The present study proposes a fast and efficient computational approach for analyzing sector pad thrust bearings operating under hydrodynamic lubrication, with the goal of reducing both iteration count and computational time compared to conventional approaches. The Reynolds equation is discretized using the finite difference method and numerically solved by the Gauss-Seidel method to obtain the pressure distribution within the lubricating film. Consequently, the study also examines the load capacity, friction force, and coefficient of friction. Several previous sweeping techniques used in the Gauss-Seidel method including full sweep (FS), half sweep (HS), and quarter sweep (QS) are examined, along with three proposed sweeping techniques namely one-eighth sweep (1/8-S), full-quarter sweep (FQS) and full-one-eighth sweep (F-1/8-S). The newly proposed FQS and F-1/8-S schemes demonstrate substantial improvements in computational efficiency and convergence over traditional approaches, while maintaining good accuracy. In contrast, the 1/8-S method shows larger deviations and reduced reliability, making it unsuitable for simulations. Overall, the FQS and F-1/8-S techniques offer a promising and effective alternative for accelerating the simulation of hydrodynamic lubrication phenomena in sector pad thrust bearings. Among these, the F-1/8-S method achieves the minimum iteration count and computational time, underscoring its advantage as the optimal choice for reducing computational effort.