Fast Gravitational Field Model using Adaptive Orthogonal Finite Element Approximation

摘要

Recent research has addressed the increasing computational challenge that the current state of the art global gravity expansions involve tens of thousands of terms in a theoretically infinite order expansion (some spherical harmonic gravity models extend to degree and order 200 with over 30,000 terms). As global gravity models become more detailed and expensive, and since, acceleration must be computed at numerous local points to generate high precision orbits), and finally, with the advent of >20,000 objects whose orbits must be propagated for Space Situational Awareness, the expense of gravity computation has emerged as a vitally important computational challenge. In this paper we consider orthogonal approximation methods to establish an FEM high accuracy global gravity field representation. The FEM model replaces the global spherical harmonic series with a family of locally precise orthogonal polynomial approximations for efficient computation. Our preliminary results showed that CPU time to compute the state of the art (degree and order 200) spherical harmonic gravity is reduced by 4 to 5 orders of magnitude while maintaining > 9 digits of accuracy. Most of the speedup is due to adopting the orthogonal FEM approach, but a radial adaptation method to modify the approximation degree is introduced that results in an additional order of magnitude speedup. The Adaptive Orthogonal Finite Element Gravity Model (AOFEGM) has wide applicability to establish a new generation of efficient trajectory propagation algorithms. For example, when used in conjunction with the orthogonal Finite Element Model (FEM) gravity approximations discussed herein, the highly parallelizable Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.