In order to reconstruct small changes in the interface of an elastic inclusion from modal measurements, we rigorously derive an asymptotic formula which is in some sense dual to the leading-order term in the asymptotic expansion of the perturbations in the eigenvalues due to interface changes of the inclusion. Based on this (dual) formula we propose an algorithm to reconstruct the interface perturbation. We also consider an optimal way of representing the interface change and the reconstruction problem using incomplete data. A discussion on resolution is included. Proposed algorithms are implemented numerically to show their viability.
Reconstruction of interface changes of an elastic inclusion from modal measurements / H., Ammari; Beretta, Elena; E., Francini; H., Kang; M., Lim. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 94:(2010), pp. 322-339. [10.1016/j.matpur.2010.02.001]
Reconstruction of interface changes of an elastic inclusion from modal measurements.
BERETTA, Elena;
2010
Abstract
In order to reconstruct small changes in the interface of an elastic inclusion from modal measurements, we rigorously derive an asymptotic formula which is in some sense dual to the leading-order term in the asymptotic expansion of the perturbations in the eigenvalues due to interface changes of the inclusion. Based on this (dual) formula we propose an algorithm to reconstruct the interface perturbation. We also consider an optimal way of representing the interface change and the reconstruction problem using incomplete data. A discussion on resolution is included. Proposed algorithms are implemented numerically to show their viability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
