Comparing Parallel Multidimensional Integration Algorithms

Abstract

We consider the design and implementation of new parallel globally adaptive multidimensional numerical integration algorithms. We describe a pair or algorithms (implemented in MPI on an IBM SP2); one uses a master-slave paradigm and other is genuinely distributed. Then we describe modification of these algorithms to take advantage of singularity detection scheme. The most obvious competitors for globally adaptive schemes in high dimensions are algorithms based on lattice rules. We compare our globally adaptive strategy with a straight forward implementation of a lattice rule algorithm paying attention to the quality of respective error estimates. The lattice rule algorithm implementations involve computing new "seeds" for larger numbers of points than used previously, a significant though straight forward computational task.