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Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method

Publication ,  Journal Article
Scovazzi, G; Carnes, B
Published in: Computer Methods in Applied Mechanics and Engineering
May 1, 2012

We propose a new approach to the enforcement of Dirichlet, Neumann, or Robin boundary conditions in finite element computations of wave propagation problems. The key idea is to enforce the boundary conditions weakly as part of the variational formulation. Due to the hyperbolic structure of the problem considered, the variational formulation does not require any penalty parameters, in contrast with what typically happens in elliptic or advection-diffusion (parabolic) problems. This article presents the implementation of the proposed boundary condition framework using a variational multiscale method for the wave equation in mixed form. We conclude with an extensive set of tests to validate the robustness and accuracy of the proposed approach. © 2012.

Duke Scholars

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

May 1, 2012

Volume

221-222

Start / End Page

117 / 131

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Scovazzi, G., & Carnes, B. (2012). Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method. Computer Methods in Applied Mechanics and Engineering, 221222, 117–131. https://doi.org/10.1016/j.cma.2012.01.018
Scovazzi, G., and B. Carnes. “Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method.” Computer Methods in Applied Mechanics and Engineering 221–222 (May 1, 2012): 117–31. https://doi.org/10.1016/j.cma.2012.01.018.
Scovazzi G, Carnes B. Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method. Computer Methods in Applied Mechanics and Engineering. 2012 May 1;221–222:117–31.
Scovazzi, G., and B. Carnes. “Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method.” Computer Methods in Applied Mechanics and Engineering, vol. 221–222, May 2012, pp. 117–31. Scopus, doi:10.1016/j.cma.2012.01.018.
Scovazzi G, Carnes B. Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method. Computer Methods in Applied Mechanics and Engineering. 2012 May 1;221–222:117–131.
Journal cover image

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

May 1, 2012

Volume

221-222

Start / End Page

117 / 131

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences