rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: A
    title: finite difference
    sub title: boundary element scheme for solving parabolic boundary value problems and supercomputing
  name:
    name part: Chen, Chih-Hsuan
    name part: 1962-
    role:
      role term: creator
  name:
    name part: Chen, Goong
    role:
      role term: degree supervisor.
  name:
    name part: Rundell, William
    role:
      role term: degree committee member.
  name:
    name part: Wehrly, Thomas
    role:
      role term: degree committee member.
  name:
    name part: Zhou, Jianxin
    role:
      role term: degree committee member.
  name:
    name part: Texas A & M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  genre: Academic theses.
  origin info:
    place:
      place term: xx
    date issued: 1994
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: viii, 89 leaves : illustrations ; 28 cm
  abstract: The heat equation is a basic partial differential equation modelling heat conduction. Many numerical methods, such as finite-difference, finite-element, and boundary element methods, have been developed to solve the heat equation numerically. In this dissertation, we use a special form of a combination of the finite-difference and boundary-element methods to solve the heat equation, where the space variable and the time variable are discretized, respectively, by boundary elements and finite differences. The procedures may be described as follows. We use a 1-step backward Euler finite difference scheme for the time variable. This leads to a Helmholtz type equation. We then use a volume potential and a simple-layer potential to represent the solution, obtaining a boundary integral equation for the unknown simple-layer density. This boundary integral equation is then discretized by boundary elements, yielding approximate solutions of the simple-layer density, which can be further integrated to yield approximate solutions of the heat equation. Here we have taken advantage of reduction of dimensionality of the methods of boundary integral equations and boundary elements. Error estimates of the numerical scheme are analyzed, and convergence is shown. Numerical computations are carried out on the Cray Y-MP supercomputer, utilizing vectorization and parallel algorithms on the supercomputer. Some numerical results and computer graphics are also illustrated.
  note: by Chih-Hsuan Chen.
  note: "Major subject: Mathematics."
  note: Vita.
  note: Ph. D. Texas A & M University 1994
  note: Includes bibliographical references.
  subject:
    topic: Major mathematics
  identifier: https://hdl.handle.net/1969.1/DISSERTATIONS-1554195
  identifier: http://proxy.library.tamu.edu/login
  related item:
    location:
      url: https://hdl.handle.net/1969.1/DISSERTATIONS-1554195
  related item:
    location:
      url: http://proxy.library.tamu.edu/login
  record info:
    record content source: TXA
    record creation date: 960531
    record change date: 20220103134936.0
    record identifier: in00001298888
    language of cataloging:
      language term: eng