Multidimensional Adaptive Quadrature Over Simplices

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dc.contributor.authorPond, Kevin R.en
dc.contributor.committeechairBorggaard, Jeffrey T.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberBurns, John A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:15:21Zen
dc.date.adate2010-09-02en
dc.date.available2014-03-14T20:15:21Zen
dc.date.issued2010-08-06en
dc.date.rdate2012-08-24en
dc.date.sdate2010-08-17en
dc.description.abstractThe objective of this work is the development of novel, efficient and reliable multidi- mensional adaptive quadrature routines defined over simplices (MAQS). MAQS pro- vides an approximation to the integral of a function defined over the unit hypercube and provides an error estimate that is used to drive a global subdivision strategy. The quadrature estimate is based on Lagrangian interpolation defined by using the vertices, edge nodes and interior points of a given simplex. The subdivision of a given simplex is chosen to allow for the reuse of points (thus function evaluations at those points) in successive refinements of the initial tessellation. While theory is developed for smooth functions, this algorithm is well suited for functions with discontinuities in dimensions three through six. Other advantages of this approach include straight-forward parallel implementation and application to integrals over polyhedral domains.en
dc.description.degreePh. D.en
dc.identifier.otheretd-08172010-151435en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08172010-151435/en
dc.identifier.urihttp://hdl.handle.net/10919/28699en
dc.publisherVirginia Techen
dc.relation.haspartPond_KR_D_2010.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmultidimensionalen
dc.subjectquadratureen
dc.subjectadaptiveen
dc.subjectsimplicesen
dc.titleMultidimensional Adaptive Quadrature Over Simplicesen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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