In this contribution, we present a software package, the Fast Gravimetric Spherical Harmonic Synthesis (FGrS), for efficient computation of different gravity functionals using global geopotential models (GGMs). FGrS is available in both an open-source code and user-friendly graphical user interface (GUI) versions. The software addresses the computational challenges associated with harmonic synthesis of ultra-high degree GGMs ( \(N > 2190\) ) using the Belikov method for evaluating fully normalized associated Legendre functions (fnALFs). FGrS supports multithreaded parallel computations for regular grids (grids on level surfaces), varied-height grids, and scattered points, significant improvements in performance. For varied-height grids, FGrS implements an innovative interpolation method that outperforms existing gradient-based approaches. In this method, gravity field functionals are interpolated from pecomputed values along multiple reference lines within each parallel. The number and distribution of reference lines are optimized based on the maximum degree of the model and the type of gravity functional, ensuring a balance between accuracy and computational efficiency. Numerical tests demonstrate that this new method achieves relative errors ranging from \(10^{-9}\) to \(10^{-6}\) for various gravimetric quantities, even in topographically complex regions such as the Himalayas. FGrS computes all major Earth gravity quantities, including gravitational potential, gravity disturbance/anomaly, height anomaly, geoid, and derivatives of the potential up to second order. Performance comparisons with other scientific software demonstrate that FGrS is significantly faster while maintaining high accuracy.
