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BIT Numerical Mathematics

, Volume 52, Issue 4, pp 801–825 | Cite as

Eigenvalue enclosures and convergence for the linearized MHD operator

  • Lyonell Boulton
  • Michael Strauss
Article

Abstract

Computation of certified enclosures for eigenvalues of benchmark linear magnetohydrodynamics (MHD) operators in the plane slab and cylindrical pinch configuration is discussed. For the plane slab, the proposed method relies upon the formulation of an eigenvalue problem associated to the Schur complement. This leads to highly accurate upper bounds for the eigenvalue. For the cylindrical configuration, a direct application of this formulation is possible, however, it cannot be rigourously justified. Therefore in this case the proposed method relies on a specialized technique based on a method proposed by Zimmermann and Mertins. It turns out that this technique is also applicable for finding accurate complementary bounds in the case of the plane slab. Convergence rates for both approaches are established.

Keywords

Eigenvalue enclosures Magnetohydrodynamics Schur complement Spectral pollution 

Mathematics Subject Classification (2010)

65F15 15A18 47B36 47B39 81-08 

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Copyright information

© Springer Science + Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Maxwell Institute for Mathematical SciencesHeriot-Watt UniversityEdinburghUK

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