非线性RLW方程的经济型差分-流线扩散法

本文对非线性正则长波(RLW)方程的周期初边值问题提出了一种基于线性有限元空间的经济型差分-流线扩散(EFDSD)法,利用能量估计方法证明了该方法的稳定性和收敛性,得到了L2模拟丰满误差估计和H1模丰满误差估计。与以前的方法相比,该方法具有稳定性能好,便于实际编程计算等优点。     

A practical determination strategy of optimal threshold parameter for matrix compression in wavelet BEM

A practical strategy is developed to determine the optimal threshold parameter for wavelet‐based boundary element (BE) analysis. The optimal parameter is determined so that the amount of storage (and computational work) is minimized without reducing the accuracy of the BE solution. In the present study, the Beylkin‐type truncation scheme is used in the matrix assembly. To avoid unnecessary integration concerning the truncated entries of a coefficient matrix, a priori estimation of the matrix entries is introduced and thus the truncated entries are determined twice: before and after matrix assembly. The optimal threshold parameter is set based on the equilibrium of the truncation and discretization errors. These errors are estimated in the residual sense. For Laplace problems the discretization error is, in particular, indicated with the potential's contribution ∥ c ∥ to the residual norm ∥ R ∥ used in error estimation for mesh adaptation. Since the normalized residual norm ∥ c ∥/∥ u ∥ ( u : the potential components of BE solution) cannot be computed without main BE analysis, the discretization error is estimated by the approximate expression constructed through subsidiary BE calculation with smaller degree of freedom (DOF). The matrix compression using the proposed optimal threshold parameter enables us to generate a sparse matrix with O(N^1+γ) (0≤γ<1) non‐zero entries. Although the quasi‐optimal memory requirements and complexity are not attained, the compression rate of a few per cent can be achieved for N～1000. Copyright © 2003 John Wiley & Sons, Ltd.     

无网格彼得洛夫伽辽金法在大变形问题中的应用

将无网格局部彼得洛夫伽辽金(MLPG)法推广应用于大变形问题。导出了非线性局部子域对称弱形式,通过对该弱形式进行线性化得到了用于非线性计算的MLPG格式,并对MLPG的计算速度进行了优化,使MLPG成为一种复杂度为O(N)的算法。几何非线性和几何与材料双重非线性的数值算例表明,相对有限元方法,MLPG在处理此类大变形问题时收敛性好,精度高,并能减小有限元分析中易遇到的网格畸变带来的困难。     

反应扩散方程的奇异摄动问题的最小二乘的有限元方法

For a kind of the singularly perturbed reaction-diffusion problem, the standard energy norm is too weak to measure adequately the errors of solutions computed by finite element methods. The multiplier of this problem gives an unbalanced norm whose different components have different orders of convergence. In the paper, we introduce a new stronger norm, construct the least-squares finite element method (LSFEM) in this new norm and develop a robust and stable numerical approach for more general singularly perturbed reaction-diffusion problems in 1D spaces. At last, numerical examples are presented to illustrate the proposed method and theoretical results.     

A quasi‐linear reproducing kernel particle method

Reproducing kernel particle method (RKPM) has been applied to many large deformation problems. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties but requires appropriate kernel support coverage of neighboring nodes to ensure kernel stability. This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment‐impact processes that commonly exist in extreme events. A new reproducing kernel formulation with ‘quasi‐linear’ reproducing conditions is introduced. In this approach, the first‐order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first‐order completeness, nearly second‐order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this quasi‐linear RKPM formulation is demonstrated by modeling several extremely large deformation and fragment‐impact problems. Copyright © 2016 John Wiley & Sons, Ltd.     

