Accelerating High-Dimensional Integration Using Lattice Rules on GPUs

Lattice rules for multiple integration yield a powerful method to approximate high-dimensional integrals for various function classes. Using generator vectors obtained from the fast component-by-component (CBC) construction of lattice rules, we incorporated rank-1 lattices for numerical integration on GPU accelerators. We show accuracy and efficiency results for a number of multivariate integrals, and compare with results obtained by Monte Carlo integration for the same functions also on GPU. The lattice rules achieve high accuracy and excellent speedups.