Dynamic analysis of thick laminated shell panel with piezoelectric layer based on three dimensional elasticity solution

Elasticity solution is presented for infinitely long, simply-supported, orthotropic, piezoelectric shell panel under dynamic pressure excitation. The direct and inverse piezoelectric effects are considered. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations (o.d.e.) with variable coefficients by means of trigonometric function expansion in circumferential direction. The resulting ordinary differential equations are solved by the finite element method. Numerical examples are presented for [0/90/P] lamination, where P indicates the piezoelectric layer. Finally the results are compared with the published results.     

Relaxation method for unsteady convection–diffusion equations

We propose and implement a relaxation method for solving unsteady linear and nonlinear convection–diffusion equations with continuous or discontinuity-like initial conditions. The method transforms a convection–diffusion equation into a relaxation system, which contains a stiff source term. The resulting relaxation system is then solved by a third-order accurate implicit–explicit (IMEX) Runge–Kutta method in time and a fifth-order finite difference WENO scheme in space. Numerical results show that the method can be used to effectively solve convection–diffusion equations with both smooth structures and discontinuities.     

A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods

A Galerkin finite element method is considered to approximate the incompressible Navier–Stokes equations together with iterative methods to solve a resulting system of algebraic equations. This system couples velocity and pressure unknowns, thus requiring a special technique for handling. We consider the Navier–Stokes equations in velocity––kinematic pressure variables as well as in velocity––Bernoulli pressure variables. The latter leads to the rotation form of nonlinear terms. This form of the equations plays an important role in our studies. A consistent stabilization method is considered from a new view point. Theory and numerical results in the paper address both the accuracy of the discrete solutions and the effectiveness of solvers and a mutual interplay between these issues when particular stabilization techniques are applied.     

Number theoretic fast algorithms for bilinear and other generalizedtransformations

Fast algorithms based on the Mersenne and Fermat number-theoretic transforms are used to perform the bilinear transformation of a continuous transfer function to a discrete equivalent. The computations are carried out in finite precision arithmetic, require no multiplications, and can be implemented in parallel using very simple processors. Although the bilinear transform is presently emphasized, similar algorithms are easily derived for any transformation from the s-plane to the z-plane involving the ratio of two polynomials with integer coefficients     

Block TERM factorization of block matrices

Duetothelimitationofcomputationalprecisionandstoragecapacity,transformsusedinlosslessdatacompressionshouldbeequivalentlyinteger-reversible.Reversibleintegertransform(orintegermapping)issuchatypeoftransformthatmapsintegerstointegersandrealizesperfectreconstruction(PR).Peoplestartedtoworkinthisarealongago,andtheirearlywork,suchasStransform[1],TStransform[2],S+Ptransform[3],andcolorspacetransforms[4],suggestedapromisingfutureofreversibleintegermappinginimagecompression,region-of-interest(ROI)…     

Finite spectrum assignment of multi-input systems with non-commensurate delays

We present a new framework for finite spectrum assignment for multi-input systems with non-commensurate delays using an algebraic approach over multidimensional polynomial matrices. By focusing on the solvability of a Bezout equation over multidimensional polynomial matrices, we derive a necessary and sufficient condition for finite spectrum assignability under which a finite number of spectra can be assigned by a control law using a ring of entire functions, i.e. Laplace transforms of all exponential time functions with compact support. Furthermore, using a solution to the Bezout equation, we present a design method for a controller that achieves finite spectrum assignment.     

一类布尔函数的代数免疫度研究

代数免疫度是近几年提出的一个衡量布尔函数密码学性质的标准。该文研究重量为奇数的布尔函数的代数免疫度和非线性度之间的关系,得到了代数免疫度固定时非线性度的下界,而且证明这个下界是紧的。代数免疫度大干d时,函数的重量有一个范围,证明了这个范围是紧的,即对任何这个范围内的整数t,都存在一个布尔函数其重量为t,代数免疫度大于d。     

An efficient multigrid preconditioner for Maxwell’s equations in micromagnetism

We consider a system of Maxwell’s and Landau-Lifshitz-Gilbert equations describing magnetization dynamics in micromagnetism. The problem is discretized by a convergent, unconditionally stable finite element method. A multigrid preconditioned Uzawa type method for the solution of the algebraic system resulting from the discretized Maxwell’s equations is constructed. The efficiency of the method is demonstrated on numerical experiments and the results are compared to those obtained by simplified models.     

Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices

Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet’s boundary conditions. We use three fully implicit finite difference schemes, two fully explicit finite difference techniques, an alternating direction implicit procedure and the Barakat and Clark type explicit formula. Theoretical and numerical comparisons between four families of methods are described. The main advantage of the alternating direction implicit finite difference technique is that the bandwidth of the sets of equations is a fixed small number that depends only on the nature of the computational molecule. This allows the use of very efficient and very fast techniques for solving the resulting tridiagonal systems of linear algebraic equations. The unique advantage of the Barakat and Clark technique is that it is unconditionally stable and is explicit in nature. Numerical results are presented followed by concluding remarks.     

