Efficient solution of symmetric eigenvalue problems from families of coupled systems

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2019-01-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
26
1789-1814
Series
SIAM Journal on Numerical Analysis, Volume 57, issue 4
Abstract
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common 2 × 2 block structure. It is assumed that the upper diagonal block varies between different versions while the lower diagonal block and the range of the coupling blocks remain unchanged. Such block structure naturally arises when studying the effect of a subsystem to the eigenmodes of the full system. The proposed method is based on interpolation of the resolvent function after some of its singularities have been removed by a spectral projection. Singular value decomposition can be used to further reduce the dimension of the computational problem. Error analysis of the method indicates exponential convergence with respect to the number of interpolation points. Theoretical results are illustrated by two numerical examples related to finite element discretization of the Laplace operator.
Description
Keywords
Acoustics, Dimension reduction, Eigenvalue problem, Subspace method
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Citation
Hannukainen , A , Malinen , J & Ojalammi , A 2019 , ' Efficient solution of symmetric eigenvalue problems from families of coupled systems ' , SIAM Journal on Numerical Analysis , vol. 57 , no. 4 , pp. 1789-1814 . https://doi.org/10.1137/18M1202323