Semi-discrete optimal transport-based centroidal Laguerre tessellation for large-scale polyhedral model generation in arbitrary domains

Tessellation-based polyhedral models underpin the computational study of a wide range of physical and biological systems, from polycrystals and porous media to bioinspired composites and trabecular bone, in which a cellular geometry governs the response. Putting such models to use, however, increasingly requires more than a representative volume element in a cuboid box: the tessellation must be generated directly inside the target domain, so that design parameters such as the number of cells and their distribution come out correct, and the cells often need to be centroidal, since seeds placed at random yield irregular shapes ill-suited to subsequent modeling workflows. We address both needs with a unified framework that generates large-scale centroidal Laguerre tessellations with prescribed size and shape distributions in both periodic and arbitrarily shaped bounded domains. A semi-discrete optimal transport solver matches the prescribed cell volumes, an adaptive and parameter-free damped Lloyd iteration enforces centroidal regularity, and Anderson acceleration lowers the centroidal iteration cost by up to ∼ 48 % for narrow to moderately skewed size distributions where extrapolation is effective. At the same time, a single geometry interface handles both domain types, including nonconvex shapes with internal voids, through periodic weighted Delaunay triangulations and restricted Voronoi diagrams. The framework scales near-linearly in time and memory, producing full three-dimensional models of up to ten million cells in minutes on a standard desktop. We demonstrate it on polycrystal RVEs with jointly prescribed grain size and shape, as well as on open-cell porous materials and trabecular bone generated directly within their target domains. When combined with a dedicated regularization step, the resulting polyhedral models become ready for finite-element analysis of polycrystal RVEs and fracture analysis of tessellation-based bioinspired organic–inorganic hybrid composites.