligned along the c-axis. The Ni sites in TbNi10Si2 do not carry any ordered magnetic moments. The compounds with R = Dy, Ho, Er, and Tm are paramagnetic down to 1.6 K and 3.0 K, respectively.
Received 10 July 2002 / Received in final form 12 September 2002 Published online 29 October 2002 相似文献
The crystal structures of the intermediate solid solution HT (high temperature) Ni1+δSn with δ=0.28, 0.52 and 0.61 (refined Ni contents) have been analyzed in detail by X-ray diffraction on single crystals. The previously reported basic atomic arrangement, i.e., a NiAs/Ni2In structure type (P63/mmc, Ni(1) on 2a, 0 0 0, Ni(2) with an occupancy δ on 2d, and Sn on 2c, ), is confirmed. However, strong anisotropic atomic displacements occur for Sn within the a-b plane of the hexagonal unit cell, which require a Gram-Charlier expansion of the probability density function of Sn in order to obtain a good fit to the diffraction data. Direction, magnitude and the concentration dependence of the displacements can be interpreted in terms of the geometrical requirements of the different local atomic configurations in the planes z=±1/4, so that the displacements can be identified as static ones. 相似文献
The paper provides a combinatorial method to decide when the space of local systems with nonvanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of Orlik–Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg–Kac classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components. 相似文献
We calculate the Borel–Moore homology of affine Springer fibers of type A associated with some regular semisimple nil elliptic elements. As a result, we obtain bigraded Sn-modules whose bigraded Frobenius series are a generalization of the symmetric functions introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov. 相似文献
When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described. 相似文献
Ynamides have recently evolved as remarkably reactive and versatile building blocks for chemical synthesis. The development of efficient and robust methods for their preparation combined with their recent commercialization have facilitated both the design of an ever-growing number of original methods based on their unique reactivity and their use in other areas such as medicinal chemistry. One crucial aspect of the reactivity of these building blocks is based on their anionic chemistry, which has been extensively studied during the last decade and enabled not only the design and development of remarkably efficient and original reactions but also brought general answers to long-standing problems in organic chemistry and contributed to the emergence of new synthetic paradigms. In this short review, the anionic chemistry of ynamides is overviewed. 相似文献
A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph. 相似文献