The monotonicity method for inclusion detection and the time harmonic elastic wave equation

TL;DR

This paper extends the monotonicity method to detect inhomogeneities in elastic bodies using time harmonic waves, providing a new approach for reconstructing material properties with numerical validation.

Contribution

It introduces an extension of the monotonicity method for inclusion detection in elastic media and demonstrates its effectiveness through numerical tests.

Findings

Successful reconstruction of inhomogeneities in elastic bodies

Extension of the monotonicity method to elastic wave equations

Numerical validation of the proposed method

Abstract

We consider the problem of reconstructing inhomogeneities in an isotropic elastic body using time harmonic waves. Here we extend the so called monotonicity method for inclusion detection and show how to determine certain types of inhomogeneities in the Lam\'e parameters and the density. We also included some numerical tests of the method.