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We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

Analysis of PDEs · Mathematics 2022-10-03 Giovanni Covi , Maarten de Hoop , Mikko Salo

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

Analysis of PDEs · Mathematics 2023-01-20 Bochao Chen , Yixian Gao , Shuguan Ji , Yang Liu

An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…

Numerical Analysis · Mathematics 2025-06-19 Xiaopeng Zhu , Zhongyi Huang

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle…

Numerical Analysis · Mathematics 2020-03-05 Ruo Li , Fanyi Yang

We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate…

Numerical Analysis · Mathematics 2021-12-06 Simon Hubmer , Ekaterina Sherina , Andreas Neubauer , Otmar Scherzer

We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…

Numerical Analysis · Mathematics 2023-02-27 Darko Volkov

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…

Numerical Analysis · Mathematics 2021-11-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

We show that the inference problem of constraining the dipole amplitude with inclusive deep inelastic scattering data can be written into a discrete linear inverse problem, in an analogous manner as can be done for computed tomography. To…

High Energy Physics - Phenomenology · Physics 2025-11-20 Henri Hänninen , Antti Kykkänen , Hjørdis Schlüter

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate…

Cosmology and Nongalactic Astrophysics · Physics 2017-12-25 Hong-Ming Zhu , Yu Yu , Ue-Li Pen , Xuelei Chen , Hao-Ran Yu

We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…

Analysis of PDEs · Mathematics 2021-10-14 Katharina Brazda , Gaspard Jankowiak , Christian Schmeiser , Ulisse Stefanelli

A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…

Numerical Analysis · Mathematics 2020-07-20 Rashmi Murthy , Yi-Hsuan Lin , Kwancheol Shin , Jennifer L. Mueller

We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…

Numerical Analysis · Mathematics 2019-02-05 Peter Hansbo , Mats G. Larson , Karl Larsson

This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the…

Analysis of PDEs · Mathematics 2024-01-25 Gunther Uhlmann , Jian Zhai

We consider the nonlinear,inverse problem of computing the stored energy function of a hyperelastic material from the full knowledge of the displacement field. The displacement field is described as solution of the nonlinear, dynamic,…

Analysis of PDEs · Mathematics 2015-11-16 Julia Seydel , Thomas Schuster

In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…

Optimization and Control · Mathematics 2025-05-09 Houcine Meftahi , Chayma Nssibi

We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…

Numerical Analysis · Mathematics 2025-06-26 Yao Sun , Yan Chang , Yukun Guo

This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are…

Systems and Control · Electrical Eng. & Systems 2024-01-24 Chris Verhoek , Ruigang Wang , Roland Tóth

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the…

Analysis of PDEs · Mathematics 2020-04-24 Walton Green , Shitao Liu

We consider the nonlinear, inverse problem of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field as well as from surface sensor measurements. The displacement field is represented…

Numerical Analysis · Mathematics 2017-12-06 Julia Seydel , Thomas Schuster