On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

Coupled Thermo-Hydro-Mechanical and Chemical Analysis of Expansive Clay Subjected to Heating and Hydration

A fully coupled formulation combining reactive transport and an existing thermo-hydro-mechanical (THM) code is presented. Special attention has been given to phenomena likely to be encountered in clay barriers used as part of containment systems of nuclear waste. The types of processes considered include hydrolysis, complex formation, oxidation/reduction reactions, acid/base reactions, precipitation/dissolution of minerals and cation exchange. Both kinetically-controlled and equilibrium-controlled reactions have been incorporated. The total analytical concentrations (including precipitated minerals) are adopted as basic transport variables and chemical equilibrium is achieved by minimizing Gibbs Free Energy. The formulation has been incorporated in a general purpose computer code capable of performing numerical analysis of engineering problems. A validation exercise concerning a laboratory experiment involving the heating and hydration of an expansive compacted clay is described.     

一类二阶两点边值问题的单调迭代方法

通过改进经典的单调迭代方法对于一类二阶两点边值的问题的正解建立了单调迭代程序。这些迭代程序都是从常值函数开始的，因而是可行并且有效的。     

Banach空间二阶非线性脉冲微分-积分方程的极值解

通过建立一个新的比较定理研究了B anach空间二阶非线性混合型脉冲微分-积分方程初值问题的极值解,所得结果推广和改进了现有文献的主要结果.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Algebraic Formulation of Quantum Decoherence

An algebraic formalism for quantum decoherence in systems with continuous evolution spectrum is introduced. A certain subalgebra, dense in the characteristic algebra of the system, is defined in such a way that Riemann–Lebesgue theorem can be used to explain decoherence in a well defined final pointer basis.     

Formulation and survey of ALE method in nonlinear solid mechanics

This paper investigates the applicability and accuracy of existing formulation methods in general purpose finite element programs to the finite strain deformation problems. The basic shortcomings in using such programs in these applications are then pointed out and the need for a different type of formulation is discussed. An arbitrary Lagrangian-Eulerian (ALE) method is proposed and a concise survey of ALE formulation is given. A consistent and complete ALE formulation is derived from the virtual work equation transformed to arbitrary computational reference configurations. Differences between the proposed formulations and similar ones in the literature are discussed. The proposed formulation presents a general approach to ALE method. It includes load correction terms and is suitable for rate-dependent and rate-independent material constitutive law. The proposed formulation reduces to both updated Lagrangian and Eulerian formulations as special cases.     

On a certain two-sided symmetric condition in magnetic field analysis and computations

A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.     

Modifications of the Wolfe Line Search Rules to Satisfy Second-Order Optimally Conditions in Unconstrained Optimization

The line search method incorporating the Wolfe conditions is modified to ensure that a descent algorithm terminates in a finite number of steps at an approximate stationary point where the second-order conditions of optimality are satisfied. A simple procedure based on conjugate directions is proposed to determine directions of negative curvature.     

An efficient algorithm for elasto-viscoplastic vibrations of multi-layered composite beams using second-order theory

An efficient time-domain algorithm for plane non-linear flexural vibrations of multi-layered composite beams, which are driven into the inelastic range by severe transverse loadings, is presented. The influence of an axial static preload is considered in the sense of the quasi-linear second-order theory of structures. The inelastic parts of strain are treated as additional sources of selfstress in the linear elastic background-structure, driving the elastic response into the inelastic one. The efficiency of this exact formulation lies in the fact that linear solution techniques can be used in their most powerful form: Rubin's useful formulation for the quasi-static second-order transfer-matrix of linear elastic structures is applied in combination with modal analysis. Having in mind multi-metal beams, the classical lamination theory is assumed to be valid. Beams with overhang composed of ideal elastic-plastic and viscoplastic layers are studied as example structures. The fictitious sources of selfstress are calculated from the different material laws of the layers in a numerical time-stepping procedure, where a generalized midpoint-rule in combination with Crisfield's secant-Newton procedure is used.