Refactoring in Maintenance and Development of Z Specifications and Proofs

Once you have proved your refinement correct, that is not the end. Real products, and their accompanying specifications, develop over time, with new improved versions having added functionality. There are new maintenance issues that arise when altering and upgrading pre-existing large specifications and their respective proofs.We show how concepts from refactoring can be used to structure this process, and provide a means for well-defined, disciplined modifications. Additionally, we discuss how the analogy between proof and refactoring, as meaning preserving transforms, can be used to suggest the development of a refactoring toolset, and thence a refinement toolset.     

一类三角形网格的局部加密方法及其应用

5卫.引言网格生成是数值计算必需解决的问题.对于许多复杂的工程实际问题,由于物理参数的变化及解的性态复杂,对求解区域的网格疏密变化都有某些特殊的要求.虽然一般的非结构网格能够适应这些要     

新型细化剂对K4169高温合金晶粒组织的影响

研究了新型细化剂对K4169高温合金晶粒组织的影响，提出了晶粒细化的机理。结果表明：加入新型细化剂不仅使凝固后基体的晶粒尺寸减小，而且可提高铸件断面等轴晶的比例。在通常浇注温度1400℃下，加入由两种三元金属间化合物所制成的复合细化剂，对合金熔体进行、不进行均匀化处理时，可使圆柱锭的晶粒分别细化至ASTM1．7级和ASTM3．2级；断面等轴晶的比例从56％分别提高到96％和99％。研究还发现细化剂加入工艺如加入单一或复合细化剂、细化剂的种类和粒度等的不同会产生不同的细化效果，本对这些现象进行了解释。     

Adaptive Geometrically Balanced Clustering of <Emphasis Type="Italic">H</Emphasis>-Matrices

In [8], a class of (data-sparse) hierarchical (-) matrices is introduced that can be used to efficiently assemble and store stiffness matrices arising in boundary element applications. In this paper, we develop and analyse modifications in the construction of an -matrix that will allow an efficient application to problems involving adaptive mesh refinement. In particular, we present a new clustering algorithm such that, when an -matrix has to be updated due to some adaptive grid refinement, the majority of the previously assembled matrix entries can be kept whereas only a few new entries resulting from the refinement have to be computed. We provide an efficient implementation of the necessary updates and prove for the resulting -matrix that the storage requirements as well as the complexity of the matrix-vector multiplication are almost linear, i.e., AMS Subject Classifications: 65F05, 65F30, 65N38, 65N50.     

An adaptive mesh refinement of quadrilateral finite element meshes based upon a posteriori error estimation of quantities of interest: linear static response

A posteriori error estimation in finite element analysis serves as an important guide to the meshing tool in an adaptive refinement process. However, the traditional posteriori error estimates, which are often defined in the energy or energy-type norms over the entire domain, provide users insufficient information regarding the accuracy of specific quantities in the solution. This paper describes an adaptive quadrilateral refinement process with a goal-oriented error estimation, in which a posteriori error is estimated with respect to the specified quantity of interest. A highlight of this paper is the demonstration of tools described in the paper used in a practical industrial environment. The performance of this process is demonstrated on several practical problems where the comparison is with the adaptive process based on the traditional error estimation.     

退火温度对ECAP挤压两道次Fe基形状记忆合金微观组织的影响

对不同退火温度时ECAP两道次Fe17.80Mn4.73Si7.80Cr4.12Ni合金的微观组织进行分析,研究变形后组织对形状恢复率的影响机理.研究结果显示,ECAP挤压后300 ℃退火,合金恢复率只有33%,提高退火温度,形状恢复率迅速升高,最佳退火温区600～650 ℃,此时恢复率高于固溶态试样.TEM分析显示挤压后晶粒明显细化,但是较低温度时,退火晶粒中包含大量的位错和亚结构,不利于肖克莱不全位错的滑移,导致恢复率很低.500 ℃退火时变形组织已经部分回复,晶内位错仍然存在,但是数量已大大减少,开始出现一些低位错密度的区域.600～650 ℃之间退火时,变形带来的位错等回复完成,层错组织仍存在,恢复率达到最大值.700 ℃退火30 min后晶粒再结晶完成,新生成晶粒在0.3～2.5 μm左右,固溶态试样晶粒100 μm,相比晶粒明显细化.     

