Efficient and scalable 3D occupancy mapping is essential for autonomous robot applications in unknown environments. However, traditional occupancy grid representations suffer from two fundamental limitations. First, explicitly storing all voxels in three-dimensional space leads to prohibitive memory consumption. Second, exhaustive ray casting incurs high update latency. A recent representation alleviate memory demands by maintaining only the voxels on the two-dimensional boundary, yet they still rely on full ray casting updates. This work advances the boundary-based framework with a highly efficient update scheme. We introduce a truncated ray casting strategy that restricts voxel traversal to the exterior of the boundary, which dramatically reduces the number of updated voxels. In addition, we propose a direct boundary update mechanism that removes the need for an auxiliary local 3D occupancy grid, further reducing memory usage and simplifying the map update pipeline. We name our framework as D-BDM. Extensive evaluations on public datasets demonstrate that our approach achieves significantly lower update time and reduced memory consumption compared with the baseline methods, as well as the prior boundary-based approach.