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BIT Numerical Mathematics

, Volume 46, Supplement 1, pp 145–170 | Cite as

A new type of boundary treatment for wave propagation

  • A.-K. Tornberg
  • B. Engquist
  • B. Gustafsson
  • P. Wahlund
Article

Abstract

Numerical approximation of wave propagation can be done very efficiently on uniform grids. The Yee scheme is a good example. A serious problem with uniform grids is the approximation of boundary conditions at a boundary not aligned with the grid. In this paper, boundary conditions are introduced by modifying appropriate material coefficients at a few grid points close to the embedded boundary. This procedure is applied to the Yee scheme and the resulting method is proven to be \(L^2\)-stable in one space dimension. Depending on the boundary approximation technique it is of first or second order accuracy even if the boundary is located at an arbitrary point relative to the grid. This boundary treatment is applied also to a higher order discretization resulting in a third order accurate method. All algorithms have the same staggered grid structure in the interior as well as across the boundaries for efficiency. A numerical example with the extension to two space dimensions is included.

Key words

wave propagation staggered grid modified coefficients irregular boundary  

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • A.-K. Tornberg
    • 1
  • B. Engquist
    • 2
  • B. Gustafsson
    • 3
  • P. Wahlund
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsUniversity of TexasAustinUSA
  3. 3.Department of Information TechnologyUppsala UniversityUppsalaSweden

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