High-Performance, High-Angular-Momentum J Engine on Graphics Processing Units

Efficient evaluation of electron repulsion integrals
(ERIs) involving
high-angular-momentum Gaussian basis functions is computationally
challenging on graphical processing units (GPUs), as traditional recurrence-based
integral algorithms generate numerous intermediates, causing significant
register pressure and memory bottlenecks. In this Article, we present
a high-performance, high-angular-momentum Coulomb-matrix (J) engine specifically optimized for GPU execution.
Our approach introduces a GPU-optimized McMurchie-Davidson recurrence
algorithm combined with a tailored integral batching scheme, designed
specifically to jointly minimize intermediate storage requirements
and redundant computation. By strategically partitioning high-angular-momentum
ERIs classes into several carefully selected sub-batches, our approach
transitions the associated integral evaluation kernels from memory-bound
to compute-bound regimes, significantly enhancing computational throughput
and reducing time to solution. Implemented in the Extreme-scale Electronic
Structure System (EXESS), our algorithm achieves
individual kernel speedups of up to 9× and improves overall J-matrix formation performance by up to 64%
across a variety of increasing-size chemical systems, including polyglycine
chains, water clusters, and boron nitride crystals, when using the
cc-pVQZ quadruple-ζ basis set on an NVIDIA A100 GPU.