Multidimensional adaptative and deterministic integration in CUDA and OpenMP

Parallelization schemes on many-core architectures, in this case, CUDA and OpenMP, are used to accelerate and improve the accuracy of adaptive multidimensional integration algorithms. The one-dimensional Gauss–Kronrod adaptive method is generalized to 3, 4, 5 and 6 dimensions. The implementation of the traditional tensor product construction of the grid and weights for multidimensional integration is revisited and reformulated taking advantages of the multi and many-core architectures. Tests performed in a set of benchmark functions show that the algorithm is numerically accurate, with accelerations as high as 800X in CUDA and 300X in the OpenMP implementation both compared to a sequential multidimensional integration algorithm.