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Eigenvalue enclosures and convergence for the linearized MHD operator

journal contribution
posted on 2023-06-08, 18:46 authored by Michael Strauss, Lyonell Boulton
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.

History

Publication status

  • Published

Journal

BIT Numerical Mathematics

ISSN

0006-3835

Publisher

Springer

Issue

4

Volume

52

Page range

801-825

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-10-22

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