Granular matter formed from non-spherical solids appears in both natural and industrial settings. These include, among others, landslides, mixing, and fluidization. The commonly used predictive method for granular matter is the discrete element method (DEM). However, DEM was initially designed for spherical particles and faces many challenges in modeling the non-spherical ones , which are prevalent. Therefore, various approaches, including multi-sphere clusters, super-quadrics and polyhedral models, were developed to approximate the irregular shapes. The polyhedral approach offers the highest level of fidelity, but comes with the biggest computational costs, particularly for non-convex particles. Hence, optimization and parallelization of codes with polyhedron-based DEM solvers are of great interest. In this work, we present recent advances in the development of our custom polyhedron-based DEM solver, focusing on parallel computing. With improvements in the solver architecture and boosted computational efficiency, the DEM code scales well at least up to 32 cores and allows for efficient coupling with computational fluid dynamics (CFD) to simulate complex particle-laden flows.