Abstract:
The technique of a numerical evaluation of eigenvalues of an operator of Laplace in a polygon is described. As an example it is considered LL-figurative area. The circle conformal mapping on this area by means of an integral of Christoffel–Schwarz is under construction. In a circle the problem dares on earlier developed by the author (together with K. I. Babenko) a technique without saturation. The problem consists in, whether this technique to piecewise smooth boundaries (the conformal mapping has on singularity boundary) is applicable. The done evaluations show that it is possible to calculate about 5 eigenvalues (for a problem of Neumann about 100 eigenvalues) an operator of Laplace in this area with two-five signs after a comma.
Keywords:
eingenvalues of an operator of Laplace, an integral of Christoffer–Schwarz, numerical algorithm without saturation.
Citation:
S. D. Algazin, “Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain”, Mat. Model., 25:4 (2013), 65–73; Math. Models Comput. Simul., 5:6 (2013), 520–526
\Bibitem{Alg13}
\by S.~D.~Algazin
\paper Computing experiments in the problem on eigenvalues for the operator of Laplace in the polygonal domain
\jour Mat. Model.
\yr 2013
\vol 25
\issue 4
\pages 65--73
\mathnet{http://mi.mathnet.ru/mm3352}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3114885}
\transl
\jour Math. Models Comput. Simul.
\yr 2013
\vol 5
\issue 6
\pages 520--526
\crossref{https://doi.org/10.1134/S2070048213060021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929087608}
Linking options:
https://www.mathnet.ru/eng/mm3352
https://www.mathnet.ru/eng/mm/v25/i4/p65
This publication is cited in the following 4 articles:
Pavel S. Solov'ev, Diana M. Korosteleva, Sergey I. Solov'ev, Lecture Notes in Computational Science and Engineering, 141, Mesh Methods for Boundary-Value Problems and Applications, 2022, 475
Korosteleva D.M., Samsonov A.A., Solov'ev P.S., Solov'ev I S., “Eigenvibrations of a Bar With Two Attached Loads”, AIP Conference Proceedings, 2315, eds. Gorkunov E., Panin V., Irschik H., Amer Inst Physics, 2020, 020024
D. M. Korosteleva, L. N. Koronova, K. O. Levinskaya, S. I. Solov'ev, A. Glezer, S. Roshchupkin, “Finite difference approximation of eigenvibrations of a bar with oscillator”, MATEC Web Conf., 329 (2020), 03030
L. N. Koronova, D. M. Korosteleva, K. O. Levinskaya, S. I. Solov'ev, A. Glezer, S. Roshchupkin, “Eigenvibrations of a beam with two mechanical resonators attached to the ends”, MATEC Web Conf., 329 (2020), 03009
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