The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials

被引：1
|
作者：
Martynova, Tatiana [1 ]
Muratova, Galina [1 ]
Oganesyan, Pavel [1 ]
Shtein, Olga [1 ]
机构：
[1] Southern Fed Univ, Vorovich Inst Math Mech & Comp Sci, Milchakova St 8a, Rostov Na Donu 344090, Russia
来源：
SYMMETRY-BASEL | 2023年 / 15卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
finite elements; eigenvalues; eigenvectors; Lanczos algorithm; generalized eigenvalue problem; symmetric definite pencil; LANCZOS METHOD;
D O I：
10.3390/sym15010171
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页数：15
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