Inverse scattering problem for detecting a defect in a magnetoelastic layer

ABSTRACT

This work is devoted to studying a direct and inverse scattering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement field over the defect's contour, a coupled system of boundary integral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the defect, an efficient numerical algorithm is developed by using the quasi-Newton iterative method. In order to check the influence of the magnetic field upon the scattering waves from the layer, a series of numerical examples is presented with different noise levels. The results showed that the magnetic field has a sensitive effect on the identification process when the external magnetic field increases, especially for the materials having a high magnetic permeability factor ${\mu }_r$. Also, a special inverse problem for predicting the external applied magnetic field, upon a copper layer having a defect with various sizes, has been performed.

Keywords:

• Magnetoelasticity
• inverse scattering problem
• time-Harmonic load
• Green's functions
• boundary integral equations

2010 Mathematics Subject Classifications:

• Partial differential equations
• Integral equations
• Mechanics of deformable solids
• Numerical analysis
• Calculus of variations and optimalcontrol
• optimization

Disclosure statement

No potential conflict of interest was reported by the author(s).