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
Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel. 相似文献
Hydrogen
peroxide is a very versatile oxidizing agent, and it is also environmentally
compatible considering that the products of its exothermic decomposition are
oxygen and water.When kept in a clean temperature-controlled environment,
the self-reaction (decomposition) rate is extremely low. However, it is well
known that even a small amount of contamination will dramatically increase
the reaction rate. This paper describes the use of the fast thermal activity
interpreter (FTAI) instrument to examine the chemical reactivity of commercially
available 50% hydrogen peroxide at two different temperatures (30 and 40°C)
both with and without contamination. The results show that at 30°C a small
amount of rust (330 ppm) increases the reaction rate of 50% hydrogen peroxide
by a factor of 50. When the temperature is increased to 40°C, the reaction
rate is further increased by almost a factor of four. The implication for
reactivity management is that at this contamination level most practical vessel
sizes would require emergency venting capability.
An evaluation
was then performed to determine the emergency venting requirement for the
safe transportation or storage of the contaminated hydrogen peroxide. It was
determined that for quantities of the material less than 5 gallons, conventional
breather vents would be sufficient to accommodate the gas evolved. However,
for larger quantities, a safety relief device would be needed. For example,
for a 400-gallon tote bin at 40°C the required minimum vent area is estimated
to be 4.3 in2, corresponding to a minimum vent
diameter of 2.3 inches. 相似文献
In this paper the algorithms for solving the p-median problem based on the Benders decomposition are investigated. A family of problems hard for solving with such algorithms is constructed and then generalized to a special NP-hard case of the p-median problem. It is shown that the effectiveness of the considered algorithms depends on the choice of the optimal values of the dual variables used in Benders cuts. In particular, the depth of the cuts can be equal to one. 相似文献
Linear mixed 0–1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP)
problems. We exploit these equivalences to transpose the concept of mixed 0–1 Gomory cuts to BLP. The first phase of our new
algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination
with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria
are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate
the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of
randomly generated problems.
Work of the authors was partially supported by FCAR, MITACS and NSERC grants. 相似文献
Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s1 and s2 to, respectively, a given vertex t1, and each vertex of a given subset of vertices T2. 相似文献
Seymour (1981) proved that the cut criterion is necessary and sufficient for the solvability of the edge-disjoint paths problem when the union of the supply graph and the demand graph is planar and Eulerian. When only planarity is required, Middendorf and Pfeiffer (1993) proved the problem to be NP-complete. For this case, Korach and Penn (1992) proved that the cut criterion is sufficient for the existence of a near-complete packing of paths. Here we generalize this result by showing how a natural strengthening of the cut criterion yields better packings of paths.Analogously to Seymour's approach, we actually prove a theorem on packing cuts in an arbitrary graph and then the planar edge-disjoint paths case is obtained by planar dualization. The main result is derived from a theorem of Seb (1990) on the structure of ±1 weightings of a bipartite graph with no negative circuits.Research partially supported by the Hungarian National Foundation for Scientific Research Grants OTKA 2118 and 4271. 相似文献
In this paper we generalize the cut strengthening method of Balas and Perregaard for 0/1 mixed-integer programming to disjunctive programs with general two-term disjunctions. We apply our results to linear programs with complementarity constraints. 相似文献
Despite repeated calls for a thorough cleanup of water pollution in the Ganges river, there are only two papers in the social sciences by Batabyal and Beladi (2017, 2019) that have shed theoretical light on this cleanup problem and its connection to the sustainability of tourism in Varanasi. Hence, we extend the above‐mentioned analyses and focus on two specific questions. First, we introduce the notion of a safe minimum standard (SMS) into the study and show how to analyze a probabilistic model of the Ganges cleanup problem when the SMS is accounted for. Second, for a representative citizen of Varanasi, we study how the magnitude of the elasticity of substitution between a composite consumption good and water quality in the Ganges—modeled by the SMS—affects the tradeoff between consumption and water quality maintenance. 相似文献