Scheduling Parallel Eigenvalue Computations in a Quantum Chemistry Code

Abstract

The application of High Performance Computing to Quantum Chemical (QC) calculations faces many challenges. A central step is the solution of the generalized eigenvalue problem of a Hamilton matrix. Although in many cases its execution time is small relative to other numerical tasks, its complexity of O(N 3) is higher, thus more significant in larger applications. For parallel QC codes, it therefore is advantageous to have a scalable solver for this step. We investigate the case where the symmetry of a molecule leads to a block-diagonal matrix structure, which complicates an efficient use of available parallel eigensolvers. We present a technique which employs a malleable parallel task scheduling (MPTS) algorithm to schedule instances of sequential and parallel eigensolver routines from LAPACK and ScaLAPACK. In this way, an efficient use of hardware resources is guaranteed while overall scalability is facilitated. Finally, we evaluate the proposed technique for electronic structure calculations of real chemical systems. For the systems considered, the performance was improved by factors of up to 8.4, compared to the previously used, non-malleable parallel scheduling approach.

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“…Roderus et al describe a case in which, as part of a larger computational problem, several sub-problems are solved independently in parallel, where one sub-problem consists of finding 'all eigenvalues and eigenvectors of a set of symmetric matrices of different size' [18]. Roderus et al describe a case in which, as part of a larger computational problem, several sub-problems are solved independently in parallel, where one sub-problem consists of finding 'all eigenvalues and eigenvectors of a set of symmetric matrices of different size' [18].…”

“…Roderus et al . describe a case in which, as part of a larger computational problem, several sub‐problems are solved independently in parallel, where one sub‐problem consists of finding ‘all eigenvalues and eigenvectors of a set of symmetric matrices of different size’ . The problem here is that the tasks are relatively coarse‐grained, and thus executing the tasks concurrently, each task on a single processor, would result in heavy load imbalance.…”