CHARACTERISTIC ALTERNATING-DIRECTION FINITE ELEMENT METHODS FOR NONRECTANGULAR REGIONS FOR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA AND ITS ANALYSIS

For coupled system of multilayer dynamics of fluids in porous media, the characteristic alternating-direction finite element methods for nourectangular regions applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, isoparametric transformation, patch approximation, operator-splitting, characteristic method, negative norm estimate, energy method, the theory of prior estimates and techniques are used. For the nourectangular regions case, optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thus the well-known theoretical problem has been thoroughly and completely solved. These methods have been successfully used in multilayer oil resources migration-accumulation numerical simulation.     

HIGHLY NONCONFORMING FINITE ELEMENT APPROXIMATIONS FOR A FOURTH ORDERVARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element spaces.Morley‘s element approximation is our special case.     

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.     

CHARACTERISTIC FINITE DIFFERENCE METHODS FOR POSITIVE SEMIDEFINITE PROBLEM OF TWO-PHASE(OIL AND WATER)MISCIBLE FLOW IN POROUS MEDIA

Numericalsimulationoftwo-phase(oilandwater)miscibleflowinporousmediaisthe'mathematicalfoundationinenergyproblems.Forapositivedefiniteproblem,thefamousmathematicianandinitiatorofnumericalsimulationofoildeposit,J.Douglas,Jr.putforwardthefamouscharacteristicfinitedifferencemethodll'2].However,fornumericalanalysistherearoseseriousdifficulties.Heonlystudiedtheperiodiccasesandcoercivelysupposedthedictionmatrixoftheconcentrationequationispositivedefinite.Butinmanypracticalsituationsthediffusionmatr…     

Bayesian image superresolution and hidden variable modeling

<正> Superresolution is an image processing technique that estimates an original high-resolutionimage from its low-resolution and degraded observations.In superresolution tasks,there have beenproblems regarding the computational cost for the estimation of high-dimensional variables.Theseproblems are now being overcome by the recent development of fast computers and the developmentof powerful computational techniques such as variational Bayesian approximation.This paper reviewsa Bayesian treatment of the superresolution problem and presents its extensions based on hierarchicalmodeling by employing hidden variables.     

MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONL INEARINTEGRO-DIFFERENTIAL EQUATIONS

1. IntroductionWe consider a Volterra integro-differential equationwith initial condition u(0) = not where f, P, k are continuous on their respective domainsJ, JxR and axs (n:~ {(t,s): 05s5t5T}) such that (1.l) possesses a unique solutionu E C'(J).It has been shown in [1] that the collocation approximation for (1.1) by discolltinuous piece--wise polynomial spline collocation at the Gauss points restore optimal local superconvergenceat the knots but does not yield global superconvergence on…     

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.     

A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

In this paper,the linear mixed finite element method is considered forthe biharmonic Dirichlet boundary value problem.Almost optimal error estimates,superconvergence estimates and the derivative error expansion are obtained.     

METHODS OF ESTIMATION FOR QUASI-INDEPENDENCE IN CONTINGENCY TABLES

1.IntroductionAnUInberofauthorshaveconsideredtheproblemoffittingmodelsofquasi-independencetocontingenCytabledatawhichareeithertriangUlarorhaveanexcludeddiagonal.hithispaperthevariousmethodsproposedforfittingthesemodelsarecompared.ItisthenshoWnthstparameterestimatesarethesamefordifferentmodelsinsomecases.Anew,verysample,easytoimplemeDtalgoritlunispreseDted.Finallysomepreviousiterstivemethodsarecomparedwiththenewmethod.2.Quasi-IndependenceModeisforContingencyamblesSupposethatatwo-waycolltin…     

IMPLICIT—EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by the finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The optimal L^2-norm error estimates are derived.     

