Electromagnetic Simulation by Curvilinear Collocated Grid Finite Difference Method

Traditional finite difference method for electromagnetic simulation is based on staggered grid, whilst researcheson collocated grid are few. We present a high-order collocated-grid finite-difference method for modellingelectromagnetic waves with a topographic ground surface by solving 2D time-domain Maxwell equations incurvilinear coordinates. The proposed method, incorporating curvilinear coordinates, collocated grids andMacCormack finite-difference scheme techniques, can describe the geometry of the irregular interface better andavoid the numerical scattering caused by the staircase approximation in the conventional finite-differencemethod for electromagnetic wavefield modelling. The first-order 2D Maxwell equations on curvilinear grids aresolved by an optimized MacCormack finite-difference scheme, first presented by Hixon (1997). As thecollocated grids are implemented, in which the electric and magnetic fields are discretized at the same grids, theinterfacial boundary conditions need to be considered. Therefore, a novel effective interface method is presentedto handle the conditions. The proposed method is verified by a series of ground penetrating radar applicationmodels, such as homogeneous space, multilayered media and buried cavity models, by comparing syntheticwaveforms with independent reference solutions, such as the analytical solution, the generalizedreflection/transmission method and an open-source program gprMax. Comparisons show that the proposedmethod does well in handling multiple reflections and curved interfaces.