Moment Matching and Modal Truncation for Linear Systems

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dc.contributor.advisorEmbree, Marken_US
dc.contributor.committeeMemberSorensen, Danny C.en_US
dc.contributor.committeeMemberWarburton, Timen_US
dc.creatorHergenroeder, AJen_US
dc.date.accessioned2013-07-24T19:31:24Zen_US
dc.date.accessioned2013-07-24T19:31:27Zen_US
dc.date.available2013-07-24T19:31:24Zen_US
dc.date.available2013-07-24T19:31:27Zen_US
dc.date.created2012-12en_US
dc.date.issued2013-07-24en_US
dc.date.submittedDecember 2012en_US
dc.date.updated2013-07-24T19:31:27Zen_US
dc.description.abstractWhile moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationHergenroeder, AJ. "Moment Matching and Modal Truncation for Linear Systems." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71657">https://hdl.handle.net/1911/71657</a>.en_US
dc.identifier.slug123456789/ETD-2012-12-328en_US
dc.identifier.urihttps://hdl.handle.net/1911/71657en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectModal truncationen_US
dc.subjectModel reductionen_US
dc.subjectMoment matchingen_US
dc.subjectDual-stage dimension reductionen_US
dc.subjectLanczosen_US
dc.subjectArnoldien_US
dc.subjectSmoothnessen_US
dc.subjectDiscrete smoothnessen_US
dc.subjectLaplacianen_US
dc.subjectHeat equationen_US
dc.subjectConvection-diffusionen_US
dc.subjectInitial boundary value problemen_US
dc.subjectFourier seriesen_US
dc.subjectCoefficient decayen_US
dc.subjectSemi-discreteen_US
dc.subjectExplicit integrationen_US
dc.subjectForward Euleren_US
dc.subjectLinear time-invariant systemsen_US
dc.titleMoment Matching and Modal Truncation for Linear Systemsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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