An <i>O(N)</i> Fast Multipole Hybrid Boundary Node Method for 3D Elasticity

The Hybrid boundary node method (Hybrid BNM) is a boundary type meshless method which based on the modified variational principle and the Moving Least Squares (MLS) approximation. Like the boundary element method (BEM), it has a dense and unsymmetrical system matrix and needs to be speeded up while solving large scale problems. This paper combines the fast multipole method (FMM) with Hybrid BNM for solving 3D elasticity problems. The formulations of the fast multipole Hybrid boundary node method (FM-HBNM) which based on spherical harmonic series are given. The computational cost is estimated and an O(N) algorithm is obtained. The algorithm is implemented on a computer code written in C++. Numerical results demonstrate the accuracy and efficiency of the proposed technique.     

Preparation of SiC Fiber Reinforced Nickel Matrix Composite

A method of preparing continuous(Al+Al2O3)-coated SiC fiber reinforced nickel matrix composite was presented,in which the diffusion between SiC fiber and nickel matrix could be prevented.Magnetron sputtering is used to deposit Ni coating on the surface of the(Al+Al2O3)-coated SiC fiber in preparation of the precursor wires.It is shown that the deposited Ni coating combines well with the(Al+Al2O3) coating and has little negative effect on the tensile strength of(Al+Al2O3)-coated SiC fiber.Solid-state diffusion bonding process is employed to prepare the(Al+Al2O3)-coated SiC fiber reinforced nickel matrix with 37% fibers in volume.The solid-state diffusion bonding process is optimized and the optimum parameters are temperature of 870,pressure of 50 MPa and holding time of 2 h.Under this condition,the precursor wires can diffuse well,composite of full density can be formed and the(Al+Al2O3) coating is effective to restrict the reaction between SiC fiber and nickel matrix.     

Water-related matrix isolation phenomena during NO2 photolysis in argon matrix

Photolysis (350-450 nm) of NO(2) molecules trapped in argon matrices at 10 K has been studied using Fourier transform infrared (FTIR) spectroscopy to examine the mobility of the photolysis products, O((3)P) and NO, and their subsequent reactions. The formation of N(2)O(5) and N(2)O(3) from reactions of these mobile species with immobilized NO(2) and N(2)O(4) is confirmed. Water molecules from the background gases in the vacuum have been found to be isolated in the argon matrix during deposition of diluted NO(2) in Ar. The entrapped water molecules along with some of their NO(2) adducts have been characterized. Exposure of the matrix to photons to photolyze NO() resulted in not only internal matrix reactions, but also an enhanced deposition of ice over the surface of the argon matrix. This is caused by photodesorption of water molecules from the walls of the matrix isolation chamber and their subsequent condensation on the matrix surface. This ice overlayer has been found to give a very significant dangling OH band and a substantial librational band in the FT-IR spectra, indicating substantial surface area and internal porosity, respectively. The potential of using photodesorbed water to establish high surface area ice interfaces with dangling OH groups for heterogeneous photoreaction studies is discussed.     

基于Woodbury非线性方法的迭代算法对比分析

在结构局部非线性求解过程中,刚度矩阵仅部分元素发生改变,此时切线刚度矩阵可写成初始刚度矩阵与其低秩修正矩阵和的形式,每个增量步的位移响应可用数学中快速求矩阵逆的Woodbury公式高效求解,但通常情况下迭代计算在结构非线性分析中是不可避免的,因此迭代算法的计算性能也对分析效率有重要影响。该文以基于Woodbury非线性方法为基础,分别采用Newton-Raphson （N-R）法、修正牛顿法、3阶两点法、4阶两点法及三点法求解其非线性平衡方程,并对比分析5种迭代算法的计算性能。利用算法时间复杂度理论,得到了5种迭代算法求解基于Woodbury非线性方法平衡方程的时间复杂度分析模型,定量对比了5种迭代算法的计算效率。通过2个数值算例,从收敛速度、时间复杂度和误差等方面对比了各迭代算法的计算性能,分析了各算法适用的非线性问题。最后,计算了5种算法求解基于Woodbury非线性方法平衡方程的综合性能指标。     

