Preconditioned conjugate gradient methods for the incompressible Navier-Stokes equations

A robust technique for solving primitive variable formulations of the incompressible Navier-Stokes equations is to use Newton iteration for the fully implicit non-linear equations. A direct sparse matrix method can be used to solve the Jacobian but is costly for large problems; an alternative is to use an iterative matrix method. This paper investigates effective ways of using a conjugate-gradient-type method with an incomplete LU factorization preconditioner for two-dimensional incompressible viscous flow problems. Special attention is paid to the ordering of unknowns, with emphasis on a minimum updating matrix (MUM) ordering. Numerical results are given for several test problems.     

PAC Studies on Zr-Based Intermetallic Compounds

The Zr₂Al, Zr₃Al₂ and Zr₆NiAl₂ intermetallic compounds were characterized by means of time differential perturbed angular correlation (TDPAC) and X-ray diffraction. Our interest in these Zr(Hf) aluminides comes from crystallization studies of Zr(Hf)-based bulk metallic glasses which have a wide supercooled liquid region.     

INTERIOR POINT PROJECTED REDUCED HESSIAN METHOD WITH TRUST REGION STRATEGY FOR NONLINEAR CONSTRAINED OPTIMIZATION

§1　IntroductionIn this paper we analyze an interior point scaling projected reduced Hessian methodwith trust region strategy for solving the nonlinear equality constrained optimizationproblem with nonnegative constraints on variables:min　f(x)s.t.　c(x) =0 (1.1)x≥0where f∶Rn→R is the smooth nonlinear function,notnecessarily convex and c(x)∶Rn→Rm(m≤n) is the vector nonlinear function.There are quite a few articles proposing localsequential quadratic programming reduced Hessian methods…     

Calculation of the deuterium electric field gradients in HD and LiD using a variation-perturbation method with a Gaussian basis set

Summary We present calculations of the deuterium electric field gradients in the HD and LiD molecules obtained with a variation-perturbation method using Gaussian atomic orbitals. The differences between our theoretical values and the corresponding experimental or best calculated values are 2%. We conclude that high accuracy can be obtained with the variation-perturbation method using either Gaussian or Slater orbitals.     

Restricted self-diffusion in an aqueous solution of poly(ethylene oxide) poly(propylene oxide) poly(ethylene oxide) triblock copolymer

 The self-diffusion behavior of a triblock copolymer (PEO–b– PPO–b–PEO) in an aqueous solution of 20% (m/m) was investigated during a temperature-induced phase transition from liquid to gel state using pulsed field gradient NMR and static light scattering. The measured self-diffusivity shows a strong dependence on the observation time in the gel phase indicating the existence of diffusion barriers in the size range of about 0.6 μm. Additional static light-scattering measurements show a structure in the same size range of several hundred nanometers, which is far above molecular or micellar sizes and thus, has to be caused by larger clusters. The similarity in the space scales suggests that the restriction of molecular propagation is correlated with the grain boundaries between the domains of the poly-crystalline structure formed by the arranged micelles. Received: 28 October 1996 Accepted: 21 March 1997     

Linear scaling of the interlayer relaxations of the vicinal Cu(p,p,p − 2) surfaces with the number of atom-rows in the terraces

We investigate the multilayer relaxation trends in the vicinal Cu(p,p,p − 2) surfaces employing the all-electron full-potential linearized augmented plane-wave method. Calculations are performed for the (3 3 1), (2 2 1), (5 5 3), (3 3 2), (7 7 5), and (4 4 3) surfaces, which have 3, 4, 5, 6, 7, and 8 atom-rows in the terrace, respectively. The following trends are identified: (i) The interlayer relaxations perpendicular to the surface scale almost linearly with the number of atom-rows in the terraces. (ii) The nearest-neighbor distances do not depend on the surface termination, but only on the local coordination. (iii) For Cu(p,p,p − 2) in which the topmost n surface layers have nearest-neighbor coordination smaller than the bulk Cu (calculated for the unrelaxed surfaces), the topmost (n − 1) interlayer spacings (d₁₂, … , d_n−1,n) contract compared with the unrelaxed spacing, while the nth interlayer spacing (d_n,n+1) expands. The next (n − 2) interlayer spacings (d_n+1,n+2, … , d_{2n−2,2n−1}) contract, while the interlayer spacing indicated by d_2n−1,2n expands. A similar rule was found for the relaxations parallel to the surfaces. These trends provide a better understanding of the atomic structure of vicinal Cu surfaces.     

Electric Field Gradients of Light Impurities in TiO2 Calculated by the Full Potential KKR Green's Function Method

The electric field gradients (EFGs) of B, N, O and Na in TiO₂ were calculated by the full potential Korringa–Kohn–Rostoker (KKR) Greens function method in the framework of the density functional theory. The agreement with the experiments was much improved from the previous calculations that were based on the muffin-tin potential model.     

无约束优化的一类共轭梯度法(英)

本文给出了一类具有4个参数的共轭梯度法，并且分析了其中两个子类的方法．证明了在步长满足更一般的Wolfe条件时，这两个子类的方法是下降算法．同时还证明了这两个子类算法的全局收敛性．     

脉冲梯度增强技术的初步研究

自行研制一套脉冲梯度场系统,配合Bruker公司MSL 300谱仪研究脉冲梯度增强的高分辨核磁共振,研制以PC/286为核心的梯度脉冲波形和幅度可任意调节的梯度场发生器;改装谱仪的¹H液体探头、增加梯度场线图.分析了脉冲梯度场产生的涡流磁场的影响;报道了利用自制梯度场系统进行的脉冲梯度增强的高分辨COSY实验.     

Conjugate residual methods for almost symmetric linear systems

This paper concerns the use of conjugate residual methods for the solution of nonsymmetric linear systems arising in applications to differential equations. We focus on an application derived from a seismic inverse problem. The linear system is a small perturbation to a symmetric positive-definite system, the nonsymmetries arising from discretization errors in the solution of certain boundary-value problems. We state and prove a new error bound for a class of generalized conjugate residual methods; we show that, in some cases, the perturbed symmetric problem can be solved with an error bound similar to the one for the conjugate residual method applied to the symmetric problem. We also discuss several applications for special distributions of eigenvalues.This work was supported in part by the National Science Foundation, Grants DMS-84-03148 and DCR-81-16779, and by the Office of Naval Research, Contract N00014-85-K-0725.