연사 : 임미경 교수  (Colorado State University)
제목 : Reconstructing Small Perturbations of an Interface
일시 : 2008.8. 14 (목) 오후 2:30
장소 : 자연과학동 2411호실

초록:
We consider the problem of determining the boundary perturbation of
inclusions from measurements of voltage potentials or eigenvalues and
eigenfunctions associated with the transmission problem for the
Laplacian. We derive asymptotic formula for the perturbations in the
measurements data due to small changes in the interface of the
inclusion. Numerical experiments to reconstruct the inclusion based on
the asymptotic expansion will be presented.

We also consider the problem of determining the boundary of scatterers from electric or acoustic far-field measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relation between the far-field data and the shape of the object. This relation is used to find the Fourier coefficients
of the perturbation of the scatterer's shape.