Transmission electron microscopy studies of nanostructured TiO2 films on various substrates

A chemical vapour deposition (CVD) synthetic route to the production of nanocrystalline titanium dioxide has been carefully investigated on various substrates. CVD was performed at a relatively low temperature of 320 °C on KCl crystal, Al foil, KBr pellet and freshly sliced MICA substrates. The influence of substrate material on film formation was studied in order to find a titanium dioxide film with good intercalation properties for an electrode in a dye-sensitized solar cell. Intercalation properties depend on average grain sizes and porosity in nanophased materials. These films were thoroughly characterized with respect to their surface morphology, crystal structure and the phase composition. Transmission electron microscopy (TEM) accompanied by selected area electron diffraction (SAED) was employed for structural characterization of TiO₂ films. The studies showed that films deposited on KCl crystal, KBr pellet and MICA are solely composed of an anatase phase whereas in the film deposited onto Al foil, the brookite phase of TiO₂ is also present. The structural parameters of anatase were determined using the Rietveld refinement of electron diffraction data. By comparison of anatase lattice parameters with their corresponding bulk values, the significant deviation in values of lattice parameters a and c in anatase phase was observed and attributed to the thin-film features. The average grain size and the grain size distribution obtained by TEM were compared for TiO₂ films deposited on different substrates.     

Study of Computational Issues in Simulation of Transient Flow in Continuous Casting

Unsteady three‐dimensional turbulent flow and heat transport in the liquid pool during continuous casting of steel slabs has been computed using several different computational models, domains, grids, and inlet conditions. The most advanced computations employ a large‐eddy simulation code, UIFLOW with a second‐order central‐differencing scheme, 1.6 million nodes and a realistic simulation domain including the complete submerged entry nozzle. The model has been validated in previous work through comparison with PIV measurements in caster water models, and with velocity and temperature measurements in an operating steel caster. The present computations are compared with flow measurements in a full‐scale water model and with heat flux measurements in a jet impingement test problem. Results are compared between model domains of the full caster with symmetric half‐caster and two‐fold symmetric quarter‐caster simulations. The effects of thermal buoyancy and the solidifying steel shell walls are studied independently. The effect of different inlet conditions is investigated by comparing results including nozzle simulations that are both coupled and uncoupled with the mold domain and a simplified nozzle geometry. The importance of the Sub‐grid scale (SGS) model for treating the small turbulent eddies is investigated through simulations with and without the Horiuti SGS K model. A rigorous grid refinement study is undertaken, which indicates criteria for choosing the element size near the walls. Accurate heat transfer predictions are more difficult to attain than accurate velocities. Finally, comparisons are made with Reynolds‐averaged approaches, including standard K‐ε and low Re‐number K‐ε model computations of the same system. The relative advantages and disadvantages of the different flow simulation methods are evaluated.     

Finite element analysis of plasticity-induced fatigue crack closure: an overview

Finite element analysis is perhaps the most commonly used numerical method to model plasticity-induced fatigue crack closure. The state-of-the-art is reviewed and a comprehensive overview is presented, summarizing issues which must be considered and emphasizing potential difficulties. These include mesh refinement level, crack advancement schemes, crack shape evolution, geometry effects, and crack opening value assessment techniques.     

Automated refinement of conformal quadrilateral and hexahedral meshes

Conformal refinement using a shrink and connect strategy, known as pillowing or buffer insertion, contracts and reconnects contiguous elements of an all‐quadrilateral or an all‐hexahedral mesh in order to locally increase vertex density without introducing hanging nodes or non‐cubical elements. Using layers as shrink sets, the present method automates the anisotropic refinement of such meshes according to a prescribed size map expressed as a Riemannian metric field. An anisotropic smoother further enhances vertex clustering to capture the features of the metric. Both two‐ and three‐dimensional test cases with analytic control metrics confirm the feasibility of the present approach and explore strategies to minimize the trade‐off between element shape quality and size conformity. Additional examples using discrete metric maps illustrate possible practical applications. Although local vertex removal and reconnection capabilities have yet to be developed, the present refinement method is a step towards an automated tool for conformal adaptation of all‐quadrilateral and all‐hexahedral meshes. Copyright © 2004 John Wiley & Sons, Ltd.