High-fidelity simulation of nuclear reactor accidents such as the rupture of a main steam line in a pressurized water reactor (PWR) requires three-dimensional core hydrodynamics modeling because of the strong effect channel cross flow has on reactor kinetics. A parallel nested Krylov linear solver was developed and implemented in the RETRAN-03 reactor systems analysis code to make such high-fidelity core modeling practical on engineering workstations. Domain decomposition techniques were also applied to the RETRAN-03 solution algorithm and demonstrated using a distributed memory parallel computer. Applications were performed for a four-loop Westinghouse PWR steam-line-break accident, and performance improvements of over a factor of 30 were achieved for models with 25 flow channels in the core. Larger models (e.g., 104-core channels), previously inaccessible because of memory limitations, were also solved with practical execution times.