Parallel Algorithms for Multidimensional Integration

Abstract

A central feature of adaptive algorithms for the numerical approximation of definite integrals is the manipulation of the list containing the sub intervals and the corresponding error estimates. Fundamentally different parallel algorithms results depending on whether the list is maintained as a single shared data structure accessible to all processors, or else as the union of non-overlapping sublists, each private to a processor. We describe several variants of this approach, and compare numerical performances of the algorithms on multi-dimensional problems.