Parallel Quasi-Monte Carlo Integration by Partitioning Low Discrepancy Sequences

A general concept for parallelizing quasi-Monte Carlo methods is introduced. By considering the distribution of computing jobs across a multiprocessor as an additional problem dimension, the straightforward application of quasiMonte Carlo methods implies parallelization. The approach in fact partitions a single low-discrepancy sequence into multiple low-discrepancy sequences. This allows for adaptive parallel processing without synchronization, i.e. communication is required only once for the final reduction of the partial results. Independent of the number of processors, the resulting algorithms are deterministic, and generalize and improve upon previous approaches.