Identification problems with given material interfaces

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• 作者：J. Haslinger ^{hasling@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author} ; R. Blaheta ^{blaheta@ugn.cas.cz" class="auth_mail" title="E-mail the corresponding author} ; R. Hrtus ; ^{hrtus@ugn.cas.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Identification of conductivity coefficients ; Control of systems by coefficients of PDE ; Algebraic sensitivity analysis ; Scalarization technique ; Pumping test
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：129-142
• 全文大小：524 K

文摘

This paper is devoted to the identification of coefficients in scalar elliptic partial differential equations using an optimal control approach. The coefficients usually can be interpreted as material characteristics and play the role of the control variable. The paper focuses on processes in domains which can be split into a finite number of materially homogeneous subdomains, i.e. the coefficients to be identified are piecewise constant on them. In addition, we assume that the material interfaces are a priori known. We prove the existence of at least one solution of the optimal control problem for a large class of cost functionals and show that solutions can be obtained as limits of solutions to the problems which are governed by finite element discretizations of the state equations. Further, the unified algebraic sensitivity analysis of the first and the second order for several least squares type cost functions is investigated. Finally, a model problem of the identification of coefficients characterizing hydraulic conductivity by pumping tests in groundwater flow modeling is numerically solved using the sequential approach and the scalarization technique.