A high-performance discrete element method solver on graphical processing units

Granular materials arise in a wide range of natural and industrial systems, yet their numerical simulation remains challenging when particle shape departs from the sphere and when the number of interacting bodies becomes large. This thesis develops a high-performance discrete element method framework for granular flow simulations that combines geometric generality with computational efficiency. The work first establishes the modeling ingredients required for consistent DEM simulations of rigid particles, including contact detection, contact-force evaluation, and time integration. It then investigates collision detection for general convex particles using the Gilbert–Johnson–Keerthi (GJK) algorithm, with emphasis on practical strategies that reduce the cost of repeated narrow-phase queries in dense granular systems. Broad-phase filtering, temporal coherence, and accelerated search updates are examined to identify robust combinations that improve performance without sacrificing generality. The framework is next extended to superquadrics, which provide a compact analytical description of many non-spherical shapes of practical interest. This makes it possible to assess when superquadrics offer an efficient and accurate surrogate for particles such as rounded cylinders and cubes, and when exact convex descriptions remain preferable. Finally, the thesis presents Grains3DGPU, a GPU-resident DEM solver for large-scale simulations of general convex and composite particles. The solver maps collision detection, contact handling, and time integration to CUDA in a way that exploits massive parallelism while limiting unnecessary data movement. Taken together, these contributions show that large-scale DEM simulations with non-spherical particles need not rely on oversimplified geometry to remain computationally feasible. By combining robust convex contact algorithms, practical shape representations, and GPU acceleration, this thesis advances DEM toward more faithful and scalable simulation of granular systems and provides a foundation for future developments in richer contact physics, multiphysics modeling, and extreme-scale particle simulation.