High-order accurate equations describing vibrations of thin bars

A method for deriving one-dimensional wave propagation equations in thin inhomogeneous anisotropic bars based on the mathematical homogenization theory for periodic media is used to obtain equations governing the longitudinal and transverse vibrations of a homogeneous circular bar. The equations are derived up to O(ε⁸) terms and take into account variable body forces and surface loads. Here, ε is the ratio of the bar’s typical thickness to the typical wavelength.     

Parametric oscillation at 2.1 μm in periodically poled RbTiOAsO4

An Nd:YAG laser-pumped periodically poled RbTiOAsO₄ (PPRTA) optical parametric oscillator (OPO) near degeneracy is reported. At a pump power of 3.7 W, a net conversion efficiency of 43% was obtained. These crystals were found to be phase-matchable for the higher order quasi-phase-matched second-harmonic generation (SHG) in the visible range. Detailed analyses of the phase-matching properties for these processes were made by using the published Sellmeier and thermo-optic dispersion formulas.     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

场协同理论在椭圆型流动中的数值验证

本文用数值模拟的方法，通过四个椭圆型流动传热的例子验证了场协同理论的正确性．结果表明，场协同理论不仅适合于抛物型流动，亦适合于复杂的有回流的椭圆型流动．     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

解奇异非光滑方程组的牛顿法和不精确牛顿法

本文主要解决奇异非光滑方程组的解法。应用一种新的次微分的外逆，我们提出了牛顿法和不精确牛顿法，它们的收敛性同时也得到了证明。这种方法能更容易在一引起实际应用中实现。这种方法可以看作是已存在的解非光滑方程组的方法的延伸。     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.