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H. Haddar

Publications and source records attributed to H. Haddar.

3 recordsLinked to original sources
arXiv2024

The linear sampling method for data generated by small random scatterers

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz--Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, Singular Value Decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.

math.NA↗
arXiv2021

Near-Field Linear Sampling Method forAxisymmetric Eddy Current Tomography

This paper is concerned with Eddy-Current (EC) nondestructive testing of conductive materials and focuses, in particular, on extending the well-known LinearSampling Method (LSM) to the case of EC equations. We first present the theoretical foundation of the LSM in the present context and in the case of point sources. We then explain how this method can be adapted to a realistic setting of EC probes. In the case of identifying the shape of external deposits from impedance measurements taken from inside of the tube (steam generator), we show how the method can be applied to measurements obtained from a sweeping set of coils. Numerical experiments suggest that good results can be achieved using only a few coils and even in the limiting case of backscattering data.

math.NA↗