Abstract: Boolean operations are a fundamental capability of any geometric kernel; their performance directly determines the modeling quality of the kernel. To address the low efficiency of existing Boolean operations and their difficulty in handling non-manifold scenarios, we propose a high-performance Boolean algorithm grounded in selective geometric complex theory. First, we introduce a V-subdivision scheme with a registration mechanism that represents transient non-manifold objects and drastically reduces intersection tests. Second, a combinatorial decomposition strategy is presented that streamlines the traditional selection and simplification operators, eliminating redundant topological element searches and repeated simplifications. Finally, a multi-pass subdivision method is devised to robustly process non-manifold solids during Boolean evaluation. The proposed approach unifies the representation of non-manifold objects and regular Boolean operands, yielding a significant speed-up. In a full-scale aircraft assembly benchmark, our algorithm outperforms OCCT by more than tenfold and matches the speed of ACIS.