Numerical Solution of Partial Symmetric Generalized Eigenvalue Problems in Piezo Device Modal Analysis

We demonstrate how different computational approaches affect the performance of solving the generalized eigenvalue problem (GEP). The layered piezo device is studied for resonance frequencies using different meshes, sparse matrix representations, and numerical methods in COMSOL Multiphysics and ACEL...

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Published in:Communications on Applied Mathematics and Computation (Online) Vol. 7; no. 3; pp. 1002 - 1015
Main Authors: Muratova, Galina V., Martynova, Tatiana S., Oganesyan, Pavel A.
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.06.2025
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Computational Science and Engineering
Eigenvalues
Eigenvectors
Finite element analysis
Iterative methods
Mathematics
Mathematics and Statistics
Matrix representation
Medical research
Modal analysis
Numerical methods
Original Paper
Sparse matrices
Sparsity
Lanczos algorithm
65F15
Modal analysis
65F10
Partial symmetric generalized eigenvalue problem (GEP)
ISSN:2096-6385, 2661-8893
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Abstract We demonstrate how different computational approaches affect the performance of solving the generalized eigenvalue problem (GEP). The layered piezo device is studied for resonance frequencies using different meshes, sparse matrix representations, and numerical methods in COMSOL Multiphysics and ACELAN-COMPOS packages. Specifically, the matrix-vector and matrix-matrix product implementation for large sparse matrices is discussed. The shift-and-invert Lanczos method is used to solve the partial symmetric GEP numerically. Different solvers are compared in terms of the efficiency. The results of numerical experiments are presented.
AbstractList We demonstrate how different computational approaches affect the performance of solving the generalized eigenvalue problem (GEP). The layered piezo device is studied for resonance frequencies using different meshes, sparse matrix representations, and numerical methods in COMSOL Multiphysics and ACELAN-COMPOS packages. Specifically, the matrix-vector and matrix-matrix product implementation for large sparse matrices is discussed. The shift-and-invert Lanczos method is used to solve the partial symmetric GEP numerically. Different solvers are compared in terms of the efficiency. The results of numerical experiments are presented.
Author Oganesyan, Pavel A.
Martynova, Tatiana S.
Muratova, Galina V.
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Modal analysis
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Partial symmetric generalized eigenvalue problem (GEP)
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SubjectTerms Algorithms
Applications of Mathematics
Computational Science and Engineering
Eigenvalues
Eigenvectors
Finite element analysis
Iterative methods
Mathematics
Mathematics and Statistics
Matrix representation
Medical research
Modal analysis
Numerical methods
Original Paper
Sparse matrices
Sparsity
Title Numerical Solution of Partial Symmetric Generalized Eigenvalue Problems in Piezo Device Modal Analysis
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