SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2009-2010
Jeudi 20 mai 2010 :
Corinna BURKARD
(IRMAR et Univ. Reading, UK)
Three-dimensional Rough Surface Reconstructions from Frequency- or Time-Domain Data.
We study the reconstruction of three-dimensional rough surfaces via a potential approach from given frequency- resp. time-measurements. Using single layer potentials for the solution of shape reconstruction problems has first been suggested by Kirsch and Kress in the case of bounded obstacles in the frequency domain. In contrast to the bounded domain case a rigorous analysis for the infinite rough surface approach cannot be carried out directly. In particular, the key difficulties of the direct problem are due to the non-compactness and unboundedness of the scattering surface and these difficulties appear similarly in the inverse problem.
To overcome these issues, we discuss a multi-section approach and prove convergence by using an analysis for the semi-finite approach. Studying also a time-domain rough surface reconstruction problem incorporates a more practical setting of shape reconstruction from time-domain measurements. The method we present is based on the causality principle in contrast to earlier work of Chandler-Wilde and Lines, and by Luke and Potthast. We include numerical examples both for a frequency and a time-domain setting in three dimensions.
