0

Full Content is available to subscribers

Subscribe/Learn More  >

A Residual Based Variational Method for Reducing Dispersion Error in Finite Element Methods

[+] Author Affiliations
Lonny L. Thompson, Prapot Kunthong

Clemson University

Paper No. IMECE2005-80551, pp. 29-40; 12 pages
doi:10.1115/IMECE2005-80551
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Noise Control and Acoustics
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Noise Control and Acoustics Division
  • ISBN: 0-7918-4225-8 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

A difficulty of the standard Galerkin finite element method has been the ability to accurately resolve oscillating wave solutions at higher frequencies. Many alternative methods have been developed including high-order methods, stabilized Galerkin methods, multi-scale variational methods, and other wave-based discretization methods. In this work, consistent residuals, both in the form of least-squares and gradient least-squares are linearly combined and added to the Galerkin variational Helmholtz equation to form a new generalized Galerkin least-squares method (GGLS). By allowing the stabilization parameters to vary spatially within each element, we are able to select optimal parameters which reduce dispersion error for all wave directions from second-order to fourth-order in nondimensional wavenumber; a substantial improvement over standard Galerkin elements. Furthermore, the stabilization parameters are frequency independent, and thus can be used for both time-harmonic solutions to the Helmholtz equation as well as direct time-integration of the wave equation, and eigenfrequency/eigenmodes analysis. Since the variational framework preserves consistency, high-order accuracy is maintained in the presence of source terms. In the case of homogeneous source terms, we show that our consistent variational framework is equivalent to integrating the underlying stiffness and mass matrices with optimally selected numerical quadrature rules. Optimal GGLS stabilization parameters and equivalent quadrature rules are determined for several element types including: bilinear quadrilateral, linear triangle, and linear tetrahedral elements. Numerical examples on unstructured meshes validate the expected high-order accuracy.

Copyright © 2005 by ASME

Figures

Tables

Interactive Graphics

Video

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In