Linear scaling computation of the Fock matrix. IX. Parallel computation of the Coulomb matrix

TL;DR

This paper introduces a parallel algorithm for computing the Coulomb matrix in quantum chemistry, achieving high efficiency and load balancing across multiple processors using an equal time partition method.

Contribution

It presents a novel parallelization approach for the Coulomb matrix calculation employing equal time partition for load balancing in quantum-chemical tree codes.

Findings

Achieves 91-98% efficiency with 128 processors in Coulomb matrix computation.

Overall efficiency of 63-81% on 128 processors with fine-grained parallelism.

Demonstrates effectiveness on both finite and periodic systems.

Abstract

We present parallelization of a quantum-chemical tree-code [J. Chem. Phys. {\bf 106}, 5526 (1997)] for linear scaling computation of the Coulomb matrix. Equal time partition [J. Chem. Phys. {\bf 118}, 9128 (2003)] is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91 -- 98 % efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63 -- 81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).