Cavities Identification from Partially Overdetermined Boundary Data in Linear Elasticity

A FEM-based topological sensitivity approach for fast qualitative identification of buried cavities from elastodynamic overdetermined boundary data

A time-domain topological sensitivity (TS) approach is developed for elastic-wave imaging of media of arbitrary geometry. The TS, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal hole, is expressed in terms of the time convolution of the free field and a supplementary adjoint field as a function of that specified location...

Artificial boundary conditions to compute correctors in linear elasticity

Identification of a Core from Boundary Data

The problem of determining the interface separating regions of constant density from boundary data of a solution of the corresponding potential equation is considered. An equivalent formulation as a nonlinear integral equation is obtained. Fourier methods are used to analyze and implement the problem. Numerical experiments based on a regularized least-squares method are presented.

Solution to Overdetermined Linear Equations

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m n) matrix A and the data vector b. This is in contrast to a least squares solution, whe...

Quasistatic Evolution of Cavities in Nonlinear Elasticity

We show the well-posedness of a free-discontinuity model in nonlinear elasticity allowing for cavitation. The model, based on global minimization, takes into account the noninterpenetration of matter and the inhomogeneties of the material. Then we prove the existence of a quasistatic evolution corresponding to this variational model that takes into account the irreversibility of the process of ...