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Abstract This work highlights the use of half-implicit numerical integration in the context of the index three differential algebraic equations (DAEs) of multibody dynamics. Although half-implicit numerical integration is well established for ordinary differential equations problems, to the best of our knowledge, no formal discussion covers its use in the context of index three DAEs of multibody dynamics. We wish to address this since when compared to fully implicit methods, half-implicit integration has two attractive features: (i) the solution method does not require the computation of the Jacobian associated with the constraint, friction, contact, or user-defined applied forces; and (ii) the solution is simpler to implement. Moreover, for nonstiff problems, half-implicit numerical integration yields a faster solution. Herein, we outline the numerical method and demonstrate it in conjunction with three mechanisms. We report on convergence order behavior and solution speed. The Python software developed to generate the results reported is available as open in a public repository for reproducibility studies. 

We report on an open-source, publicly available C++ software module called Chrono::GPU, which uses the Discrete Element Method (DEM) to simulate large granular systems on Graphics Processing Unit (GPU) cards. The solver supports the integration of granular material with geometries defined by triangle meshes, as well as co-simulation with the multi-physics simulation engine Chrono. Chrono::GPU adopts a smooth contact formulation and implements various common contact force models, such as the Hertzian model for normal force and the Mindlin friction force model, which takes into account the history of tangential displacement, rolling frictional torques, and cohesion. We report on the code structure and highlight its use of mixed data types for reducing the memory footprint and increasing simulation speed. We discuss several validation tests (wave propagation, rotating drum, direct shear test, crater test) that compare the simulation results against experimental data or results reported in the literature. In another benchmark test, we demonstrate linear scaling with a problem size up to the GPU memory capacity; specifically, for systems with 130 million DEM elements. The simulation infrastructure is demonstrated in conjunction with simulations of the NASA Curiosity rover, which is currently active on Mars.