We present strategies for the parallel computation of the
integrals typically arising in finite element problems.
In order to deal efficiently with difficulties in the integrands affecting
the domain in areas of which the exact locations may be unknown,
a parallel adaptive strategy is applied to the entire domain. The
elements comprising the domain form the initial pool of subregions in the
adaptive strategy and are refined further where needed,
thereby allowing load sharing or a load balanced global priority queue
within each participating process group.