Piecewise constant level set algorithm for an inverse elliptic problem in nonlinear electromagnetism

TL;DR

This paper introduces a piecewise constant level set algorithm for solving inverse elliptic problems in nonlinear electromagnetism, effectively reconstructing complex shapes of inhomogeneities or cracks in magnetic materials.

Contribution

The paper develops a novel level set method using the Lagrangian multiplier and adjoint techniques for shape reconstruction in nonlinear magnetic materials.

Findings

Algorithm successfully reconstructs complex shapes.

Demonstrates robustness and effectiveness.

Applicable to inhomogeneity and crack detection.

Abstract

An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means of the Lagrangian multiplier method, we derive the first variation w.r.t the level set function and obtain the descent direction by the adjoint variable method. Numerical results show the robustness and effectiveness of our algorithm applied to reconstruct some complex shapes.