Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Currently, the most efficient numerical techniques for evaluating high-dimensional integrals are based on Monte Carlo and quasi-Monte Carlo techniques. These tasks require a significant amount of computation and are therefore often executed on parallel computer systems. In order to keep the communic...

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Vydáno v:	Parallel algorithms and applications Ročník 18; číslo 1-2; s. 13 - 26
Hlavní autoři:	Entacher, Karl, Schell, Thomas, Schmid, Wolfgang Ch, Uhl, Andreas
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Taylor & Francis Group 01.05.2003
Témata:	(Quasi)-Monte Carlo methods Low-discrepancy sequences Numerical integration Parallel algorithms Pseudo-random numbers
ISSN:	1063-7192
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Popis
Shrnutí:	Currently, the most efficient numerical techniques for evaluating high-dimensional integrals are based on Monte Carlo and quasi-Monte Carlo techniques. These tasks require a significant amount of computation and are therefore often executed on parallel computer systems. In order to keep the communication amount within a parallel system to a minimum, each processing element (PE) requires its own source of integration nodes. Therefore, techniques for using separately initialized and disjoint portions of a given point set on a single PE are classically employed. Using the so-called substreams may lead to dramatic errors in the results under certain circumstances. In this work, we compare the possible defects employing leaped quasi-Monte Carlo and Monte Carlo substreams. Apart from comparing the magnitude of the observed integration errors we give an overview under which circumstances (i.e. parallel programming models) such errors can occur.
ISSN:	1063-7192
DOI:	10.1080/1063719031000088021