Scalable Software for Multivariate Integration on Hybrid Platforms

The paper describes the software infrastructure of the PARINT package for multivariate numerical integration, layered over a hybrid parallel environment with distributed memory computations (on MPI). The parallel problem distribution is typically performed on the region level in the adaptive partitioning procedure. Our objective has been to provide the end-user with state of the art problem solving power packaged as portable software. We will give test results of the multivariate ParInt engine, with significant speedups for a set of 3-loop Feynman integrals. An extrapolation with respect to the dimensional regularization parameter ( ) is applied to sequences of multivariate ParInt results Q( ) to obtain the leading asymptotic expansion coefficients as → 0. This paper further introduces a novel method for a parallel computation of the Q( ) sequence as the components of the integral of a vector function.