high performance computing on graphics processing units: hgpu.org

Problems in many areas give rise to computationally expensive integrals that beg the need of efficient techniques to solve them, e.g., in computational finance for the modeling of cash flows; for the computation of Feynman loop integrals in high energy physics; and in stochastic geometry with applications to computer graphics. We demonstrate feasible numerical approaches in the framework of the PARINT multivariate integration package. The parallel environment is provided by the cluster of the High Performance Computational Science (HPCS) laboratory, with 22 (16- or 32-core) nodes, NVIDIA GPUs, and Intel Xeon Phi coprocessors. Monte Carlo integration is implemented in CUDA C and can utilize dynamic parallelism on the K20 GPUs, which enables the CUDA kernel to launch child kernels (recursively or iteratively), which will be used to evaluate chunks of sample points. Roundoff error guards are necessary in view of the large computation. An accurate computation of Feynman loop integrals is achieved with iterated integration using one-dimensional modules from the QUADPACK package, where the function evaluations are performed with multi-threading using OpenMP. The parallel performance is assessed for various types of integrals.