Finite element investigation of the ground states of the helium trimers 4He3 and 4He2–3He

A three‐dimensional finite element method is applied to the ground states of the symmetric and asymmetric atomic helium trimers ⁴He₃ and ⁴He₂–³He. Three different He–He interaction potentials of hard‐core nature were studied. Two extrapolation procedures based on the convergence properties of the finite element method are investigated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

本征值有限元近似的一个抽象误差估计式

设T：LZ（fi）MLZ（fi）是自共轭全连续算子，SgCLZ（fi）是分片。次有限元空间，几：LZ、St是有限秩自共轭算子，IITh-Tllo、0（h、0）．考虑本征值问题：及其近似用（·，·）和DD·D【。·分别表示h（m中内积和范数·ID·卜F表示w认｝（m中范数，简记D卜队。为D卜卜·因为T自共轭全连续，所以它有可数无穷个本征值h，人，...人，...．其相应的本征函数（2丹构成完全标准直交系，所以VZELZ（m设几的本征值为A。l，汕。，...，汕n，相应的本征函数为如山，卜则。二1·不失一般性，可EitL。设tik一大干二＞，E是到Ah对应的本…     

一些特殊的p核p群

给出了一些特殊的p核p群的分类,并给出了一些非正则p核p群的例子.     

Finite size effect on the Raman frequency of phonons in nano-semiconductors

A comprehensive study on Raman spectroscopy with different excitation wavelengths, sample sizes, and sample shapes for optic phonons (OPs) and acoustic phonons (APs) in polar and non-polar nano-semiconductors has been performed. The study affirms that the finite size effect does not appear in the OPs of polar nano-semiconductors, while it exists in all other types of phonons. The absence of the FSE is confirmed to originate from the long-range Fr¨ohlich interaction and the breaking of translation symmetry. The result indicates that the Raman spectra of OPs cannot be used as a method to characterize the scale and crystalline property of polar nano-semiconductors.     

Using symbolic computation software packages in production of multidimensional finite volume‐based large eddy simulation codes

The numerical simulation of turbulence is one of the most challenging tasks in the field of the modern computational science. At present, the most advanced approach is the large eddy simulation (LES) technique wherein a formal separation between resolved (large) and unresolved (small) scales of the motion is in effect by means of a filtering operation applied onto the governing equations. However, LES requires very sophisticated numerical discretizations in terms of both accuracy and efficiency. Often, the modelling of the unresolved subgrid scale terms adds further computational complexities. This paper illustrates the suitability in using software packages for symbolic computation (in the present case, Maple© for helping in the production of subroutines for a new multidimensional, high‐order accurate finite volume‐based LES code. Specifically, it will be detailed how producing, rapidly and efficiently, the routines for computing convective, diffusive as well as subgrid scale modelling fluxes. It is particularly detailed how exploiting the package for differential calculus and linear algebra for the analytical integration of the flux polynomials over the finite volume faces. The structure of the LES code is illustrated, and an accuracy analysis of the local truncation errors is performed comparing the third‐order accurate multidimensional upwind and the classical second‐order centred reconstruction in the wavenumbers space. Then, some numerical results for the turbulent plane channel and some brief points concerning the parallelization issue are addressed. Copyright © 2012 John Wiley & Sons, Ltd.     

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

The accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.     

An adaptive enrichment algorithm for advection‐dominated problems

We are interested in developing a numerical framework well suited for advection–diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. To resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular, we show that the method is not very sensitive to the choice of the enrichment and develop an adaptive algorithm to automatically choose the enrichment functions.Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients

This paper is concerned with the development of efficient iterative methods for solving the linear system of equations arising from stochastic FEMs for single‐phase fluid flow in porous media. It is assumed that the conductivity coefficient varies randomly in space according to some given correlation function and is approximated using a truncated Karhunen–Loève expansion. Distinct discretizations of the deterministic and stochastic spaces are required for implementations of the stochastic FEM. In this paper, the deterministic space is discretized using classical finite elements and the stochastic space using a polynomial chaos expansion. The highly structured linear systems which result from this discretization mean that Krylov subspace iterative solvers are extremely effective. The performance of a range of preconditioned iterative methods is investigated and evaluated in terms of robustness with respect to mesh size and variability of the conductivity coefficient. An efficient symmetric block Gauss–Seidel preconditioner is proposed for problems in which the conductivity coefficient has a large standard deviation.The companion paper, herein, referred to as Part 2, considers the situation in which Gaussian random fields are transformed into lognormal ones by projecting the truncated Karhunen–Loève expansion onto a polynomial chaos basis. This results in a stochastic nonlinear problem because the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Copyright © 2013 John Wiley & Sons, Ltd.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.