2006/06/26 by Ville Kolehmainen, Kolehmainen, Ville, Matti Lassas +3
Computer Science · Engineering · Mathematics · #35J25 #35R30 #58J32 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.math/0606640
openalex publication_date 2006/06/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider the inverse conductivity problem in a strictly convex domain\nwhose boundary is not known. Usually the numerical reconstruction from the\nmeasured current and voltage data is done assuming the domain has a known fixed\ngeometry. However, in practical applications the geometry of the domain is\nusually not known. This introduces an error, and effectively changes the\nproblem into an anisotropic one. The main result of this paper is a uniqueness\nresult characterizing the isotropic conductivities on convex domains in terms\nof measurements done on a different domain, which we call the model domain, up\nto an affine isometry. As data for the inverse problem, we assume the\nRobin-to-Neumann map and the contact impedance function on the boundary of the\nmodel domain to be given.\n Also, we present a minimization algorithm based on the use of Cotton--York\ntensor, that finds the pushforward of the isotropic conductivity to our model\ndomain, and also finds the boundary of the original domain up to an affine\nisometry. This algorithm works also in dimensions higher than three, but then\nthe Cotton--York tensor has to replaced with the Weyl--tensor.\n