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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 BoultonComputation 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.
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Publication status
- Published
Journal
BIT Numerical MathematicsISSN
0006-3835Publisher
SpringerExternal DOI
Issue
4Volume
52Page range
801-825Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2014-10-22Usage metrics
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