时空地理加权回归模型的时空非平稳性检验

针对时空地理加权回归模型,通过时空加权距离构造权重矩阵,采用地理加权拟合技术得到回归系数的逐点估计. 构造合适的统计量对回归系数进行关于时间和空间的非平稳性检验,利用三阶矩χ²逼近方法计算检验的p值. 最后,模拟算例和实际例子都说明该检验方法的有效性.     

AN EXTRAPOLATION METHODFOR FINITE ELEMENT APPROXIMATION OF INTEGRODIFFERENTIAL EQUATIONS WITH PARAMETERS

In this paper,we discuss the accelerating convergence method for finite elementapproximation of integro-differential equations with parameters.As applications,we give theerror estimates of finite element for the first kind of Fredholm integral equation,particularlyfor the Volterra integral equation with kernel condition k(x,x)=0.     

ITERATIVE METHODS OF OBTAINING ESTIMATES FOR INCOMPLETE CONTINGENCY TABLES

An iterative method of De Jong,Greig and Madan(1985)for obtaining maximum likelihoodestimates for contingency tables derived from a Mover-Stayer model is considered.It is shown that thismethod works for other sampling schemes leading to incomplete contingency tables.Moreover,compar-isons indicate that the method is very fast.     

THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHOD FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

1.IntroductionThefiaiteelementprobabilitycomputationalmethodisakindofnumericalcalculationtecboqueofauniquestyle.Themethodshavebeendevelopedduringthefiftiestosixesforuseindeferencemethodll'2'3)andforsolvingsystemofalgebraicequations.Inengineeringandphysicsproblems,oftenwehavetosolvetheconcelltratedloadproblem.Inthiscase,weneedonlytoknowthevaluesofthefunctionatafewnodalpoilltsofthedomain.Itwillwastealotoftimetocomputetheunnecessaryvaluesofthefunctionbythefiniteelemelltmethods(ordeferencemethods…     

Recursive Identification of Quantized Linear Systems

This paper studies the identification of linear systems with quantized output observations.Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorithms with expanding truncations(SAAWET). Under suitable conditions, it is shown that the estimates converge to the true values almost surely.     

基于特殊阵列的相干信源二维测向新方法

基于特殊天线阵列,提出了一种有相干源存在情况下的二维波达方向(DOA)估计的新方法。该方法利用天线阵列结构的特点来构建一个特殊的协方差矩阵,再根据2-D ESPRIT方法实现二维DOA估计。该方法不需采用空间平滑技术,也不需谱峰搜索,而且参数可以实现自动配对。最后计算机仿真验证了该方法的有效性。     

成败型产品环境因子的经典近似限

利用Poisson近似和正态近似,本文导出了二项分布,负二项分布以及二项～负二项分布环境因子的经典近似限。     

基于部分交叉验证的多准则序贯近似建模方法

提高序贯近似建模的精度和收敛效率,关键在于制定合理有效的序贯抽样准则。针对如何有效获取目标系统信息进行近似建模,同时提高建模精度和收敛效率,提出了基于部分交叉验证的多准则序贯近似建模方法。通过融合部分交叉验证误差估计准则、极大序贯建模累积变化准则和极大熵准则的特征和优势,可实现对全空间全面抽样和对不规则区域重点抽样,进而提高近似模型的精度和收敛效率。算例测试表明该方法在提高序贯近似建模精度和收敛效率方面可行有效。     

CONVERGENCE PROPERTIES OF PROJECTED GRADIENT METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR CONVEX CONSTRAINED OPTIMIZATION

1. IntroductionGiven some function f(x): Wu - FI over a nonempty closed set n C W", one is interestedin solving the fOllowing optimization problem with constraints amin f(x)s.t. x E n (1.1)where f(x): Q C Wu - FI is twice continuously differentiable. This problem has receivedconsiderable attention extensively. The linear constrained case where n is a polyhedron is ofspecial inferest. Recently, there are quite a few articles proposing projected gradient methodsto solve the problem (see, fo…     

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.