基于任意比例的混合ADI-FDTD亚网格技术实现及其在三维GPR场景仿真中的应用

      Arbitrary-Ratio-based Subgrid Implementations of Hybrid ADI-FDTD and its applications in 3D Dispersive GPR Problems

      • 摘要: 在探地雷达(Ground penetrating radar,GPR)系统建模与仿真中,时域有限差分方法(FDTD)通常需要求解大量未知量,导致计算成本显著增加,在一定程度上限制了其应用优势。为解决这一问题,本文提出了一种混合亚网格ADI-FDTD方法,用于模拟具有耗散、色散和非均匀特性的复杂三维GPR场景。该方式实现了奇数与偶数倍粗细网格的灵活划分,在电磁建模中具有较强的适应性。此外,在细网格区域采用无条件稳定的ADI-FDTD方法,使整个仿真域能够使用统一的时间步长,从而避免了时间插值的复杂性。针对GPR应用中具有色散特性的土壤,本文擦用Z变化技术,将Debye色散媒质的频域相关电磁参数转换至时域,并将其代入FDTD和ADI-FDTD方法的计算框架中,避免了卷积计算,使数值实现更为简洁高效。最后,通过对经典GPR场景的数值模拟,验证了所提方法的正确性与有效性.

         

        Abstract: In modeling and simulating ground-penetrating radar (GPR) systems, the finite-difference time-domain (FDTD) method often involves solving a large number of unknowns, which significantly increases computational cost and constrains its practical applicability. To overcome this limitation, this study proposes a hybrid subgridding ADI-FDTD method for simulating complex three-dimensional GPR scenarios characterized by dissipation, dispersion, and inhomogeneity. The method supports subgrid partitioning with both odd and even refinement ratios, thereby enhancing adaptability in electromagnetic modeling. In fine-grid regions, the unconditionally stable ADI-FDTD scheme is employed, enabling the entire computational domain to share a uniform time step and thus avoiding the complexity of temporal interpolation. For dispersive soils commonly encountered in GPR applications, the Z-transform technique is applied to convert the frequency-dependent parameters of Debye media into the time domain.

         

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