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Volume 15
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10.3390/sym15010171
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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
Vorovich Institute of Mathematics, Mechanics and Computer Science, Milchakova Street 8a, Southern Federal University, 344090 Rostov-on-Don, Russia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2023, 15(1), 171; https://doi.org/10.3390/sym15010171
Submission received: 8 November 2022 / Revised: 19 December 2022 / Accepted: 28 December 2022 / Published: 6 January 2023
(This article belongs to the Special Issue Mesh Methods—Numerical Analysis and Experiments II)
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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 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.
Keywords: finite elements; eigenvalues; eigenvectors; Lanczos algorithm; generalized eigenvalue problem; symmetric definite pencil finite elements; eigenvalues; eigenvectors; Lanczos algorithm; generalized eigenvalue problem; symmetric definite pencil

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MDPI and ACS Style

Martynova, T.; Muratova, G.; Oganesyan, P.; Shtein, O. The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials. Symmetry 2023, 15, 171. https://doi.org/10.3390/sym15010171

AMA Style

Martynova T, Muratova G, Oganesyan P, Shtein O. The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials. Symmetry. 2023; 15(1):171. https://doi.org/10.3390/sym15010171

Chicago/Turabian Style

Martynova, Tatiana, Galina Muratova, Pavel Oganesyan, and Olga Shtein. 2023. "The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials" Symmetry 15, no. 1: 171. https://doi.org/10.3390/sym15010171

APA Style

Martynova, T., Muratova, G., Oganesyan, P., & Shtein, O. (2023). The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials. Symmetry, 15(1), 171. https://doi.org/10.3390/sym15010171

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