Statistical gravitational lensing on the Mark III hypercube

We describe a parallel algorithm for the nonlinear optics problem of gravitational lensing. The method is a “ray-tracing” method which studies the statistical properties of the image population associated with a gravitational lens. A parallel computer is needed because the spatial resolution requirements of the problem make the program too large to run on conventional machines. The program is implemented on the Mark III hypercube to take maximum advantage of this machine's 128 Mbytes of memory. The concurrent implementation uses a scattered domain decomposition and the CrOS III communications routines. The communications in the problem are so irregular that no completely satisfactory implementation was made in terms of the execution time of the program: the maximum speed-up relative to a sequential implementation is a factor of 4 on a 32 node machine. However, the goal of efficiently using all of the Mark III's memory was achieved, and the execution time was not the limiting factor in the problem. If the crystal router were used, the implementation would be much more efficient. Development of the program was terminated at this stage, however, because we were able to extract the physics of interest without the more sophisticated communications routines.