Accelerating the finite element method for calculating the full 2-body problem with CUDA

Binary asteroids in solar systems usually have irregularly shaped components; and their internal structures, though lacking direct measurements, are suspected to be uneven given the theoretical considerations of their formation history. This poses a huge challenge to precise dynamic modelling. The finite element method (FEM) is capable of modelling asteroids with irregular shapes and heterogeneous internal structures with good convergence. However, the implementation of the FEM in the full 2-body problem is usually time-consuming for single-core CPU processing. We note that the computing process is comprised of serialized independent calculations that can be parallelized with inexpensive and ubiquitous graphics processing unit (GPU) hardware. We propose a parallel algorithm to accelerate the FEM to calculate the full 2-body problem with CUDA (Compute Unified Device Architecture). Benchmarking tests are performed to verify this method, which is later applied to the study of the motion of the binary asteroid system (66391) 1999KW4. Simulations with more than 10 thousand nodes on a single graphics card exhibit a speedup of up to two orders of magnitude over using a single-core CPU. Both the achieved speedup(s) and the numerical simulation result accuracy suggest that CUDA-based GPU programming can be used in the FEM for computational full 2-body problem methods with efficiency and reliability. As an application, we studied the motion of the binary asteroid system (65803) Didymos, the target object of the DART mission. With the simulation results, we show the influences of the irregular shape/uneven internal structure of the primary on the postimpact motion of the secondary. The code is available at https://github.com/yyu86/femF2BP.git.