The present study aims to introduce the linear sampling method for cavity/inclusion detection in a two-dimensional Laplace problem by measuring data on the boundary. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. There has been no specific attempt to apply this method to the identification of cavities/inclusions in the Laplace equation although it has been used in the context of inverse problems such as acoustics, electromagnetism and elastostatics. Therefore, the implementation of the linear sampling method, coupled with the finite element method, is emphasized in this study. A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.
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