High accuracy analysis of the finite element method for nonlinear viscoelastic wave equations with nonlinear boundary conditions

The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.     

A posteriori error analysis of nonconforming methods for the eigenvalue problem

This paper extends the unifying theory for a posteriori error analysis of the nonconforming finite element methods to the second order elliptic eigenvalue problem. In particular, the author proposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems and prove its reliability and efficiency based on two assumptions concerning both the weak continuity and the weak orthogonality of the nonconforming finite element spaces, respectively. In addition, the author examines these two assumptions for those nonconforming methods checked in literature for the Laplace, Stokes, and the linear elasticity problems.     

Remarks on a benchmark nonlinear constrained optimization problem

1 .INTRODUCTIONThe benchmark nonlinear constrained problemwas originally put forward by Hi mmelblau[1]in1972 , and ever since then it has been regardedas a benchmark nonlinear constrained opti miza-tion problem for intelligence opti mization algo-rithms . However , just because of the citationerror made by Homaifar[2]in 1994 , two abso-lutely different results are obtained by independ-ent researchers . This problem is reevaluated inthe present study and the best-known solutionfor the“mis…     

一类"非常规"系统的仿真方法

精密机电元件可化为非线性“非常规”平面梁柱有限元系统。基于这个系统的共同特征，构造了这类‘非常规。的通用数学模型及其迭加解法．基于不同的“非常规”条件，构造五类具体的迭加解法及同步为束算法．基于不同的系统特征，构造了三类具体系统安装到工作过程的数学模型．采用“非常规”非线性有限元与正交回归设计相结合的方法，建立了表征系统工作状态及具体性能的拟合算式，并对仿真方法的精度和系统寿命进行了讨论．     

基于有限单元的贝叶斯滤波估计算法

现代工程系统具有较强的非线性特性,针对这类非线性系统的状态估计问题,提出基于有限单元的贝叶斯原理估计的非线性滤波方法。采用有限单元法逼近系统状态的先验概率解,即前向Kolmogorov方程的解,通过贝叶斯估计得到状态的后验信息。将其方法应用到惯性/地形组合导航系统中,仿真结果表明该方法的可行性。     

DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM

In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.     

求解非光滑最优控制问题的自适应网格优化

针对传统直接配点法在求解非光滑最优控制问题时存在离散误差大、精度低的问题, 提出了一种自适应直接配点法。利用局部分段插值多项式逼近最优解, 将最优控制问题离散为非线性规划问题, 并给出了离散误差估计方法, 根据离散误差的大小确定区间内节点的加密量, 提出了自适应网格优化算法, 利用该算法将大部分节点配置在非光滑区域以降低离散误差。最后通过仿真算例将所提算法与传统直接配点法和文献中的拟谱自适应算法分别进行比较,验证了所提算法的高精度和有效性。     

GALERKIN ALTERNATING-DIRECTION METHODS FOR NONRECTANGULAR REGIONS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

For the transient behavior of a semiconductor device, the modified method of characteristics with alternating-direction finite element procedures for nonrectangular region is put forward. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, symmetrical reflection, energy method, negative norm estimate and a prior estimates and techniques, are employed. In the nonrectangular region case, optimal order estimates in L2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved.     

THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR—SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.     

Theoretical Computation of Nonlinear System Equations of Heavier Pellets Movements for Two Phase Flow

This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

An Interactive Two-Level Multiobjective Decision Method

In view of two-level multiobjective decision making problem, and employing satisfactoriness of     

An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with L~1-Control Cost

Elliptic PDE-constrained optimal control problems with L~1-control cost(L~1-EOCP) are considered. To solve L~1-EOCP, the primal-dual active set(PDAS) method, which is a special semismooth Newton(SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers(ADMM), we consider extending the ADMM to L~1-EOCP. To discretize L~1-EOCP, the piecewise linear finite element(FE) is considered. However, different from the finite dimensional l~1-norm, the discretized L~1-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L~1-norm and L~2-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem,an inexact heterogeneous ADMM(ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set(PDAS)method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates,but also show that the ihADMM and the two-phase strategy are highly efficient.     

