Adaptive Mesh Refinement for Radar Sounder Data Simulation with a 2-D Finite-Difference Time-Domain Technique

Radar sounders (RS) are powerful tools for studying extraterrestrial bodies. Recent innovations in RS simulation techniques have improved RS design and data interpretation. However, many challenges persist in the simulation of RS data, which require further improvements in simulation techniques. Numerical simulation tools like the finite-difference time-domain (FDTD) method accurately model complex targets but are computationally expensive and sensitive to numerical dispersion. To overcome these issues, we propose a novel approach integrating Adaptive Mesh Refinement (AMR) with two-dimensional (2-D) FDTD. The proposed approach is adaptive and recursive, i.e., it can identify regions that require refinement and adjust the mesh across multiple levels. A major challenge with multi-resolution simulation techniques is handling the coarse-fine boundary, which can lead to numerical instability. We address this issue by maintaining consistent FDTD stability criteria for each level of refinement. Our proposed approach not only saves computational resources but also ensures numerical stability. The proposed approach is tested in three scenarios: 1) scattering from a perfect electric conductor (PEC) circular cylinder, 2) scattering from a dielectric circular cylinder, and 3) scattering from a random surface with a buried scatterer. Radar cross-section (RCS) plots and radargrams are generated to study the effectiveness and sensitivity of the proposed approach.