Inverse problems and invisibility cloaking for FEM models and resistor networks
Lassas, M., Salo, M., & Tzou, L. (2015). Inverse problems and invisibility cloaking for FEM models and resistor networks. Mathematical Models and Methods in Applied Sciences, 25(2), 309-342. https://doi.org/10.1142/S0218202515500116
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Mathematical Models and Methods in Applied SciencesDate
2015Copyright
© 2015 World Scientific Publishing Company. This is a final draft version of an article whose final and definitive form has been published by World Scientific Publishing Company. Published in this repository with the kind permission of the publisher.
In this paper we consider inverse problems for resistor networks
and for models obtained via the Finite Element Method (FEM)
for the conductivity equation. These correspond to discrete versions of
the inverse conductivity problem of Calder´on. We characterize FEM
models corresponding to a given triangulation of the domain that are
equivalent to certain resistor networks, and apply the results to study
nonuniqueness of the discrete inverse problem. It turns out that the degree
of nonuniqueness for the discrete problem is larger than the one for
the partial differential equation. We also study invisibility cloaking for
FEM models, and show how an arbitrary body can be surrounded with
a layer so that the cloaked body has the same boundary measurements
as a given background medium.
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World Scientific Publishing Co. Pte. Ltd.ISSN Search the Publication Forum
1793-6314Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/24784385
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