Comparison of multigrid algorithms for high‐order continuous finite element discretizations

We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h‐multigrid and p‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd.     

High‐ and low‐temperature phases in isostructural 4‐chloro‐3‐nitroaniline and 4‐iodo‐3‐nitroaniline

The structures of 4‐chloro‐3‐nitroaniline, C₆H₅ClN₂O₂, (I), and 4‐iodo‐3‐nitroaniline, C₆H₅IN₂O₂, (II), are isomorphs and both undergo continuous (second order) phase transitions at 237 and 200 K, respectively. The structures, as well as their phase transitions, have been studied by single‐crystal X‐ray diffraction, Raman spectroscopy and difference scanning calorimetry experiments. Both high‐temperature phases (293 K) show disorder of the nitro substituents, which are inclined towards the benzene‐ring planes at two different orientations. In the low‐temperature phases (120 K), both inclination angles are well maintained, while the disorder is removed. Concomitantly, the b axis doubles with respect to the room‐temperature cell. Each of the low‐temperature phases of (I) and (II) contains two pairs of independent molecules, where the molecules in each pair are related by noncrystallographic inversion centres. The molecules within each pair have the same absolute value of the inclination angle. The Flack parameter of the low‐temperature phases is very close to 0.5, indicating inversion twinning. This can be envisaged as stacking faults in the low‐temperature phases. It seems that competition between the primary amine–nitro N—H...O hydrogen bonds which form three‐centred hydrogen bonds is the reason for the disorder of the nitro groups, as well as for the phase transition in both (I) and (II). The backbones of the structures are formed by N—H...N hydrogen bonding of moderate strength which results in the graph‐set motif C(3). This graph‐set motif forms a zigzag chain parallel to the monoclinic b axis and is maintained in both the high‐ and the low‐temperature structures. The primary amine groups are pyramidal, with similar geometric values in all four determinations. The high‐temperature phase of (II) has been described previously [Garden et al. (2004). Acta Cryst. C 60 , o328–o330].     

An investigation on surface tensions of Pb-free solder materials

Surface tensions of some Pb-free solder systems such as Ag–Bi–Sn with cross-sections Ag/Bi = 1/1, Ag/Bi = 1/2, Ag/Bi = 2/1, In–Sn–Zn with cross-sections Sn/In = 1/1, Sn/In = 1/3 and (Ag₇Cu₃)_100?x Sn_x with cross-section Ag/Cu = 7/3 are calculated from the sub-binary surface tension data using the models, such as the Muggianu, Kohler, Toop models, Butler’s equation and Chou’s General Solution Model (GSM) at 873, 923 and 1073 K, respectively. The surface tension of In–Sn–Zn increases wavily with increasing amount of Zn and it is found that the best models are the GSM for both cross-sections in question while GSM becomes the best model for (Ag₇Cu₃)_100?x Sn_x alloy in the whole experimental range. Moreover, the surface tension of (Ag₇Cu₃)_100?x Sn_x decreases slightly with increasing amount of Sn. The Muggianu, Butler and Butler models are determined as the best models for the cross-sections in the order given above for entire measurement range, respectively, and the surface tension of Ag–Bi–Sn decreases slightly with an increasing amount of Bi and Ag but increases with increasing Sn in liquid alloys.     

A simulation method of aircraft plumes for real-time imaging

Real-time infrared simulation technology can provide a large number of infrared images under different conditions to support the design, test and evaluation of a system having infrared imaging equipment with very low costs. By synthesizing heat transfer, infrared physics, fluid mechanics and computer graphics, a real-time infrared simulation method is proposed based on the method of characteristics to predict the infrared feature of aircraft plumes, which tries to obtain a good balance between simulation precision and computation efficiency. The temperature and pressure distribution in the under-expansion status can be rapidly solved with dynamically changing flight statuses and engine working states. And a modified C–G (Curtis–Godson) spectral band model that combines the plume streamlines with the conventional C–G spectral band model was implemented to calculate the non-uniformly distributed radiation parameters inside a plume field. The simulation result was analyzed and compared with the CFD++, which validates the credibility and efficiency of the proposed simulation method.     

Geometric phase in a composite system subjected to decoherence

In this paper, we investigate the geometric phase of a composite system which is composed of two spin- particles driven by a time-varying magnetic field. Firstly, we consider the special case that only one subsystem driven by time-varying magnetic field. Using the quantum jump approach, we calculate the geometric phase associated with the adiabatic evolution of the system subjected to decoherence. The results show that the lowest order corrections to the phase in the no-jump trajectory is only quadratic in decoherence coefficient. Then, both subsystem driven by time-varying magnetic field is considered, we show that the geometric phase is related to the exchange-interaction coefficient and polar angle of the magnetic field.     

Analysis of Non-innocence of Phosphaquinodimethane Ligands when Charge and Aromaticity Come into Play

Several phosphaquinodimethanes and their M(CO)₅ complexes (M=Cr, Mo, W) and model derivatives have been theoretically investigated regarding the quest of non-innocence. Computed structural and electronic properties of the P-Me/NH₂ substituted phosphaquinodimethanes and tungsten complexes revealed an interesting non-innocent ligand behaviour for the radical anion complexes with distonic ion character and a strong rearomatization of the middle phenyl ring. The latter was further probed taking also geometric aromaticity (HOMA) and quinoid distortion parameters (HOMQc) into account, as well as NICS(1). Furthermore, the effect of the P-substitution was investigated for real (or plausible) complexes and their free ligands focusing on the resulting aromaticity at the middle phenyl ring and vertical one-electron redox processes. The best picture of ligand engagement in redox changes was provided by representing NICS(1) values versus HOMA and the new geometric distortion parameter HOMQc8.     

基于频率调制激光驱动的囚禁离子几何相位逻辑门

为了避免激光相位的起伏对几何相位逻辑门保真度的影响, 提出一种基于囚禁离子的量子几何相位逻辑门的新方案。该机制是利用一束频率调制的行波激光场作用于两个囚禁离子上实现的。它的优点有：操作简单,仅需一步就能实现。不灵敏于激光场的相位也不需要对囚禁离子进行个别寻址。     

基于机器视觉的车辆保险盒在线检测研究

摘要: 车辆保险盒作为汽车电控系统中的一个重要的元器件,其质量好坏直接影响汽车的性能,传统的车辆保险盒检测主要依靠人工检测,检测费时费力,针对该问题,提出一种基于视觉的车辆保险盒在线检测方法,分析了产品图像校正到标准模板图像的位置误差,采用SURF(Speeded Up Robust Feature)算法和平面单应性理论将待检产品图像变换到标准模板位置,利用颜色直方图匹配和模板匹配完成保险盒上元件的检测。实验结果证明,该方法检测效率高,稳定可靠,能够满足在线检测的要求,具有一定实用价值。     

几何画板模拟阿贝折射仪测折射率

几何画板模拟阿贝折射仪测量液体折射率的过程,相对传统教学手段,更加科学直观并动态演示。通过修改棱镜折射率和待测液体折射率的参数,通过直观几何光学分析,得到为何阿贝折射仪必须满足棱镜折射率大于待测折射率。利用程序易修改特点研究,棱镜不同顶角和考虑色散现象的模拟结果,定量研究差别。     

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (U-PFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.