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:
    title: Spatial scaling for the numerical approximation of problems on unbounded domains
  name:
    name part: Trenev, Dimitar Vasilev.
    role:
      role term: creator
  name:
    name part: Bramble, J. H. (James H.)
    role:
      role term: thesis advisor.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: In this dissertation we describe a coordinate scaling technique for the numerical approximation of solutions to certain problems posed on unbounded domains in two and three dimensions. This technique amounts to introducing variable coefficients into the problem, which results in defining a solution coinciding with the solution to the original problem inside a bounded domain of interest and rapidly decaying outside of it. The decay of the solution to the modified problem allows us to truncate the problem to a bounded domain and subsequently solve the finite element approximation problem on a finite domain. The particular problems that we consider are exterior problems for the Laplace equation and the time-harmonic acoustic and elastic wave scattering problems. We introduce a real scaling change of variables for the Laplace equation and experimentally compare its performance to the performance of the existing alternative approaches for the numerical approximation of this problem. Proceeding from the real scaling transformation, we introduce a version of the perfectly matched layer (PML) absorbing boundary as a complex coordinate shift and apply it to the exterior Helmholtz (acoustic scattering) equation. We outline the analysis of the continuous PML problem, discuss the implementation of a numerical method for its approximation and present computational results illustrating its efficiency. We then discuss in detail the analysis of the elastic wave PML problem and its numerical discretiazation. We show that the continuous problem is well-posed for sufficiently large truncation domain, and the discrete problem is well-posed on the truncated domain for a sufficiently small PML damping parameter. We discuss ways of avoiding the latter restriction. Finally, we consider a new non-spherical scaling for the Laplace and Helmholtz equation. We present computational results with such scalings and conduct numerical experiments coupling real scaling with PML as means to increase t…
  note: by Dimitar Vasilev Trenev.
  note: "Major Subject: Mathematics"
  note: Title from author supplied metadata (automated record created 2011-02-28 11:02:00).
  note: Electronic resource.
  note: Doctor of Philosophy Texas A&M University 2009 http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7280
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major mathematics
  subject:
    topic: Elastic wave scatering
  subject:
    topic: Unbounded domain
  subject:
    topic: PML
  subject:
    topic: Numerical approximation
  subject:
    topic: Helmholtz equation
  identifier: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7280
  record info:
    record content source: TXA
    record creation date: 110308
    record change date: 20151202115637.0
    record identifier: in00002654933