Version 1
: Received: 16 November 2023 / Approved: 16 November 2023 / Online: 17 November 2023 (09:47:12 CET)
How to cite:
Martynova, T.; Muratova, G.; Oganesyan, P. Numerical Solving of the Partial Generalized Symmetric Eigenproblems for Piezodevices with the Shift-and-Invert Lanczos Method. Preprints2023, 2023111122. https://doi.org/10.20944/preprints202311.1122.v1
Martynova, T.; Muratova, G.; Oganesyan, P. Numerical Solving of the Partial Generalized Symmetric Eigenproblems for Piezodevices with the Shift-and-Invert Lanczos Method. Preprints 2023, 2023111122. https://doi.org/10.20944/preprints202311.1122.v1
Martynova, T.; Muratova, G.; Oganesyan, P. Numerical Solving of the Partial Generalized Symmetric Eigenproblems for Piezodevices with the Shift-and-Invert Lanczos Method. Preprints2023, 2023111122. https://doi.org/10.20944/preprints202311.1122.v1
APA Style
Martynova, T., Muratova, G., & Oganesyan, P. (2023). Numerical Solving of the Partial Generalized Symmetric Eigenproblems for Piezodevices with the Shift-and-Invert Lanczos Method. Preprints. https://doi.org/10.20944/preprints202311.1122.v1
Chicago/Turabian Style
Martynova, T., Galina Muratova and Pavel Oganesyan. 2023 "Numerical Solving of the Partial Generalized Symmetric Eigenproblems for Piezodevices with the Shift-and-Invert Lanczos Method" Preprints. https://doi.org/10.20944/preprints202311.1122.v1
Abstract
In the research we consider a structure-fluid interaction of oscillating piezodevice and acoustic liquid. Such problem requires finding resonance or anti-resonance frequencies of the solid structure to use them in the latter frequency-response analyses step. After finite element discretization of the issue, we need to solve a generalized eigenvalue problem (GEP). The most efficient numerical method for solving the partial GEP is the shift-and-invert Lanczos method. Each step of this algorithm requires solving a large scale system of linear algebraic equations (SLAEs) with special properties. Various ways of ordering grid nodes lead to coefficient matrices with different structure. Several methods are compared in terms of efficiency. The results of the numerical experiments are presented.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
