CONDUCTIVITY INTERFACE PROBLEMS. PART I: SMALL PERTURBATIONS OF AN INTERFACE

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We derive high-order terms in the asymptotic expansions of boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with C(2)-boundary. Our derivation is rigorous and based on layer potential techniques. The asymptotic expansion in this paper is valid for C(1)-perturbations and inclusions with extreme conductivities. It extends those already derived for small volume conductivity inclusions and leads us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the inclusion based on boundary measurements. We perform some numerical experiments using the algorithm to test its effectiveness.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2010-05
Language
English
Article Type
Article
Citation

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.362, no.5, pp.2435 - 2449

ISSN
0002-9947
DOI
10.1090/S0002-9947-09-04842-9
URI
http://hdl.handle.net/10203/97673
Appears in Collection
MA-Journal Papers(저널논문)
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