Shape reconstruction in linear elasticity: standard and linearized monotonicity method
Sarah Eberle,Bastian Harrach +1 more
Reads0
Chats0
TLDR
The so-called standard as well as linearized monotonicity tests in order to detect and reconstruct inclusions in elastic bodies are introduced and compared with each other.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.read more
Citations
More filters
Journal ArticleDOI
Lipschitz stability estimate and reconstruction of Lam\'e parameters in linear elasticity
TL;DR: In this article, the authors consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map and prove a Lipschitz stability estimate for Lame parameters with certain regularity assumptions.
Journal ArticleDOI
Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity
TL;DR: A Lipschitz stability estimate for Lamé parameters with certain regularity assumptions is prove to prove to solve the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map.
Journal ArticleDOI
Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
Bastian Harrach,Yi-Hsuan Lin +1 more
TL;DR: In this article , the authors investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data, based on higher order linearization and monotonicity approaches, and determine the diffusion and absorption coefficients together with the shape of a cavity simultaneously by knowing the corresponding localized Dirichlet-Neumann operator.
Posted Content
Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity
Sarah Eberle,Bastian Harrach +1 more
TL;DR: In this article, the shape reconstruction of inclusions in elastic bodies is solved by converting monotonicity methods into a regularization method for a data-fitting functional without losing the convergence properties of the monotonivity methods, which is a significant improvement over standard regularization techniques, which do not have a rigorous theory of convergence.
Journal ArticleDOI
A FEM-based direct method for identification of Young’s modulus and boundary conditions in three-dimensional linear elasticity from local observation
TL;DR: In this article , a direct inverse method based on the finite element method (FEM) was proposed to recover Young's modulus and boundary conditions of a linear elastic material with the measurements only on a part of its boundary.
References
More filters
Journal ArticleDOI
Global uniqueness for an inverse boundary value problem arising in elasticity
Gen Nakamura,Gunther Uhlmann +1 more
TL;DR: In this paper, the Lame parameters of an elastic, isotropic, inhomogeneous medium in dimensionsn ≥ 3 were determined by making measurements of the displacements and corresponding stresses at the boundary of the medium.
Journal ArticleDOI
A new non-iterative inversion method for electrical resistance tomography
TL;DR: In this paper, a non-iterative inversion method based on the monotonicity of the resistance matrix and its numerical approximations is proposed for resistivity retrieval in electrical resistance tomography (ERT).
Journal ArticleDOI
Monotonicity-based shape reconstruction in electrical impedance tomography ∗
Bastian Harrach,Marcel Ullrich +1 more
TL;DR: A converse of this simple monotonicity relation is presented and used to solve the shape reconstruction problem in EIT and find the outer shape of a region where the conductivity differs from a known background conductivity.
Journal ArticleDOI
Size estimation of inclusion
TL;DR: In this paper, Kang et al. presented a system of integral inequalities for the inverse conductivity problem for an anisotropic elastic body and obtained similar estimates for a known reference conductor or elasctic body.
Journal ArticleDOI
On uniqueness in diffuse optical tomography
TL;DR: In this paper, the authors show that it suffices to restrict ourselves to piecewise constant diffusion and piecewise analytic absorption coefficients to regain uniqueness, and show that both parameters can simultaneously be determined from complete measurement data on an arbitrarily small part of the boundary.
Related Papers (5)
Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
Sarah Eberle,Bastian Harrach +1 more