Compatible algorithm for integrations on a block domain of any shape for three-dimensional discontinuous deformation analysis

This work calculates the integrations of convex and concave polyhedrons in three-dimensional discontinuous deformation analysis (3D DDA) using a novel method. With this novel method, mathematical topology is applied to the integration, and the numerical mesh used by the Finite Element Method (FEM) is not needed to subdivide polyhedrons into tetrahedrons or hexahedrons. Examples demonstrate the accuracy of the proposed method for integrating convex and concave polyhedrons with planar boundaries.