Discontinuous precipitation of Cr2N in a high nitrogen,chromium-manganese austenitic stainless steel

The main purpose of the present work is to study the effect of a high nitrogen content (1 wt% N), on the microstructural evolution of a Cr-Mn austenitic stainless steel aged over the [400–900 °C] temperature interval. Thermal treatments carried out between 700 and 900 °C lead to the decomposition of the nitrogen supersaturated austenitic matrix by discontinuous precipitation of Cr₂N particles. The microstructural features of the reaction are described and analysed. In the present case, the cellular precipitation of Cr₂N is a peculiar and complex phenomenon which involves two diffusion mechanisms: the diffusion of an interstitial element (nitrogen) and the diffusion of a substitutional one (chromium). The nucleation of the discontinuous precipitation arises from a reduction of the surface energy of the precipitates. Furthermore, the precipitation growth is a non-steady state process, because the reaction is governed at first by the intergranular diffusion of chromium, and then tends to be controlled by its bulk diffusion. Consequently, the features of this discontinuous precipitation do not fit in with the assumptions of usual theories, which have been established for binary substitutional systems that transform in steady state conditions. This discontinuous precipitation brings about a slight hardening. Then, the hardness of the aged samples can be described by an additive relationship between the hardness of the precipitation cells and that of the untransformed matrix. Beside the discontinuous precipitation of Cr₂N, sigma phase forms with significant volume fractions.     

带限函数外推算法收敛性研究

Gerchberg-Papoulis(G-P)算法是解决带限信号外推问题的一个广泛使用的迭代算法。在数据存在噪声时,本文论证了G-P迭代算法的收敛性不再成立,其原因是相应的线性算子在L^2范数下是非压缩算子,并以数值模拟说明了这一问题。针对这一问题,我们提出改进的Gerchberg-Papoulis(IG-P)算法,并研究了该算法在L^2范数下的收敛性质。数值模拟结果表明,IG-P迭代算法具有较好的信号分辨能力和收敛性质。     

The convergence behaviour of iterative methods on severely stretched grids

In this paper we examine the dramatic influence that a severe stretching of finite difference grids can have on the convergence behaviour of iterative methods. For the most important classes of iterative methods this phenomenon is considered for a simple model problem with various boundary conditions and an exponential grid. It is shown that grid compression near 2 Neumann boundary or in the centre can make the convergence of some methods extremely slow, whereas grid compression near a Dirichlet boundary can be very advantageous. More theoretical insight is obtained by analysing the spectrum of the Jacob: matrix for one- and two-dimensional problems. Several bounds on dominant eigenvalues of this matrix are given. The final conclusions are also applicable to problems with a variable diffusion coefficient and convection-diffusion equations solved by central difference schemes.     

Nonvolatile gating effects on radicals-containing vanadium oxide nanowires by gas molecule absorption and diffusion

The charge conduction of a single nanowire of radicals-containing vanadium oxides was experimentally studied and found to be modulated by different gas exposures, showing a gating effect by the adsorption and absorption of different gas molecules. After N(2) and O(2) gas are introduced, the nanowires show an abrupt increase of the resistance but show the opposite trend within a longer timescale of several ks. The introduction of N(2) and O(2) can respectively 'write' the nanowire into high and low resistance states, which are metastable in a high vacuum. The long-term gating effect which was attributed to the interlayer diffusion of the gas molecules can be registered on the nanowire in the high vacuum environment.     

Fourier transform infrared-probed O(3P) microreactor: demonstration with ethylene reactions in argon matrix

To demonstrate the development of an oxygen atom microreactor in the form of liquid-helium-cooled solid argon matrix deposited on an infrared (IR) window, the oxidation of ethylene by mobile O atoms has been investigated. O atom diffusion through the argon matrix is confirmed and used to examine ethylene-oxygen atom reactions. In a bench-scale matrix isolation system probed with a Fourier transform infrared (FT-IR) spectrometer, matrices of solid Ar at 8-10 K doped with NO2 and ethylene have been prepared on a ZnSe window within an evacuated cryostat. The matrices have been photolyzed using 350-450 nm photons, and the reaction products resulting from the reaction of O(3P), one of the photolysis products of NO2, with ethylene have been identified using FT-IR and a Gaussian 98W simulation program. These products include oxirane, acetaldehyde, ethyl nitrite radical, and ketene. The temperature effect in the range of 10-30 K on the products formed has also been investigated. The reaction mechanisms are discussed and the viability of the solid Ar matrix being a low temperature microreactor to examine reaction mechanisms of mobile oxygen atoms is elaborated.     

Application of extended finite element method in damage progress simulation of fiber reinforced composites

Damage initiation and propagation in unidirectional glass fiber reinforced epoxy matrix composites under tension load were simulated in this study. Cell models with both single fiber and multi-fiber were modeled by extended finite element method (XFEM) in ABAQUS environment. The damage progresses in the cells were investigated and then the nominal stress–strain curves as well as stress distributions in the fiber and matrix were obtained. Results indicate that the XFEM is an effective modeling technique to study the initiation and propagation of a crack along an arbitrary, mesh-independent, solution-dependent path. In addition, convergence difficulties are familiar issues while carrying out damage and fracture analysis when employing numerical simulation. Several methods, which are helpful to resolve these convergence problems, were presented. Baseline simulations about damage initiation and propagation in composites indicate that a larger value of viscous regularization causes the peak of the reaction force to be higher. A smaller viscosity parameter is better than bigger one. Other advanced techniques, include using automatic stabilization and customized general solution controls, are also adoptable to improve convergence in ABAQUS/Standard analysis.     

Comparison of two O(N) methods for total-energy semi-empirical tight-binding calculation

We compare two O(N) methods, to calculate the total energy of a system, based on a local evaluation of the density matrix (DM) via the Lanczos-Haydock recursion scheme. We have recently introduced the first method, in which an approximated DM is directly computed from the local tridiagonalized hamiltonian (LTH). In the second method, the DM is obtained from the diagonalized LTH without any further approximation. The use of the first method is restricted to temperatures higher than 1000 K, but there is no limitation for the second one. The methods are compared when applied to a grain boundary in silicon and germanium.     

对流扩散方程的特征线EFG算法

为了消除对流扩散方程因对流占优引起的数值震荡,本文首先将其转化为特征形式,并利用移动最小二乘基函数,构建了特征线无单元Galerkin方法．再对新建方法进行收敛性分析,分别给出关于支持域半径和时间步长的两种误差估计．最后,分别针对一维和二维算例进行了数值计算,并与有限元法进行了比较．数值结果表明,本文算法收敛性好,可以消除数值震荡,且通过选取合适的罚因子和支持域的无量纲尺寸,计算精度比有限元法更高,是求解对流占优扩散方程的一种有效程数值计算方法．     

Simultaneous inversion for a diffusion coefficient and a spatially dependent source term in the SFADE

This paper deals with an inverse problem of determining a diffusion coefficient and a spatially dependent source term simultaneously in one-dimensional (1-D) space fractional advection–diffusion equation with final observations using the optimal perturbation regularization algorithm. An implicit finite difference scheme for solving the forward problem is set forth, and a fine estimation to the spectrum radius of the coefficient matrix of the difference scheme is given with which unconditional stability and convergence are proved. The simultaneous inversion problem is transformed to a minimization problem, and existence of solution to the minimum problem is proved by continuity of the input–output mapping. The optimal perturbation algorithm is introduced to solve the inverse problem, and numerical inversions are performed with the source function taking on different forms and the diffusion coefficient taking on different values, respectively. The inversion solutions give good approximations to the exact solutions demonstrating that the optimal perturbation algorithm with the Sigmoid-type regularization parameter is efficient for the simultaneous inversion problem in the space fractional diffusion equation.