The inverse scattering problem of an interior cavity with three different boundary conditions is considered. Bayesian method is used to reconstruct the shape of the cavity from scattered fields incited by point source(s) and measured on a closed curve inside the cavity. We prove the well-posedness in Bayesian perspective and present numerical examples to show the viability of the method.
a b s t r a c tThis paper is concerned with the diffraction by a polygonal-line grating. Using the Fourier-Bessel functions that capture the singularities at corners, and representing the diffraction field towards infinity by a truncation of the Rayleigh expansion, we propose a least-squares finite element method for solving the problem. We analyze the convergence and give an error estimate for the method. Numerical experiments are also presented to show the effectiveness of our method.
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