Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows. This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary (IB) method developed in our previous work. For the moving structure modeled using the sharp interface IB method, a recursive box method is developed for efficiently classifying the background grid nodes. For the particles modeled using the diffuse interface IB method, a 'master-slave' approach is adopted. For the particle-particle interaction (PPI) and particle-structure interaction (PSI), a fast algorithm for classifying the active and inactive Lagrangian points, which discretize the particle surface, is developed for the 'dry' contact approach. The results show that the proposed recursive box method can reduce the classifying time from 52 seconds to 0.3 seconds. Acceptable parallel efficiency is obtained for cases with different particle concentrations. Furthermore, the lubrication model is utilized when a particle approaches a wall, enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem. At last, the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls
