A nonuniform cylindrical FDTD algorithm with PML for borehole radar modeling

Using the conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid to simulate wave propagation in media with cylindrical structures will cause staircasing error. Furthermore, to accommodate the accurate geometrical representation for both small and large structures in the same problem, many unnecessary cells will be wasted in the large region if the conventional uniform grid is used. In order to avoid these two problems, a three-dimensional FDTD algorithm with a nonuniform cylindrical grid is developed for inhomogeneous conductive media. Two modified perfectly matched layer (PML) absorbing boundary conditions for cylindrical coordinates are presented. The algorithm have been extensively validated. Applications of this algorithm are shown for borehole radar modeling