Fast Trajectory Generation in High Fidelity Geopotentials using Finite Elements, Mascons, and Parallelism

We propose to investigate the feasibility of obtaining fast and accurate trajectories using global geopotential models representing departures from the two-body plus J2 terms. The proposed geopotential formulations and numerical integration methods rely on multi-core processors and the emerging massive parallel capabilities of Graphics Processing Units (GPUs) available to common personal computers. Two approaches of modeling the geopotential are proposed. 1) Finite Element Approach: modernize existing finite element models of the geopotential and trade memory for computational speed through the interpolation of a pre-computed mesh. 2) Mascon Approach: model thousands of mascons within the Earth and tap into the fine-grained parallelism of the affordable and commonly available GPUs. Integration of equations of motion will be performed using parallel explicit and implicit methods as well as modern energy preserving (symplectic) techniques that are ideally suited for conservative problems such as the non-spherical earth. The deliverables of Phase I will be prototype geopotential models and example simulations of high-fidelity trajectories which can ultimately be moved into operations to benefit a wide variety of SSA activities. Using a single desktop computer, we target simulation speed improvements of two orders of magnitude compared to conventional geopotential formulations and serial approaches. BENEFIT: It is anticipated that parts of the proposed research will achieve two orders of magnitude improvement in gravitational acceleration calculation. The parallel implementation and fast integration schemes will further improve trajectory calculation speed, which will benefit the Air Force SSA activities and a wide range of other industries. The commercial applications of the proposed research will involve sales of software and services to governmental agencies and contractors such as NASA, military, aerospace corporations, and software companies supporting the earth and space science industries. Apart from the apparent spacecraft trajectory applications, the proposed computation schemes using GPUs and parallel numerical integration have a wide range of applications, including computational fluid dynamics, structural analysis, large-scale optimization, etc.