An element decomposition method with variance strain stabilization

An element decomposition method with variance strain stabilization(EDM-VSS) is proposed. In the present EDM-VSS, the quadrilateral element is first divided into four sub-triangular cells, and the local strains in sub-triangular cells are obtained using linear interpolation function. For each quadrilateral element, the strain of the whole quadrilateral is the weighted average value of the local strains, which means only one integration point is adopted to construct the stiffness matrix. The stabilization item of the stiffness matrix is constructed by variance of the local strains, which can eliminate the instability of the one-point integration formulation and largely increase the accuracy of the element. Compared with conventional full integration quadrilateral element, the EDM-VSS achieves more accurate results and expends much lower computational cost. More importantly, as no mapping or coordinate transformation is involved in the present EDM-VSS, the restriction on the conventional quadrilateral elements can be removed and problem domain can be discretized in more flexible ways. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied to demonstrate the efficiency of the present EDM-VSS.

EFFECTS OF RARE EARTH ELEMENTS ON THE CHARACTERISTICS OF AUTO-TEMPERING AND DECOMPOSITION OF MARTENSITE FOR A LOW CARBON Si-Mn-V STEELS

The effect of rare earth metals(REM)on the characteristics of auto-tempering and decomposition of martensite for low-carbon and low-alloy steels(20SiMn2V and 20SiMn2VRE)was investigated using TEM,dilatometer and microhardness test.Results show that both ε.and θ carbides,during auto-tempering, may precipitate from the low-carbon martensite matrix at the same time in the 20SiMn2V steel,however,the precipitation of the ε-carbides can be inhibited by the REM contained in the 20SiMn2 VRE steel,resulting in change of the type of precipitated carbides and decrease of the extent of auto-tempering.The“in-situ”ob- servations show that the decomposition of martensite is also inhibited by the REM contained in the 20SiMn2 VRE steel during low temperature tempering.

Global attractor for Klein-Gordon-Schrodinger lattice system

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schroedinger equation （KGS lattice system）. We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using ＂End Tails＂ of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

THE OPTIMAL PRECONDITIONING IN THE DOMAIN DECOMPOSITION METHOD FOR WILSON ELEMENT

This paper discusses the optimal preconditioning in the domain decomposition method for Wilson element. The process of the preconditioning is composed of the resolution of a small scale global problem based on a coarser grid and a number of independent local subproblems, which can be chosen arbitrarily. The condition number of the preconditioned system is estimated by some characteristic numbers related to global and local subproblems. With a proper selection, the optimal preconditioner can be obtained, while the condition number is independent of the scale of the problem and the number of subproblems.

TRACE AVERAGING DOMAIN DECOMPOSITION METHOD WITH NONCONFORMING FINITE ELEMENTS

We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. We show its geometric convergence and present the dependence of the convergence factor on the relaxation factor, the subdomain diameter H and the mesh parameter h. In essence;, this method is equivalent to the simple iterative method for the preconditioned capacitance equation. The preconditioner implied in this iteration is easily invertible and can be applied to preconditioning the capacitance matrix with the condition number no more than O((1 + In H/h)max(1 + H-2, 1 + In H/h)).

Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for κ-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-SchrSdinger Equation

In this paper, we establish the existence of a global attractor for a coupled κ-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-SchrSdinger Equation. An estimate of the upper bound of the Kohnogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented .