High accuracy nonconforming finite elements for fourth order problems

The approach of nonconforming finite element method admits users to solve the partial differential equations with lower complexity,but the accuracy is usually low.In this paper,we present a family of highaccuracy nonconforming finite element methods for fourth order problems in arbitrary dimensions.The finite element methods are given in a unified way with respect to the dimension.This is an effort to reveal the balance between the accuracy and the complexity of finite element methods.     

Numerical simulations for a variable order fractional cable equation

In this article, Crank-Nicolson method is used to study the variable order fractional cable equation. The variable order fractional derivatives are described in the RiemannLiouville and the Gr¨unwald-Letnikov sense. The stability analysis of the proposed technique is discussed. Numerical results are provided and compared with exact solutions to show the accuracy of the proposed technique.     

THE OPTIMAL CONTROL SYSTEM OF 3D HORIZONTAL WELL AND ITS APPLICATION

A multi-objective optimal control model for nonlinear multilevel dynamicalsystem is built in this paper. The existence of the solutions to this systemand the controllability and the polykeys of the control are discussed. In orderto obtain the global optimal solution, Uniform Design method is introducedto select initial1 feasible points, then an improved Hooke-jeeves algorithm isproposed. The new algorithm and its corresponding software we developed hasvalidated in more than 12 horizontal wells, which show their advantages suchas less length of trajectory designed, more accuracy of target hitting and lesstime-consuming comparison with present conventional method.     

AN EFFICIENT ADER DISCONTINUOUS GALERKIN SCHEME FOR DIRECTLY SOLVING HAMILTON-JACOBI EQUATION

This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.     

EDGE-ORIENTED HEXAGONAL ELEMENTS

In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space Q1^（3） and are edge-oriented, analogical to the case of the rotated Q1 quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the L^2 norm. This theoretical result is confirmed by the numerical tests.     

DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES

The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the     

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy gen...     

A projection method and Kronecker product preconditioner for solving Sylvester tensor equations

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.     

对偶算法的进一步研究

The dual algorithm for minimax problems is further studied in this paper. The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm. At last ,the numerical experiments are reported to validate the analysis results.     

Regular solutions for multiplicative stochastic Landau-Lifshitz-Gilbert equation and blow-up phenomena

The two-dimensional Landau-Lifshitz-Gilbert equation of motion for a classical magnetic moment perturbed by a multiplicative noise is considered. This equation is highly nonlinear in nature and, for this reason, many mathematical results in stochastic partial differential equations (SPDEs) cannot be applied. The aim of this work is to introduce the difference method to handle SPDEs and prove the existence of regular martingale solutions in dimension two. Some blow-up phenomena are presented, which are drastically different from the deterministic case. Finally, to yield correct thermal-equilibrium properties, Stratonovitch integral is used instead of Ito integral.     

A Fourier spectral method for fractional-in-space Cahn–Hilliard equation

In this paper, a fractional extension of the Cahn–Hilliard (CH) phase field model is proposed, i.e. the fractional-in-space CH equation. The fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case. An unconditionally energy stable Fourier spectral scheme is developed to solve the fractional equation with periodic or Neumann boundary conditions. This method is of spectral accuracy in space and of second-order accuracy in time. The main advantages of this method are that it yields high precision and high efficiency. Moreover, an extra stabilizing term is added to obey the energy decay property while maintaining accuracy and simplicity. Numerical experiments are presented to confirm the accuracy and effectiveness of the proposed method.     

Regarding the accuracy of optimal eighth-order methods

It is widely known that when the order of root solvers increases, their accuracy comes up as well. In light of this, most of the researchers in this field of study have tried to increase the order of known schemes for obtaining optimal three-step eighth-order methods in which there are four evaluations per iteration. The aim of this article is to challenge this standpoint when the starting points are in the vicinity of the root, but not so close. Toward this end, a novel method of order six with the same number of evaluations per iteration is suggested and demonstrated while its accuracy is better than the accuracy of optimal eighth-order schemes for such initial guesses. The superiority of the developed technique is confirmed by numerical examples.     

