Shape reconstruction in linear elasticity: standard and linearized monotonicity method. (15th March 2021)

• Record Type: Journal Article
• Authors: Eberle, Sarah; Harrach, Bastian
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-15
• Subjects: linear elasticity -- inverse problem -- shape reconstruction -- monotoni-city method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abc8a9
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a former article of the authors. Thus, we introduce the so-called standard as well as linearized monotonicity tests in order to detect and reconstruct inclusions. In addition, we compare these methods with each other and present several numerical test examples.