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Considered in this paper is a Cauchy problem governed by an elliptic partial differential equation. In the Cauchy problem, one wants to recover the unknown Neumann and Dirichlet data on a part of the boundary from the measured Neumann and Dirichlet data, usually contaminated with noise, on the remaining part of the boundary. The Cauchy problem is an inverse problem with severe ill-posedness. In this paper, a coupled complex boundary method (CCBM), originally proposed in [Cheng XL, Gong RF, Han W, et al. A novel coupled complex boundary method for solving inverse source problems. Inverse Prob. 2014;30:055002], is applied to solve the Cauchy problem stably. With the CCBM, all the data, including the known and unknown ones on the boundary are used in a complex Robin boundary on the whole boundary. As a result, the Cauchy problem is transferred into a complex Robin boundary problem of finding the unknown data such that the imaginary part of the solution equals zero in the domain. Then the Tikhonov regularization is applied to the resulting new formulation. Some theoretical analysis is performed on the CCBM-based Tikhonov regularization framework. Moreover, through the adjoint technique, a simple solver is proposed to compute the regularized solution. The finite-element method is used for the discretization. Numerical results are given to show the feasibility and effectiveness of the proposed method. 相似文献
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数值计算中一类病态不适定问题的求解方法 总被引:1,自引:0,他引:1
利用奇异值分解研究了工程计算中常见的最小二乘法及大条件数下病态问题的不适定,并给出了具体的求解方法,结果表明,该算法是有效的。 相似文献
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Generation of optimal correlations by simulated annealing for ill-conditioned least-squares solution
A typical process of determining parameters of empirical correlation is collecting measurements of experiments and applying least-squares method with over-determined number of variable data. Least-squares problems occur frequently in the parameter identification of linear/nonlinear dynamic models, model fitting using dimensionless variables in flow interfacial treatment, heat transfer and pressure drop models, etc. Considering the inevitable measurement noise and careless experimental design, the ill-posedness property of the least-squares method can arise and limit the accuracy of the assumed correlation structures. In this paper, a method of simulated annealing is proposed for estimating power-law parameters of the empirical correlation of experimental data. The method is applied to the determination of the hydrogen removal correlation being used in reactor containment analysis. The analysis results show the remarkable improvement in accuracy and robustness for the noisy measurement data. 相似文献
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改进Landweber预迭代ERT图像重建算法 总被引:2,自引:0,他引:2
由于电阻层析成像问题本身严重病态,导致重建图像分辨率较低。为了提高重建图像精度,提出一种改进Landweber预迭代图像重建算法。首先,利用改进粒子群算法离线优化灵敏度矩阵,改善其病态程度,同时缩小满足算法收敛条件的增益因子取值范围;再设置4种典型流型,计算算法重建图像与其相关系数的平均值,并将平均值作为适应度函数,利用改进粒子群算法离线选择Landweber预迭代算法增益因子,并将改进算法应用于两相流典型流型与复合流型图像重建。实验结果表明,相同实验条件下,与在线预迭代(offline iteration online reconstruction,OIOR)算法、经验选择增益因子Landweber预迭代算法相比,新算法有效提高了图像重建质量,而与修正牛顿-拉夫逊算法相比,在不影响成像精度的前提下,提高了算法实时性。 相似文献
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针对各向异性扩散方程中的“病态性”问题,从能量函数的角度对其原因进行分析,并依据稳定性的要求选择合适的扩散系数。采用几种不同的扩散系数加以对比实验。实验证明,改进后的扩散系数可以较好的消除“阶梯效应”。 相似文献
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基于Tikhonov正则化方法,对一种第一类Fredholm积分方程进行离散正则化处理,得到了求解一类带扰动离散数据二阶导数的稳定算法,它在数据的误差水平已知和未知情况下均可应用.基于Richardson外推算法对半离散正则化算法进行了改进.最后设计了全面、系统的数值试验,对现行几种二阶数值微分算法的性能进行测试、比较... 相似文献
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电阻抗成像技术(EIT)是解决接地网腐蚀定位问题的方法之一,为了改善接地网 EIT 逆问题的病态性,提高求解稳定
性以及重建图像清晰度,提出了经典吉洪诺夫正则化(Tikhonov)和全变差正则化(TV)相结合的混合正则化(Tikhonov-TV)接地
网成像算法。 首先,在循环测量原理的基础上,创新地借助 COMSOL 与 MATLAB 联合仿真求取接地网 EIT 正问题模型电压数
据;其次,在理论分析基础上,通过 Tikhonov-TV 正则化的 EIT 算法分别求解基于先验拓扑信息和未知拓扑信息的两种接地网逆
问题模型的场域电阻率分布;最后仿真和实验对比了 Tikhonov、TV 以及 Tikhonov-TV 3 种正则化算法的接地网 EIT 重建图像,并
采用电阻率均方误差(Resistivity MSE)和截线电阻率曲线图来衡量图像质量,实验得出基于先验拓扑信息的 1 处和 2 处腐蚀情
况下 Resistivity MSE 分别达到 1. 27×10
-15 和 1. 59×10
-15
,电阻率均方误差最小。 结果表明,提出的 Tikhonov-TV 正则化算法有效
地改善了 EIT 逆问题的病态性,收敛性能最优,重建图像效果优于 Tikhonov 和 TV 正则化算法。 相似文献
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文章首先指出土体邓肯-张模型的参数反演存在两种不适定问题。根据参数反演时不同区间反演目标函数的性质,结合不适定问题的经典定义,提出参数反演的区间适定和区间不适定的概念,给出适定区间和不适定区间的定义。基于函数单调性和函数导数性质,给出单双参数反演情形下确定适定区间和不适定区间的方法。研究结果表明,基于区间适定和区间不适定理论的参数反演,能够有效确定邓肯-张模型参数反演的适定区间和反演结果。 相似文献