Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov di...Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversion展开更多
图像的非局部变分修复(Non-local Total Variation,NLTV)技术未考虑破损区域边界的连续性,从而在修复区域产生阶梯现象,影响非局部变分模型的修复性能。为实现图像修复边界区域的连续性,将罗宾边界算子引入到非局部拉格朗日方程中,利用...图像的非局部变分修复(Non-local Total Variation,NLTV)技术未考虑破损区域边界的连续性,从而在修复区域产生阶梯现象,影响非局部变分模型的修复性能。为实现图像修复边界区域的连续性,将罗宾边界算子引入到非局部拉格朗日方程中,利用破损程度实现对图像修复扩散强度自适应控制,建立自适应连续性非局部变分(Adaptive Continuous Non-local Total Variation,ACNLTV)的修复模型,给出该模型的交替极小化求解过程。与非局部变分模型的对比实验证明,提出的ACNLTV模型消除了阶梯现象,更好地修复图像的细节信息,峰值信噪比与结构相似性分别提高了0.5 dB与0.2,图像修复性能更优。展开更多
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the γ is a piecewise constant function. By the integral representation formula ...In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the γ is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.展开更多
This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a ...This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.展开更多
文摘Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversion
文摘图像的非局部变分修复(Non-local Total Variation,NLTV)技术未考虑破损区域边界的连续性,从而在修复区域产生阶梯现象,影响非局部变分模型的修复性能。为实现图像修复边界区域的连续性,将罗宾边界算子引入到非局部拉格朗日方程中,利用破损程度实现对图像修复扩散强度自适应控制,建立自适应连续性非局部变分(Adaptive Continuous Non-local Total Variation,ACNLTV)的修复模型,给出该模型的交替极小化求解过程。与非局部变分模型的对比实验证明,提出的ACNLTV模型消除了阶梯现象,更好地修复图像的细节信息,峰值信噪比与结构相似性分别提高了0.5 dB与0.2,图像修复性能更优。
基金This research is partially supported by NFS of China (No. 10271032).
文摘In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the γ is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given.
文摘This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.
