Topological derivative applied to cavity identification from elastodynamic surface measurements
Keywords:
cavity identification, elastodynamics, inverse scattering, adjoint field method, shape sensitivity, topological derivativeAbstract
This article is concerned with the use of topological derivative as a tool for preliminary elastic-wave probing of bounded or unbounded solids for buried objects. A formulation for computing the topological derivative field, based on an adjoint solution, is presented. A set of numerical results is included to illustrate the utility of topological derivative for outlining the cavity location and size prior to doing an actual inversion of measurements. The results presented here were obtained from a BIE solution, but the proposed methodology is applicable to other computational platforms such as the finite element method.
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References
[COL92] COLTON D., KRESS R., Inverse acoustic and electromagnetic scattering theory,
Springer-Verlag, 1992.
[GAR01] GARREAU S., GUILLAUME P., MASMOUDI M., “The topological asymptotic for
PDE systems: the elasticity case.”, SIAM J. Contr. Opt., vol. 39, 2001, p. 1756–1778.
[GUZ03] GUZINA B. B., NINTCHEU FATA S., BONNET M., “On the stress-wave imaging of
cavities in a semi-infinite solid”, Int. J. Solids Struct., vol. 40, 2003, p. 1505–1523.
[GUZ04] GUZINA B. B., BONNET M., “Topological derivative for the inverse scattering of
elastic waves”, Quart. J. Mech. Appl. Math., vol. 57, 2004, p. 161–179.
[NIN03] NINTCHEU FATA S., GUZINA B. B., BONNET M., “A Computational Basis for Elastodynamic
Cavity Identification in a Semi-Infinite Solid”, Comp. Mech., vol. 32, 2003,
p. 370–380.
[PAK99] PAK R. Y. S., GUZINA B. B., “Seismic soil-structure interaction analysis by direct
boundary element methods.”, Int. J. Solids Struct., vol. 36, 1999, p. 4743–4766.
[SOK99] SOKOLOWSKI J., ZOCHOWSKI A., “On the topological derivative in shape optimization.”,
SIAM J. Control Optim., vol. 37, 1999, p. 1251–1272.
