Eigenvalue enclosures and convergence for the linearized MHD operator

Lyonell Boulton, Michael David Strauss

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)801-825
Number of pages25
JournalBIT Numerical Mathematics
Volume52
Issue number4
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • Eigenvalue enclosures
  • Magnetohydrodynamics
  • Schur complement
  • Spectral pollution
  • VARIATIONAL-PRINCIPLES
  • SPECTRAL POLLUTION
  • RELATIVE SPECTRA
  • PLASMA

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