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

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.