Solving the volume integral equation in axisymmetric inhomogeneous media using the conjugate gradient fast Hankel transform method

In this paper we present a new method to solve the volume integral equation governing the electromagnetic wave propagation in axisymmetric inhomogeneous media. The integral equation is first formulated using a one-dimensional Green's function and then solved using the conjugate gradient fast Hankel transform method. The use of the one-dimensional Green's function reduces the number of unknowns significantly, thereby accelerating the iterative procedure. Several numerical results are used to show the efficiency and accuracy of this new approach as well as its applications in electromagnetic subsurface sensing.