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1.
AbstractWe study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results. 相似文献
2.
Watson S.J. Barry D.A. Schotting R.J. Hassanizadeh S.M. 《Transport in Porous Media》2002,47(2):149-167
Recently, it has been suggested that Darcy's Law might not be applicable for modelling miscible, density-dependent flow in porous media. To investigate this, three sets of careful laboratory column experiments were performed on coarse and medium sands, consisting of upward displacement of water by sodium chloride solutions with concentrations ranging from 5 to 200g/l. Data on salt concentrations and water pressures were collected in horizontal transects along the flow direction. Salt concentration data were also collected in the influent and exit lines. The experimental data were analysed using a simplified approach based on Darcy's Law alone, applied with the assumption of a sharp interface. Darcy's Law was used to estimate porous medium permeability by fitting predictions to experimental data. Consistent estimates of permeability were obtained for each set of experiments. The results indicate that Darcy's Law adequately describes high concentration displacements through saturated coarse- and medium-grained porous media. 相似文献
3.
改进的移动最小二乘法 总被引:4,自引:2,他引:4
近年来发展的无网格方法大多采用移动员小二乘法来构造试函数,而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的,从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进,避免出现病态方程组,且在计算过程中不需要进行短阵求逆运算,提高了计算速度。之后,借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。 相似文献
4.
《Analytical letters》2012,45(11):2051-2058
Abstract The use of partial least-squares spectrophotometric calibration for the simultaneous determination of suppositories in a multicomponent formulation is presented. This method is applied to the deternination of acetaminophen and phenobarbital in suppository preparations. The results show that these components in a molar ratio of about 61:1 in suppositories have been determined simultaneously with high precision. 相似文献
5.
In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper. 相似文献
6.
Hui Guo 《Applied mathematics and computation》2011,217(9):4682-4690
In this paper, we introduce two novel split least-squares mixed element procedures for pseudo-parabolic equations. By selecting the least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable u, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable σ. Optimal order error estimates are developed. A numerical example is given to show the efficiency of the introduced schemes. 相似文献
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针对飞行器气动力多源数据融合、飞行试验气动辨识问题,提出了一种基于Chebyshev-Taylor-Fourier混合级数模型函数、不确定度平衡权函数和加权最小二乘原理的多源数据融合和辨识方法.该方法采用二元Chebyshev级数、Taylor级数和Fourier级数技术建立飞行器气动模型函数,采用权函数技术平衡各数据源间的不同精度和不确定度,采用最小二乘法原理确定超定方程组解,从而获得Chebyshev-Taylor-Fourier混合级数模型函数的各项参数值,最终确定多源数据融合的飞行器气动力(力矩)系数模型函数数学表达式.典型的应用实例表明该方法高效实用、精度可靠,工程应用前景良好. 相似文献
10.
The AME 2020 atomic mass evaluation (I). Evaluation of input data,and adjustment procedures 下载免费PDF全文
This is the first of two articles(Part I and Part II)that presents the results of the new atomic mass evaluation,Ame2020.It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II.This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction,decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties.All input data,including both the accepted and rejected ones,are tabulated and compared with the adjusted values obtained from the least-squares fit analysis.Differences with the previous Ame2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to Ame users. 相似文献