The Graduate Program in Computational Mathematical Modelling PPGMMC will hold, on Tuesday 29nd August, at 13:00 am, in Room 107 of the Informatics Centre of UFPB, Linaldo Cavalcanti Campus – Mangabeira, another lecture.
Prof. Jairo Rocha de Faria
Department of Scientific Computation – Informatics Centre – UFPB
Title: Shape sensitivity analysis for some geometric inverse problems for wave equation
Abstract: We propose a new reconstruction algorithm based upon first and second-order shape derivative to solve some geometric inverse problems for the wave equation. This inverse problem is affiliated to elastography technique which is a noninvasive diagnostic method that uses an ultrasound device and evaluates the stiffness of the organs to differentiate benign lesions (softer and more elastic) from malignant ones (which are generally stiffer). This procedure presents important medical applications, like quantification of the degree of liver fibrosis, early detection of lesions of malignant potential in the breast and thyroid, diagnosis of acute pancreatitis, etc. Some numerical experiments are performed, taking into account the D’Alembert formula, for simpler cases, or the method of fundamental solutions, for more complex ones. We obtain very accurate results, even for noisy data, taking into account linear and non-linear cases.