布尔函数代数免疫度的研究

代数免疫度是度量布尔函数抵抗代数攻击的重要指标。为了抗代数攻击,布尔函数应具有较高的代数免疫度。对于给定的奇数n,得到一个具有最大代数免疫度的布尔函数重量的可除性结果,同时,在任意有限域上,针对关系式fg=h,研究了它的代数免疫度,给出了一些重要结果。     

A collocation finite element-finite difference solution for developing isothermal flow between two parallel plates

This paper presents a finite element-finite difference method for the solution of the boundary layer equations for developing flow between two parallel plates. Due to the parabolic nature of the equations it was possible to discretize the transverse flow direction with one-dimensional Hermite cubic finite elements and the axial flow direction with a backward finite difference approximation. The collocation finite element-finite difference approximation was found to be appropriate for the modeling of the non-linear convection terms in the axial momentum equation. The resulting system of mixed linear and non-linear algebraic equations was solved using the Newton-Raphson method. Several numerical experiments were conducted to study the behavior of the solution with respect to the element size and number, order of finite difference approximation, and the marching step size.     

Finite element analysis of long-period water waves

The finite element representation of the nonlinear equations governing the unsteady flow of the two-dimensional long-period shallow water wave is considered. The approximate solution assumes, that the flow is only a slight perturbation of an existing flow. With this assumption a finite element formulation in terms of discrete nodal values of velocity and water height is generated using Galerkin's method. The resulting matrix equation for an arbitrary triangular-based space-time element constitutes a set of linear algebraic equations solvable for nodal values of the flow variables. The topological properties of estuaries are treated and with the solution thus obtained, numerical results are shown for the North Sea.     

Finite element analysis of viscous,incompressible fluid flow: Part 1 : Basic methodology

A numerical procedure is developed for the analysis of general two-dimensional flows of viscous, incompressible fluids using the finite element method. The partial differential equations describing the continuum motion of the fluid are discretized by using an integral energy balance approach in conjunction with the finite element approximation. The nonlinear algebraic equations resulting from the discretization process are solved using a Picard iteration technique.A number of computational procedures are developed that allow significant reductions to be made in the computational effort required for the analysis of many flow problems. These techniques include a coarse-to-fine-mesh rezone procedure for the detailed study of regions of particular interest in a flow field and a special finite element to model far-field regions in external flow problems.     

Construction of 1-resilient Boolean functions with optimum algebraic immunity

In this paper, for an integer n≥10, two classes of n-variable Boolean functions with optimum algebraic immunity (AI) are constructed, and their nonlinearities are also determined. Based on non-degenerate linear transforms to the proposed functions, we can obtain 1-resilient n-variable Boolean functions with optimum AI and high nonlinearity if n?1 is never equal to any power of 2.     

Tracing post-limit-point paths with reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for predicting the post-limit-point paths of structures. In the proposed approach the structure is discretized by using displacement finite element models. The nodal displacement vector is expressed as a linear combination of a small number of vectors and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of nonlinear algebraic equations.To circumvent the difficulties associated with the singularity of the stiffness matrix at limit points, a constraint equation, defining a generalized arc-length in the solution space, is added to the system of nonlinear algebraic equations and the Rayleigh-Ritz approximation functions (or basis vectors) are chosen to consist of a nonlinear solution of the discretized structure and its various order derivatives with respect to the generalized arc-length. The potential of the proposed approach and its advantages over the reduced basis-load control technique are outlined. The effectiveness of the proposed approach is demonstrated by means of numerical examples of structural problems with snap-through and snap-back phenomena.     

Propagating systems of dense linear integer constraints

In interval propagation approaches to solving nonlinear constraints over reals it is common to build stronger propagators from systems of linear equations. This, as far as we are aware, is not pursued for integer finite domain propagation. In this paper we show how we use interval Gauss–Jordan elimination to build stronger propagators for an integer propagation solver. In a similar fashion we present an interval Fourier elimination preconditioning technique to generate redundant linear constraints from a system of linear inequalities. We show how to convert the resulting interval propagators into integer propagators. This allows us to use existing integer solvers. We give experiments that show how these preconditioning techniques can improve propagation performance on dense systems.     

Least squares support vector regression for solving Volterra integral equations

In this paper, a numerical approach is proposed based on least squares support vector regression for solving Volterra integral equations of the first and second kind. The proposed method is based on using a hybrid of support vector regression with an orthogonal kernel and Galerkin and collocation spectral methods. An optimization problem is derived and transformed to solving a system of algebraic equations. The resulting system is discussed in terms of the structure of the involving matrices and the error propagation. Numerical results are presented to show the sparsity of resulting system as well as the efficiency of the method.

     

The standard H∞ problem in systems with a singleinput delay

The standard H_∞ problem is solved for LTI systems with a single, pure input lag. The solution is based on state-space analysis, mixing a finite-dimensional and an abstract evolution model. Utilizing the relatively simple structure of these distributed systems, the associated operator Riccati equations are reduced to a combination of two algebraic Riccati equations and one differential Riccati equation over the delay interval. The results easily extend to finite time and time-varying problems where the algebraic Riccati equations are substituted by differential Riccati equations over the process time duration     

从所需校正网络相频或幅频曲綫計算传递函数的方法

本文提供了一种从所需校正网络相频或幅频曲线计算校正网络传递函数的方法.利用最小二乘法的变形,通过解线性代数方程组可以得到传递函数系数的最或然值.本文提供的公式适合于用数字电子计算机计算.     

A Class of Domain Decomposition Preconditioners for <Emphasis Type="Italic">hp</Emphasis>-Discontinuous Galerkin Finite Element Methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.