High-performance GPU-accelerated evaluation of electron repulsion integrals

A novel methodology for the evaluation of two electron integrals up to f functions using Graphics Processing Units (GPUs) is presented. The Head-Gordon-Pople recursion relationships are solved via a simple heuristic methodology to minimize the number of evaluated intermediates in the recursion trees. Automatic code generation is used to generate highly optimized CUDA kernels. A novel approach for f functions is presented in which integral classes are split into smaller subclasses to minimize register pressure and exploit additional parallelism at the cost of recomputing a small number of intermediates. Alongside optimized kernels, the ERI evaluation scheme works in conjunction with an efficient work distribution scheme which guarantees load-balancing during computation. The new HGP scheme shows excellent speedups of 2x to above 60x against existing GPU code. Additionally, when coupled with digestion into the Fock matrix, the scaling is excellent on up to 7 GPUs with an 85% parallel efficiency for the 6-31G(d) basis set. [GRAPHICS] .