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Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation

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dc.contributor.authorCamphouse, Russell C.en
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:31:15Zen
dc.date.adate1999-02-08en
dc.date.available2014-03-14T20:31:15Zen
dc.date.issued1999-01-27en
dc.date.rdate1999-02-08en
dc.date.sdate1999-02-01en
dc.description.abstractThis work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the gas and the substrate results in the deposition of a compound thin film on the substrate. Two different numerical approximations are implemented to produce numerical solutions describing the conduction of thermal energy in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on thermal conduction throughout the reactor. Once insight is gained with respect to the aforementioned conditions, optimal design and control can be investigated. This work represents a first step in our long term goal of developing optimal design and control of such CVD systems. This work has been funded through Partnerships in Research Excellence and Transition (PRET) grant number F49620-96-1-0329.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-020199-095313en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-020199-095313/en
dc.identifier.urihttp://hdl.handle.net/10919/31104en
dc.publisherVirginia Techen
dc.relation.haspartelect.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectparabolic partial differential equationen
dc.subjectfinite differenceen
dc.subjectsemi-discreteen
dc.subjectobject-oriented programmingen
dc.titleApproximations and Object-Oriented Implementation for a Parabolic Partial Differential Equationen
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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