Solvers for $\mathcal{O}(N)$ Electronic Structure in the Strong Scaling Limit

Abstract

We present a hybrid OpenMP/Charm++ framework for solving the $\mathcal{O}(N)$ Self-Consistent-Field eigenvalue problem with parallelism in the strong scaling regime, $P\gg N$, 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 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 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${}_2$O]${}_N$, $N\in \{30,90,150\}$, $P/N\approx \{819,273,164\}$) and find support for an increasingly strong scalability with increasing system size $N$.

Presented at the 12th Annual Workshop on Charm++ and its Applications

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