An Implementation-Based Exploration of HAPOD: Hierarchical Approximate Proper Orthogonal Decomposition

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dc.contributor.authorBeach, Benjamin Josiahen
dc.contributor.committeechairGugercin, Serkanen
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberEmbree, Mark P.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2018-01-26T09:00:31Zen
dc.date.available2018-01-26T09:00:31Zen
dc.date.issued2018-01-25en
dc.description.abstractProper Orthogonal Decomposition (POD), combined with the Method of Snapshots and Galerkin projection, is a popular method for the model order reduction of nonlinear PDEs. The POD requires the left singular vectors from the singular value decomposition (SVD) of an n-by-m "snapshot matrix" S, each column of which represents the computed state of the system at a given time. However, the direct computation of this decomposition can be computationally expensive, particularly for snapshot matrices that are too large to fit in memory. Hierarchical Approximate POD (HAPOD) (Himpe 2016) is a recent method for the approximate truncated SVD that requires only a single pass over S, is easily parallelizable, and can be computationally cheaper than direct SVD, all while guaranteeing the requested accuracy for the resulting basis. This method processes the columns of S in blocks based on a predefined rooted tree of processors, concatenating the outputs from each stage to form the inputs for the next. However, depending on the selected parameter values and the properties of S, the performance of HAPOD may be no better than that of direct SVD. In this work, we numerically explore the parameter values and snapshot matrix properties for which HAPOD is computationally advantageous over the full SVD and compare its performance to that of a parallelized incremental SVD method (Brand 2002, Brand 2003, and Arrighi2015). In particular, in addition to the two major processor tree structures detailed in the initial publication of HAPOD (Himpe2016), we explore the viability of a new structure designed with an MPI implementation in mind.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:14205en
dc.identifier.urihttp://hdl.handle.net/10919/81938en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectReduced Order Modelingen
dc.subjectProper Orthogonal Decompositionen
dc.subjectTruncated Singular Value Decompositionen
dc.subjectParallel Computingen
dc.subjectMine Fire Dynamicsen
dc.titleAn Implementation-Based Exploration of HAPOD: Hierarchical Approximate Proper Orthogonal Decompositionen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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