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Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

Frankcombe, Terry J.; Smith, Sean C.

Description

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equationsolution methods while maintaining the speed of a partial...[Show more]

dc.contributor.authorFrankcombe, Terry J.
dc.contributor.authorSmith, Sean C.
dc.date.accessioned2015-11-10T23:30:47Z
dc.date.available2015-11-10T23:30:47Z
dc.identifier.issn0021-9606
dc.identifier.urihttp://hdl.handle.net/1885/16457
dc.description.abstractIn this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equationsolution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates.
dc.description.sponsorshipWe gratefully acknowledge the support of the Australian Research Council in funding this work ~Discovery Project Grant No. DP0211019
dc.publisherAmerican Institute of Physics (AIP)
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0021-9606..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 11/11/15). Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.1628214
dc.sourceThe Journal of Chemical Physics
dc.subjectKeywords: Acetylene; Algorithms; Approximation theory; Eigenvalues and eigenfunctions; Integration; Isomerization; Matrix algebra; Ordinary differential equations; Pressure; Rate constants; Temperature; Vectors; Cholesky factorization; Diffusion approximation; Gas
dc.titleFast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion
dc.typeJournal article
local.description.notesImported from ARIES. At the time of publication Frankcombe was affiliated with Centre for Computational Molecular Science, Chemistry Building 68, University of Queensland,
local.identifier.citationvolume119
dc.date.issued2003-12-22
local.identifier.absfor030304
local.identifier.ariespublicationu4133361xPUB223
local.publisher.urlhttps://www.aip.org/
local.type.statusPublished Version
local.contributor.affiliationFrankcombe, Terry, College of Physical and Mathematical Sciences, CPMS Research School of Chemistry, RSC General, The Australian National University
local.contributor.affiliationSmith, Sean C, University of Queensland, Australia
dc.relationhttp://purl.org/au-research/grants/arc/DP0211019
local.bibliographicCitation.issue24
local.bibliographicCitation.startpage12741
local.bibliographicCitation.lastpage12748
local.identifier.doi10.1063/1.1628214
dc.date.updated2015-12-09T08:34:26Z
local.identifier.scopusID2-s2.0-0942268406
CollectionsANU Research Publications

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