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Absorbing Boundaries and Layers

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Encyclopedia of Applied and Computational Mathematics

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Synonyms

Artificial; Computational; Free-Space; Nonreflective; Open or Far-Field Boundary Conditions; Sponge Layers

Summary

Absorbing boundaries and layers are used to limit the computational domain in the numerical approximation of partial differential equations in infinite domains, such as wave propagation problems or computational fluid dynamics.

In a typical seismic problem, the wave equation \(\mathcal{L}_{u} = f\) must be solved in the subsurface with data g on the surface; the solution u is sought in the domain D S in magenta in Fig. 1. The domain in blue is a computational layer L C ; their union is the computational domain D C .

Absorbing Boundaries and Layers, Fig. 1
figure 11 figure 11

Absorbing layer (courtesy of L. Métivier [19])

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Author information

Authors and Affiliations

  1. Laboratoire Analyse, Géométrie and Applications, UMR 7539 CNRS, Université Paris, Avenue J.B. Clément, 93430, Villetaneuse, France

    Laurence Halpern

Authors
  1. Laurence Halpern
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Editor information

Editors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Björn Engquist

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Halpern, L. (2015). Absorbing Boundaries and Layers. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_366

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