2013/07/05 by Matti Lassas, Mikko Salo, Lassas, Matti +3
Computer Science · Engineering · Mathematics · #05C50 #35R30 #65N30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1307.1539
openalex publication_date 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider inverse problems for resistor networks and for\nmodels obtained via the Finite Element Method (FEM) for the conductivity\nequation. These correspond to discrete versions of the inverse conductivity\nproblem of Calder 'on. We characterize FEM models corresponding to a given\ntriangulation of the domain that are equivalent to certain resistor networks,\nand apply the results to study nonuniqueness of the discrete inverse problem.\nIt turns out that the degree of nonuniqueness for the discrete problem is\nlarger than the one for the partial differential equation. We also study\ninvisibility cloaking for FEM models, and show how an arbitrary body can be\nsurrounded with a layer so that the cloaked body has the same boundary\nmeasurements as a given background medium.\n