High-Precision Simulation of Discontinuous Galerkin Algorithm in Dispersive Media for 3D Ground Penetrating Radar Based on CFS-PML

Ground penetrating radar (GPR) has emerged as a critical tool for subsurface characterization due to its three-dimensional imaging capabilities in complex geological environments. Nevertheless, existing numerical methods for modeling electromagnetic wave propagation in dispersive media face persistent challenges in balancing modeling accuracy, computational efficiency, and multi-scale adaptability. Conventional approaches often struggle to simultaneously address broadband dispersion characterization, unstructured mesh compatibility for intricate geometries, and optimal boundary reflection suppression. This study proposes a three-dimensional discontinuous Galerkin time-domain (DGTD) algorithm integrated with a complex frequency-shifted perfectly matched layer (CFS-PML) to overcome these limitations. Through the development of an auxiliary differential equation framework for Debye media, the computational complexity of 3D DGTD simulations is effectively reduced. Combined with unstructured mesh discretization, the method enables adaptive modeling of geometrically complex geological structures. Furthermore, the CFS-PML boundary condition is extended to handle broadband wave absorption in lossy media, demonstrating superior performance over conventional uniaxial PML under wide-frequency and oblique incidence conditions. Numerical experiments on a 3D dispersive goaf model reveal electromagnetic energy attenuation patterns, particularly highlighting the amplified dispersion effects on deep anomalous reflectors. The proposed framework synergistically addresses multi-scale modeling precision, dispersion response, and boundary reflection control, establishing a high-fidelity simulation platform for 3D GPR investigations of subsurface targets in heterogeneous dispersive environments.