Over the last decade, the role of neutronics modeling has been shifting from analysis of each component separately to high fidelity, full-scale analysis of the nuclear systems' entire domains. The high accuracy, associated with minimizing modeling approximations and including more physical and geometric details, is now feasible because of advancements in computing hardware and development of efficient modeling methods. The hybrid Monte Carlo/deterministic techniques, CADIS and FW-CADIS, dramatically increase the efficiency of neutronics modeling, but their use in the design of very large and geometrically complex nuclear systems can be restricted by the availability of computing resources for their preliminary deterministic calculations and the large computer memory requirements of their final Monte Carlo calculations. To reduce the computational time and memory requirements of the CADIS and FW-CADIS methods, while maintaining their efficiency improvements, three automatic mesh adaptivity algorithms were developed and added to the AutomateD VAriaNce reducTion Generator (ADVANTG) code. First, a macromaterial approach, which mixes the materials for the deterministic calculations, enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm improves the accuracy of structured mesh deterministic calculations by developing meshes that capture as much geometric detail as possible without exceeding some maximum number of mesh elements, usually determined by the availability of computing resources. Finally, a weight window coarsening algorithm decouples the weight window mesh from the mesh of the deterministic calculations to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to increase the efficiency of a FW-CADIS calculation of the prompt dose rate throughout the entire ITER experimental facility. This calculation represents a very challenging shielding problem because of the immense size and complexity of the ITER structure. Compared to a FW-CADIS calculation with the same storage size of the variance reduction parameters, the use of the three algorithms resulted in a 23.3% increase in the regions where the dose rate results are achieved in a 10 day Monte Carlo calculation and increased the efficiency of the Monte Carlo simulation by a factor of 3.4.