Localization of immersed obstacles from boundary measurements

Abstract

A direct method for the localization of obstacles in a Stokes system is presented and theoretically justified. The method is based on the so called reciprocity gap functional and is illustrated with several numerical simulations.

Detecting the localization of elastic inclusions and Lamé coefficients

“…Formulae (16) require two boundary measurements: One for computing R(vx)/R(v1) -recall that the prescribed (non null) displacement must satisfy orthogonal conditions (9). Furthermore, if we take the displacement satisfying (17) g • e i ⊥ e j , i, j = 1, 2 then the aforementioned orthogonal conditions are satisfied, without the knowledge of λ and µ. Moreover, the approximation R(vx)/R(v1) depends only on the available Cauchy data.…”

“…[3]) and in a Stokes system (cf. [17]). The idea is to consider appropriate test functions in order to retrieve the centroid of the obstacle.…”

“…So far, we have presented simulations for the location of elastic inclusions. The considered displacements satisfy(17) hence no information regarding λ and µ was considered. We now use these values in(16) for the reconstruction of Lamé coefficients.…”