2D electromagnetic simulation for ground penetrating radar with a topographic ground surface by the curvilinear collocated-grid finite-difference method combined with equivalent field method

In this paper, we extend the curvilinear collocated-grid finite-difference method, which has been developed in the study of seismology, to the 2D electromagnetic simulation of ground penetrating radar (GPR). The method combines curvilinear coordinate and collocated grid, so it can better describe the geometry of the irregular interfaces than traditional finite difference method and is more efficient than finite element method which is suitable for complex geometries. Due to the differences in interfacial condition between elastic waves and electromagnetic waves, a novel scheme of equivalent electromagnetic fields is introduced to explicitly ensure discontinuous interfacial boundary conditions with collocated grid. Furthermore, this approach eliminates the need for orthogonality of the grid at the interface, which reduces the complexity of mesh generation. The proposed method is verified for a series of ground penetrating radar application models, by comparing synthetic waveforms with independent reference solutions. The perfect consistency of the comparisons indicates the accuracy of our new method in the simulation of GPR. Compared with the second-order gprMax, the proposed method is proved to be more efficient in terms of computing time and memory. Combination of collocated grid and the novel equivalent field method leads to reliable and accurate solutions of EM fields even on the ground surface.