On Application of Collocation Method for Solving Inverse Problem of Diffraction by an Inhomogeneous Solid

Abstract: The problem of reconstruction of an unknown refractive index of an inhomogeneous body is considered. The two-step method for solving the problem is applied. Collocation method for solving singular integro-differential equations is used. Piecewise linear compactly supported basis functions are introduced. Two ways to determine collocation points inside the inhomogeneity domain are suggested. Several two-dimensional problems are numerically solved using the the two-step method. Tikhonov regularization is used for accurate solving integral equations of the inverse diffraction problem with noisy near field data. © Pleiades Publishing, Ltd. 2024.