Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Parallel globally adaptive algorithms for multi-dimensional integration
Applied Numerical Mathematics - Special issue on massively parallel computing and applications
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We consider the design and implementation of new parallel globally adaptive multidimensional numerical integration algorithms. We describe a pair of algorithms (implemented in MPI on an IBM SP2); one uses a master-slave paradigm and the other is genuinely distributed. Then, we describe modifications of these algorithms to take advantage of a 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 the straightforward implementation of a lattice rule algorithm paying attention to the quality of the respective error estimates. The lattice rule algorithm implementations involve computing new "seeds" for larger numbers of points than used previously, a significant though straightforward computational task.