An OpenMP/MPI approach to the parallelization of iterative four-atom quantum mechanics

We present an approach to parallel iterative four-atom quantum mechanics calculations in a computing environment of distributed memory nodes, each node consisting of a group of processors with a shared memory. We parallelize the action of the Hamiltonian matrix on a vector, which is the main computational bottleneck in both iterative calculations of eigenvalues and eigenvectors and the iterative determination of quantum dynamics information via, e.g., wavepacket methods. OpenMP is used to facilitate the parallel work within each node, and MPI is used to communicate information between nodes. For a realistic problem the approach is shown to scale very well up to 512 processors at the NERSC computing facility, working at up to 20% of the theoretical peak performance rate. The highest total floating point rate we achieve is 0.16 Tflops, using 768 processors. Our approach should also be applicable to quantum dynamics problems with more than four atoms.