数学
离散化
收敛速度
凸性
应用数学
趋同(经济学)
反问题
数值分析
边界(拓扑)
平滑度
反向
数学优化
数学分析
几何学
计算机科学
经济增长
计算机网络
金融经济学
频道(广播)
经济
作者
Youssef Ouakrim,Idriss Boutaayamou,Youness El Yazidi,A. Zafrar
标识
DOI:10.1088/1361-6420/acdf4c
摘要
Abstract The paper presents a numerical method for identifying discontinuous conductivities in elliptic equations from boundary observations. The solutions to this inverse problem are obtained through a constrained optimization problem, where the cost functional is a combination of the Kohn–Vogelius and Total Variation functionals. Instead of regularizing the Total Variation stabilization functional, which is commonly used in the literature, we introduce an Alternating Direction Method of Multipliers to preserve the favorable properties of non-smoothness and convexity. The discretization is carried out using a mixed finite element/volume method, while the numerical solutions are iteratively computed using a variant of the Uzawa algorithm. We show the surjectivity of the derivatives of the constraints related to the discrete optimization problem and derive a source condition for the discrete inverse problem. We then investigate the convergence analysis and establish the convergence rate. Finally, we conclude with some numerical experiments to illustrate the efficiency of the proposed method.
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