Abstract: To meet the stringent requirements of high-precision neutron transport calculations for next-generation advanced reactor cores, such as those featuring complex heterogeneous fuel assemblies, strong spectral interactions, and intricate geometrical configurations, this paper presented a comprehensive investigation into a generalized coarse mesh finite difference (CMFD) acceleration method that exhibited strong geometric adaptability and robust numerical performance. The direct application of the three-dimensional method of characteristics (MOC) to full-core problems, while offering superior accuracy in treating anisotropic scattering and complex boundary conditions, remains computationally prohibitive due to its excessively large memory footprint and prolonged execution times, particularly when fine spatial meshes and high angular quadrature orders are employed. To overcome these bottlenecks, this work builded upon the in-house developed three-dimensional MOC code, ANT-MOC, and systematically derived the CMFD acceleration theoretical models for three representative mesh topologies: Standard orthogonal quadrilateral meshes, which were widely used in light water reactor analyses; Hexagonal meshes, which were essential for sodium-cooled fast reactors and other advanced reactor designs with triangular or hexagonal lattice structures; And irregular pentagonal meshes, which may arise from specific assembly geometries or degenerate mesh configurations in unstructured grid applications. The derivation rigorously preserved the conservation laws and ensures consistency between the fine-mesh transport solution and the coarse-mesh diffusion-based correction factors, thereby guaranteeing numerical stability and acceleration effectiveness across diverse reactor types. Furthermore, a modular and extensible CMFD acceleration module was developed, which incorporated several advanced features, including flexible energy group compression capabilities that allowed for dynamic condensation of multi-group cross sections into few-group representations during iterative sweeps, as well as a multi-level integrated acceleration strategy that synergistically combined CMFD with other acceleration techniques such as asymptotic diffusion synthetic acceleration and coarse-mesh rebalance to further enhance convergence rates for large-scale problems. To fully exploit modern high-performance computing architectures, a parallel optimization strategy based on red-black Gauss-Seidel iterative ordering was implemented, which effectively reduces data dependencies and communication overhead by decoupling neighboring mesh cells through a checkerboard coloring scheme, thus enabling efficient distributed-memory parallelization with near-ideal scaling behavior. The acceleration performance was rigorously validated using two internationally recognized benchmark problems: The C5G7 benchmark, which represented a typical pressurized water reactor (PWR) configuration with mixed oxide and uranium oxide fuel assemblies and strong spatial heterogeneity, and the China Experimental Fast Reactor (CEFR) benchmark, which featured a fast-spectrum core with sodium coolant and unique control rod arrangements. Comprehensive numerical experiments demonstrate that for the PWR benchmark cases, the proposed CMFD acceleration achieves a remarkable reduction in computation time, saving more than 90% of the total CPU hours compared to the unaccelerated MOC solution, while for the fast reactor benchmark, which exhibits significantly different neutron mean free paths and spectral characteristics, the time savings still reach a substantial 30% to 45%, thereby confirming the method’s effectiveness across both thermal and fast spectra. In all test cases, the maximum relative deviation of the assembly-wise power distribution from high-fidelity reference solutions remains consistently below 0.9% at a stringent 99% confidence level, indicating that the acceleration does not compromise the solution accuracy. Overall, the study conclusively demonstrates that the developed general CMFD acceleration method not only dramatically improves computational efficiency, making full-core three-dimensional MOC calculations practically feasible for routine design and analysis, but also maintains excellent geometric adaptability, numerical robustness, and scalability, thus providing a powerful and versatile tool for advanced reactor physics simulations and supporting future innovations in nuclear reactor core design and safety analysis.