On a high-order numerical scheme for the Lippmann-Schwinger equation in layered medium

Abstract

We consider the direct wave scattering problem from a penetrable obstacle located either in a homogeneous or in a layered background, motivated for example by the simulation of propagation from ultrasound or from buried electromagnetic material via GPR (ground-penetrating radar) or electromagnetic induction devices. Starting from a volume integral equation (the Lippmann-Schwinger equation), we devise a collocation method in which the singularity is analytically treated, and the basis functions for the remainder are piecewise continuous polynomials of arbitrary degree. This allows the simulation of scattered fields due to penetrable obstacles with spatially varying permittivity and conductivity, for which some examples are discussed.