A direct method for reconstructing inclusions and boundary conditions from electrostatic data. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Harris, Isaac
• Is Part Of: Applicable analysis. Volume 102:Issue 5(2023)
• Page Start: 1511
• Page End: 1529
• Publication Date: 2023-03-24
• Subjects: Inverse boundary value problems -- shape reconstruction -- boundary impedance -- sampling methods -- integral equations; 35J05 -- 45Q05 -- 65R30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1991326
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we will discuss the use of the Linear Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the Dirichlet to Neumann mapping can be used to reconstruct impenetrable sub-regions via a sampling method. We also propose a direct method based on boundary integral equations to reconstruct the impedance parameter using the reconstructed boundary of the inclusion from the knowledge of multiple Cauchy pairs which can be computed from Dirichlet to Neumann mapping. Some numerical reconstructions are presented in two space dimensions.