Investigation of Transverse Terrain Effects on Loran‐C ASF Using Multi‐GPU Based Parameter‐Optimised 3D‐FDTD

ABSTRACT

Traditional two‐dimensional (2D) modelling of Loran‐C additional secondary factor (ASF) fails to capture transverse terrain effects. In this paper, a parameter‐optimised three‐dimensional finite‐difference time‐domain (PO‐3D‐FDTD) method accelerated by multiple graphics processing units (multi‐GPU) is applied to solve Loran‐C ASF over irregular terrain. By introducing anisotropic parameters into the 3D‐FDTD formulas, the numerical dispersion error is significantly reduced. A multi‐GPU implementation enables accelerated computation and large‐scale ASF prediction. For the tested large‐scale model, the four‐GPU PO‐3D‐FDTD simulation required 0.79 h, whereas the conventional CPU‐based 3D‐FDTD was estimated to require several thousand hours. The transverse terrain effects on Loran‐C ASF are investigated through Gaussian‐shaped mountain paths. Pronounced differences between the 2D‐ and 3D‐FDTD predictions are observed in the shadow and flank regions, particularly for higher mountains. These differences are associated with lateral propagation and transverse field redistribution that are not represented by the 2D formulation, reaching several hundred nanoseconds in the tested single‐mountain cases. Furthermore, more complex ASF interference patterns are observed between two separated mountains, with the maximum 2D‐3D difference reaching approximately 1.55 μs.