The authors have worked together over five years to develop a general methodology for parallel disk based computation. This includes: construction of a permutation representation for Thompson's group, acting on 143,127,000 points; construction of a permutation representation for the Baby Monster group (second largest of the sporadic simple groups), acting on 13,571,955,000 points; and a condensation computation for Fi_23 acting on 11,739,046,176 points that resolves an open problem in the Modular Atlas Project. At heart, these problems are search problems. The work typically required a multi-threaded, distributed program using the 30 nodes and corresponding local disks in parallel. Aggregate disk space used ranged as high as 8 terabytes. The need for the highest efficiency led to the discovery of one new search method, and the re-discovery of several other search methods. This is summarized in a taxonomy of parallel disk-based search algorithms. In addition, a new, open source package is presented that automates the difficult task of developing such parallel disk-based software. Lessons learned about the difficulties of such large computations are also presented.