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Keywords = symmetric definite pencil

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15 pages, 1224 KiB  
Article
The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials
by Tatiana Martynova, Galina Muratova, Pavel Oganesyan and Olga Shtein
Symmetry 2023, 15(1), 171; https://doi.org/10.3390/sym15010171 - 6 Jan 2023
Cited by 3 | Viewed by 2380
Abstract
The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and therefore the process proceeds with the semi-inner product defined [...] Read more.
The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and therefore the process proceeds with the semi-inner product defined by this matrix. The shift-and-invert Lanczos algorithm is used to find multiple eigenvalues closest to some shift and the corresponding eigenvectors. The results of the numerical experiments are presented. Full article
(This article belongs to the Special Issue Mesh Methods—Numerical Analysis and Experiments II)
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