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Shifted Laplacian RAS Solvers for the Helmholtz Equation

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Book cover Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

We consider the Helmholtz equation: \(\begin{array}{llll}\qquad\qquad-\varDelta u^*\;-k^2u^*\;=\;f\quad \mathrm{in}\quad \varOmega \\ \\ u^*\;=\;g_D\;\mathrm{on}\;\partial{\varOmega_D},\;\frac{\partial u^*}{\partial n}\;=\;g_N\;\mathrm{on}\;\partial {\varOmega_N},\;\frac{\partial u^*}{\partial n}\;+\;iku^*\;=\;g_S\;\mathrm\;\mathrm{on}\;\partial{\varOmega_S}\end{array}\) where \(\varOmega\) is a bounded polygonal region in k2, and the \(\partial{\varOmega_D},\;\partial{\varOmega_N}\;\mathrm{and}\;\partial{\varOmega_S}\) correspond to subsets of \(\varOmega\) where the Dirichlet, Neumann and Sommerfeld boundary conditions are imposed.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, South Dakota State University, Brookings, SD, 57007, USA

    Jung-Han Kimn

  2. Mathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609, USA

    Marcus Sarkis

  3. Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Marcus Sarkis

Authors
  1. Jung-Han Kimn
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  2. Marcus Sarkis
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Corresponding author

Correspondence to Jung-Han Kimn .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Kimn, JH., Sarkis, M. (2013). Shifted Laplacian RAS Solvers for the Helmholtz Equation. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_16

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