On the solution of direct and inverse multiple scattering problems for mixed sound-soft, sound-hard and penetrable objects. (2nd September 2020)

• Record Type: Journal Article
• Authors: Rapún, M–L
• Is Part Of: Inverse problems. Volume 36:Number 9(2020)
• Publication Date: 2020-09-02
• Subjects: mixed boundary conditions -- boundary integral methods -- inverse multiple scattering problem -- shape reconstruction -- topological energy -- multifrequency; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab98a2
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this work we consider a scattering problem governed by the two-dimensional Helmholtz equation, where some objects of different nature (sound-hard, sound-soft and penetrable) are present in the background medium. First we propose and analyze a system of boundary integral equations to solve the direct problem. After that, we propose a numerical method based on the computation of a multifrequency topological energy based imaging functional to find the shape of the objects (without knowing their nature) from measurements of the total field at a set of observation points. Numerical examples show that the proposed indicator function is able to detect objects of different nature and/or shape and size when processing noisy data for a rich enough range of frequencies.