Reconstruction of three-dimensional dielectric objects through integral equation method

Reconstruction of unknown dielectric objects by integral equation approach requires efficient numerical solutions for volume integral equations (VIEs) based on the Born iterative method (BIM) or its variations. Traditionally, the VIEs are solved by the method of moments (MoM) in which the flux density is represented with the Schaubert-Wilton-Glisson (SWG) basis function. However, the MoM with the SWG basis function may not be convenient for solving inverse scattering problems because of the unknown profiles of objects. In this work, we propose a Nyström scheme to solve the forward scattering VIE (FSVIE) for reconstructing three-dimensional (3D) unknown dielectric objects. The merits of the scheme include simple mechanism of implementation and lower requirement on mesh quality. A numerical example is presented to illustrate the scheme.