Solvers for O (N) Electronic Structure in the Strong Scaling Limit.

We present a hybrid OpenMP/Charm++ framework for solving the O(N) self-consistent-field eigenvalue problem with parallelism in the strong scaling regime, P >> N, where P is the number of cores, and N is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72-C98], and involves a recursive, task-parallel algorithm, often employed by generalized N-Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Employing classic technologies associated with generalized N-Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistence-based load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H2O](N), N is an element of {30, 90, 150}, P/N approximate to {819, 273, 164}) and find support for an increasingly strong scalability with increasing system size N.