Solvers for O (N) Electronic Structure in the Strong Scaling Limit [article]

Nicolas Bock and Matt Challacombe and Laxmikant V. Kalé
<span title="2015-10-20">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 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 C72, 2013], and involves a
more &raquo; ... , 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 over-decomposition, 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 ([H_2O]_N, N ∈{ 30, 90, 150 }, P/N ≈{ 819, 273, 164 }) and find support for an increasingly strong scalability with increasing system size N.
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