A SINGLE STEP SCHEME WITH HIGH ACCURACY FOR PARABOLIC PROBLEM

1 IntroductionConsider one-dimellsional parabolic problem in fl = (0, 1)and its weak formulatioll: find u(t) E S0 = {v 6 H'(fl), v(0) = 0} 8uch thatwhere the coefficients a(x) and b(x) are independent of t, Au = --(au')' ha, a(x) 2 ao > 0, b 20, and bilinear fOrm A(u, v) = fol(au'V' buv)dx i8 So-coercive, i.e. A(u, v) 2 ullu1li, u ESO, u > 0.Make in n = (0, 1) a subdivision: xo = 0 < x1 < x2 <.' < xn = 1. Set an elenlentry = (xj--l, xj), nddpoint xj--1/2 = (ry n--1)/2 and steplengt…     

基于GA-SVM的水资源可持续利用评价

把水资源可持续利用评价问题看成是一个分类问题,利用支持向量机良好的鲁棒性和分类精确性进行评价,并用遗传算法优化了SVM的参数,使其分类精确度更高.对黑龙江省十三个地区进行了实例应用,与人工神经网络和GD-IIM法的结果进行了比较,结果表明,支持向量机模型简单、通用、精度高,可在水资源可持续利用实际评价中推广应用.     

一种新的叠层板壳高阶理论

本文提出了一种新的叠层板壳高阶理论,然后又研究了正交对称叠层板,反对称叠层板,圆柱弯曲和球壳弯曲问题.为了检验理论的准确性,文中计算了几个特殊例子,数值结果和精确解吻合得相当好,说明本理论具有较高的准确度,且表现出未知数较少,解题方便的优点.     

A new component mode synthesis method: Quasi-static mode compensation

A new component mode synthesis method is presented in this paper that combines the computational efficiency of the well-known constraint mode approach with the dynamic compensation accuracy obtained by higher-order expansion methods. Instead of employing static constraint modes, quasi-static modes are used to capture inertial effects of the truncated modes. The method is ideally suited for mid-band frequency analysis in which both high-frequency and low-frequency modes may be omitted. A tuning parameter, designated as the centering frequency, controls the dynamic range of the quasi-static modes. Numerical examples are provided which demonstrate the improved accuracy of the proposed method.     

Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions

In this paper, a new difference scheme based on quartic splines is derived for solving linear and nonlinear second-order ordinary differential equations subject to Neumann-type boundary conditions. The scheme can achieve sixth order accuracy at the interior nodal points and fourth order accuracy at and near the boundary, which is superior to the well-known Numerov’s scheme with the accuracy being fourth order. Convergence analysis of the present method for linear cases is discussed. Finally, numerical results for both linear and nonlinear cases are given to illustrate the efficiency of our method.     

Heuristics for feature selection in mathematical programming discriminant analysis models

In developing a classification model for assigning observations of unknown class to one of a number of specified classes using the values of a set of features associated with each observation, it is often desirable to base the classifier on a limited number of features. Mathematical programming discriminant analysis methods for developing classification models can be extended for feature selection. Classification accuracy can be used as the feature selection criterion by using a mixed integer programming (MIP) model in which a binary variable is associated with each training sample observation, but the binary variable requirements limit the size of problems to which this approach can be applied. Heuristic feature selection methods for problems with large numbers of observations are developed in this paper. These heuristic procedures, which are based on the MIP model for maximizing classification accuracy, are then applied to three credit scoring data sets.     

A new method for estimating the forecast quality with consideration for the errors of calculating the unknown parameters

In this study, the problem of estimating the forecast accuracy of a model is considered. A widespread practice is to approximate the population expectation of the forecast accuracy by the sample expectation, which is equivalent to the uniform consideration for the deviations of the forecast from the exact value of a quantity for all time moments. If the vector of unknown parameters is estimated at each step only from the preceding observations, the significance of the deviations is not the same at all time moments. In this study, we propose a method that takes into account the forecast errors with different weights. The problem of constructing the most accurate estimate of the forecast quality, a parameter from which the condition for the optimal weights can be derived, is formalized. Monte-Carlo experiments are used to compare the accuracy of the methods for estimating the forecast quality in the cases when the observations are taken into account with the same weights, with optimum weights, and with the weights calculated using a numerical procedure.     

Finite difference spectral approximation for the time‐space fractional telegraph equation and its parameter estimation

The object of this paper is to present the numerical solution of the time‐space fractional telegraph equation. The proposed method is based on the finite difference scheme in temporal direction and Fourier spectral method in spatial direction. The fast Fourier transform (FFT) technique is applied to practical computation. The stability and convergence analysis are strictly proven, which shows that this method is stable and convergent with (2?α) order accuracy in time and spectral accuracy in space. Moreover, the Levenberg‐Marquardt (L‐M) iterative method is employed for the parameter estimation. Finally, some numerical examples are given to confirm the theoretical analysis.