Fast Gravitational Field Model Using Adaptive Orthogonal Finite Element Approximation
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abstract
Recent research has addressed the issue that high degree and order gravity expansions involve tens of thousands of terms in a theoretically infinite order spherical harmonic expansion (some gravity models extend to degree and order 200 with over 30,000 terms) which in principle must be computed at every integration step to obtain the acceleration consistent with the gravity model. We propose to evaluate these gravity model interpolation models and use them in conjunction with the modified Picard path approximation methods. It was decided to consider analogous orthogonal approximation methods to interpolate, an FEM model, high (degree, order) gravity fields, by replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. Our preliminary results showed that 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 gain is due to adopting the orthogonal FEM approach, but radial adaptation of the approximation degree gains an additional order of magnitude speedup. The efficient data base storage/access of the local coefficients is studied, which utilizes porting the algorithm to the NVIDIA GPU. This paper will address the accuracy and efficiency in both a C++ serial PC architecture as well as a PC/GPU architecture. The Adaptive Orthogonal Finite Element Gravity Model (AOFEGM) is expected to have broad potential for speeding the trajectory propagation algorithms; for example, used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.
