Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
Sarah Eberle,Bastian Harrach +1 more
TLDR
In this paper, the inverse problem of shape reconstruction of inclusions in elastic bodies is dealt with, based on the monotonicity property of the Neumann-to-Dirichlet operator.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
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.
Journal ArticleDOI
Monotonicity Principle in tomography of nonlinear conducting materials
TL;DR: In this article, the authors show that the Monotonicity principle for the Dirichlet Energy in nonlinear problems holds under mild assumptions, and they show that apart from linear and p-Laplacian cases, it is impossible to transfer this monotonicity result from the DtN operator to the Dn operator.
Journal ArticleDOI
Monotonicity-based regularization for shape reconstruction in linear elasticity
TL;DR: In this article , the shape reconstruction of inclusions in elastic bodies is considered and a regularization method for a data-fitting functional without losing the convergence properties of the monotonicity methods is proposed.
Posted Content
Monotonicity Principle for Nonlinear Electrical Conductivity Tomography
TL;DR: In this paper, a nonlinear inverse electrical conductivity problem consisting in reconstructing the (nonlinear) electrical conductivities starting from boundary measurements in steady currents operations is considered, where a key role is played by the Monotonicity Principle, consisting in a monotone relation connecting the unknown material property to the (measured) Dirichlet-to-Neumann operator.
References
More filters
Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
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.
Related Papers (5)
Shape reconstruction in linear elasticity: standard and linearized monotonicity method
Sarah Eberle,Bastian Harrach +1 more