Analysis of influencing factors of the discontinuous Galerkin algorithm for ground penetrating radar

The discontinuous Galerkin time-domain (DGTD) algorithm has become an effective method for forward numerical simulation of Ground Penetrating Radar (GPR), due to its conservation, stability, high precision and discontinuity. To improve the computational efficiency and accuracy of DGTD, we analyzed its related influencing factors in detail, including numerical flux, temporal integration scheme, grid size and basis function order, and mesh generation methods. Through the numerical case, we verified that the partially penalized numerical flux of tau=1/2 in local Lax-Friedrichs can not only eliminate the spurious solution, but also improve the computational accuracy. Under the same precision, the low-storage explicit Runge-Kutta scheme (LSERK) has better stability and lower storage advantages than the other two temporal integration schemes, especially in large complex models and 3D forward simulation. The convergence of the error can be improved by increasing the order of the basis function or the number of meshes. The experimental results reveal the order of basic function N and the size of the grid d are closely concerned with the wavelength lambda, for example, an appropriate definition is d/N approximate to lambda/15. When the number of cells is roughly the same, the mesh generation methods has little influence on the high-order DGTD algorithm, indicating that DGTD has good adaptability to the grid. Finally, we used the DGTD algorithm to simulate the Martian Utopian Plain model for GPR, which verifies that the DGTD algorithm based on the optimal parameters has high simulation accuracy and can lay a theoretical foundation for the interpretation of the GPR measured data of the Martian Utopian Plain.