结构元线性生成的模糊线性微分系统

主要目的是利用模糊结构元方法来解决模糊线性微分系统的模糊初值问题.首先，简单地介绍了模糊结构元方法，根据该方法定义了线性生成的模糊线性微分系统.其次，利用由模糊结构元线性表示的模糊值函数和模糊值函数的导数，研究了模糊线性微分系统的求解问题，给出了系统解存在的充要条件.最后，将给出一个实际例子，进一步表明了该方法的有效性.     

SINS/CNS/GPS integrated navigation algorithm based on UKF

A new nonlinear algorithm is proposed for strapdown inertial navigation system (SINS)/celestial navigation system (CNS)/global positioning system (GPS) integrated navigation systems. The algorithm employs a nonlinear system error model which can be modified by unscented Kalman filter (UKF) to give predictions of local filters. And these predictions can be fused by the federated Kalman filter. In the system error model, the rotation vector is introduced to denote vehicle’s attitude and has less variables tha...     

基于多特显点的无人机分布式相参雷达相位同步误差估计方法

分布式相参雷达(distributed coherent aperture radar, DCAR)实现全相参的关键是相位同步。然而,滤波器网格失配、单元雷达较强机动性及姿态变化等因素均会对DCAR的相位同步带来不利影响,为此,针对DCAR的相位同步问题,该文提出了一种基于多特显点的无人机DCAR相位同步误差估计方法。该方法首先提出了利用多项式迭代方法消除由于滤波器网格失配引进的残余相位,并根据惯导提供的姿态信息对DCAR回波进行姿态补偿,然后提出了利用Taylor估计法对各单元雷达位置误差进行估计,再根据自校正算法估计出了剩余相位误差,最后对DCAR系统校准以实现相位同步。仿真实验验证了研究结论的正确性。     

基于非对称交互多模型弹道导弹跟踪

弹道导弹飞行三个阶段的动力学模型异常复杂且非线性强,在未知导弹任何先验信息前提下如何连续地跟踪整个弹道已成为目前亟待解决的难题。针对该问题,提出了一种实时非对称交互多模型跟踪算法,它根据弹道不同阶段的受力情况建立相应的跟踪模型。该算法采用非对称的状态交互以及基于熵信息变化的模型概率更新方法对导弹进行实时状态估计,并将其中一个无迹滤波器的非线性状态估计用改进离散方法实现,提高了实时性。仿真实验表明,该跟踪算法能够较精确地从弹道主动段连续地跟踪到再入段,并且能较大幅度地减小模型切换之间的跟踪误差。     

Nonconforming finite element method for nonlinear parabolic equations

<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.     

基于粒子群优化的卡尔曼滤波去耦算法

针对相控阵雷达导引头由于前向通道增益和波束控制增益刻度尺度不同引起的扩展卡尔曼滤波(extended Kalman filter, EKF)去耦中误差量过大的问题,提出了基于粒子群优化的EKF去耦算法。采用了最小均方差为适应度函数,对两个增益参数进行组合优化,然后通过建立EKF的系统模型,推导了提取的视线角速率与增益参数之间的关系,使得滤波后的估计值为最优的后验估计。最后,通过仿真表明该算法可以很好地解决误差量过大的问题,并验证了所提算法在相控阵雷达导引头去耦和视线角速率提取中的有效性。     

A Robust Output—Feedback Controller for a Class of Uncertain Nonlinear Systems

1　IntroductionRecently,the nonlinear output- feedback control problems are solved successfully by usingbackstepping for a class of nonlinear systems. The partialstate feedback control problemsolved in Jiang and Praly,1996 is more general than the output- feedback control problem.However,the assumptions made in the paper are too restrictive which does not only re-quire the existence of c,γ andψ1 to be ascertained a priori,but also require them to beknown for an unknown system. If c,γ can n…