A scalable divide-and-conquer algorithm combining coarse and fine-grain parallelization

We describe an efficient algorithm for carrying out a "divide-and-conquer" fit of a molecule's electronic density on massively parallel computers. Near linear speedups are achieved with up to 48 processors on a Cray T3E, and our results indicate that similar efficiencies could be attained on an even greater number of processors. To achieve optimum efficiency, the algorithm combines coarse and fine-grain parallelization and adapts itself to the existing ratio of processors to subsystems. The subsystems employed in our divide-and-conquer approach can also be made smaller or bigger, depending on the number of processors available. This allows us to further reduce the wallclock time and improve the method's overall efficiency. The strategies implemented in this paper can be extended to any other divide-and-conquer method used within an ab initio, density functional, or semi-empirical quantum mechanical program.