Shape reconstruction in linear elasticity: standard and linearized monotonicity method
نویسندگان
چکیده
In this paper, we deal with the inverse problem of shape reconstruction inclusions in elastic bodies. The main idea is based on monotonicity property Neumann-to-Dirichlet operator presented a former article authors. Thus, introduce so-called standard as well linearized tests order to detect and reconstruct inclusions. addition, compare these methods each other present several numerical test examples.
منابع مشابه
Shape Based Image Reconstruction Using Linearized Deformations.
We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrat...
متن کاملMonotonicity-Based Shape Reconstruction in Electrical Impedance Tomography
Current-voltage measurements in electrical impedance tomography (EIT) can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators. With this ordering, a pointwise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements. We present a converse of this simple monotonicity relat...
متن کاملLinearized Inverse Sca'itering Problems in Elasticity
Using the single-scattering approximation we invert for the material parameters of an acoustic two-parameter medium and then for a three-parameter isotropic elastic medium. Our procedure is related to various methods of depth migration in seismics, i.e. methods for locating major discontinuities in the subsurface material without specifying which quantities are discontinuous or by how much they...
متن کاملShape Gradient Computation in Isogeometric Analysis for Linear Elasticity
The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows to overcome these difficulties by using a unique geometrical representation that yields a direct relationship...
متن کاملAn Algebraic Multigrid Method for Linear Elasticity
We present an algebraic multigrid (AMG) method for the efficient solution of linear (block-)systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block-interpolation, described in thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inverse Problems
سال: 2021
ISSN: ['0266-5611', '1361-6420']
DOI: https://doi.org/10.1088/1361-6420/abc8a9