The Linear Sampling Method for an Open Crack and an Impenetrable Obstacle

ABSTRACT We consider the scattering problem of time‐harmonic acoustic waves by an impenetrable obstacle and an open arc with mixed boundary conditions on the plane. Employing the boundary integral method, we establish the well‐posedness of the direct problem. Subsequent to demonstrating the uniqueness of the inverse problem, we furnish a theoretical proof for the linear sampling method. Additionally, we show several numerical simulation results obtained through this method.