A High Efficiency Discontinuous Galerkin Method for 3D Ground-Penetrating Radar Simulation

As an effective geophysical tool, ground penetrating radar (GPR) is widely used for environmental and engineering detections. Numerous numerical simulation algorithms have been developed to improve the computational efficiency of GPR simulations, enabling the modeling of complex structures. The discontinuous Galerkin method is a high efficiency numerical simulation algorithm which can deal with complex geometry. This method uses numerical fluxes to ensure the continuity between elements, allowing Maxwell’s equations to be solved within each element without the need to assemble a global matrix or solve large systems of linear equations. As a result, memory consumption can be significantly reduced, and parallel solvers can be applied at the element level, facilitating the construction of high-order schemes to enhance computational accuracy. In this paper, we apply the discontinuous Galerkin (DG) method based on unstructured meshes to 3D GPR simulation. To verify the accuracy of our algorithm, we simulate a full-space vacuum and a cuboid in a homogeneous medium and compare results, respectively, with the analytical solutions and those from the finite-difference method. The results demonstrate that, for the same error level, the proposed DG method has significant advantages over the FDTD method, with less than 20% of the memory consumption and calculation time. Additionally, we evaluate the effectiveness of our method by simulating targets in an undulating subsurface, and further demonstrate its capability for simulating complex models.