Title page for ETD etd-020199-095313


Type of Document Master's Thesis
Author Camphouse, Russell C.
Author's Email Address rcamphou@math.vt.edu
URN etd-020199-095313
Title Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Borggaard, Jeffrey T. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Keywords
  • parabolic partial differential equation
  • finite difference
  • semi-discrete
  • object-oriented programming
Date of Defense 1999-01-27
Availability unrestricted
Abstract
This 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.

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