Caubet, Fabien and Dambrine, Marc and Harbrecht, Helmut. (2019) A new method for the data completion problem and application to obstacle detection. SIAM journal on applied mathematics, 79 (1). pp. 415435.
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Official URL: https://edoc.unibas.ch/69693/
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Abstract
The present article is devoted to the study of two wellknown inverse problems, that is, the data completion problem and the inverse obstacle problem. The general idea is to reconstruct some boundary conditions and/or to identify an obstacle or void of different conductivity which is contained in a domain, from measurements of voltage and currents on the outer boundary of the domain. We focus here on Laplace's equation. First, we use a penalized KohnVogelius functional in order to numerically solve the data completion problem, which consists in recovering some boundary conditions from partial Cauchy data. The functional to be minimized is quadratic, hence we compute its minimum by solving the linearized equation. Second, we propose to build an iterative method for the inverse obstacle problem based on the combination of the previously mentioned data completion subproblem and the socalled trial method. The underlying boundary value problems are efficiently computed by means of boundary integral equations and several numerical simulations show the applicability and feasibility of our new approach. For the numerical simulations, we focus on starshaped domains in the twodimensional case.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht) 

UniBasel Contributors:  Harbrecht, Helmut 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  Society for Industrial and Applied Mathematics 
ISSN:  00361399 
eISSN:  1095712X 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
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edoc DOI:  
Last Modified:  19 Mar 2019 14:06 
Deposited On:  19 Mar 2019 14:06 
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