Numerical integration of overlap electron densities: parallelization strategies for a good load balancing using OpenMP

Abstract Here we present a comprehensive assessment of how different OpenMP directives influence the computation speedup for the creation of the overlap electron density using linear combinations of atomic Gaussian-type orbitals. Also, we present the computational performance of a simple algorithm for numerical integration, based on the division of integration space in subspaces (with adaptive sizes considering its integral values - ASII). This algorithm is implemented and compared with the VEGAS algorithm with integrand parallelization. Here we present the performance comparison of 12 different sets of OpenMP directives and collapse clauses, and 15 different basis sets, that were tested for Br2 and H2O2 model systems. The OpenMP directives and clauses tests pointed to the schedule = dynamic or static, Nindex = 1, and collapse (2) clause as the best strategy for a load-balanced parallel computation. The ASII method presents speedup performance compared with a modern parallel implementation of the VEGAS algorithm. The best speedup obtained for the computation at a 64 core platform was ca. 48.0. A GitHub link with the built library and a simple example are also available.