10 million unknowns: Is it that big?

At the Center for Computational Electromagnetics at the University of Illinois, we recently solved a very-large-scale electromagnetic scattering problem. We computed the bistatic radar cross-section of a full-size aircraft at 8 GHz, involving the solution of a dense matrix equation with nearly 10.2 million unknowns. We regarded this as the "ultimate test" of a massively parallel implementation of the Multilevel Fast Multipole Algorithm (MLFMA), called ScaleME. In this paper, we narrate the technical difficulties faced and the experience gained from a very informal point of view. We shall describe the various methods developed for surmounting each of the obstacles.