On a Hybrid method for shape reconstruction of a buried object in an elastostatic half plane

Roman Chapko

doi:10.3934/ipi.2009.3.199

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2009, Volume 3, Issue 2: 199-210. Doi: 10.3934/ipi.2009.3.199

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On a Hybrid method for shape reconstruction of a buried object in an elastostatic half plane

Roman Chapko^1,

1.
Faculty of Applied Mathematics and Computer Science, Ivan Franko National University of Lviv, 79000 Lviv

Received: October 2008

Revised: March 2009

Published: May 2009

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Abstract

We apply the hybrid method for determining the shape of a bounded object in the elastostatic half plane from given Cauchy data on the boundary. The identifiability of the shape is investigated. For the integral representation of the function and the traction on the boundaries, the Green's function approach based on Kelvin's fundamental solution is used. The approximation of the integral operators with various singularities is made by trigonometrical and sinc quadratures. The presented numerical experiments exhibit the feasibility of the hybrid method for the system of differential equations and its stability in the case of noisy data.

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Mathematics Subject Classification: Primary: 35R25, 65N21; Secondary: 45Q02, 47J06, 65R32.

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