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Numerical simulation of vector wave scattering from three-dimensional (3-D) target and rough surface composite model is investigated with a 3-D multilevel UV method. Due to the adoption of RWG basis functions for accurate modeling of vector current, the oscillation of the interaction matrix elements brings difficulty to directly apply the UV decomposition method. Based on the reordering of the interaction strength and the sampling according to the characteristics distribution of the interaction, an EM-interaction-based sampling algorithm is developed for the accurate reconstruction of the far interaction submatrix with UV decomposition method. Combined with multilevel division of the total composite model, the 3-D multilevel UV method incorporating the new sampling algorithm is developed for vector wave scattering from 3-D complex target above or on a random rough surface. The 3-D multilevel UV method yields a complexity of O(N log N) for the setup time of the impedance matrix, the solve time of the matrix iterative solution and also for the memory requirements. The accuracy and the efficiency of the 3-D multilevel UV method is compared and validated with the full MOM method and the ACA method in the tested cases. Finally, the applications of a target above or on the rough surface, for example, a ship on the sea surface, have been accomplished and analyzed.