Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (3): 1002-1015.doi: 10.1007/s42967-025-00487-1

• ORIGINAL PAPERS • 上一篇    下一篇

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

Galina V. Muratova, Tatiana S. Martynova, Pavel A. Oganesyan   

  1. Vorovich I. I. Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don 344090, Russia
  • 收稿日期:2023-12-07 修回日期:2024-05-09 接受日期:2024-06-05 出版日期:2025-09-20 发布日期:2025-05-23
  • 通讯作者: Galina V. Muratova, muratova@sfedu.ru;Tatiana S. Martynova, martynova@sfedu.ru;Pavel A. Oganesyan, poganesyan@sfedu.ru E-mail:muratova@sfedu.ru;martynova@sfedu.ru;poganesyan@sfedu.ru
  • 基金资助:
    This study was funded by a grant of the Russian Science Foundation N 22-21-00318, https://rscf.ru/project/22-21-00318/ at Southern Federal University.

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

Galina V. Muratova, Tatiana S. Martynova, Pavel A. Oganesyan   

  1. Vorovich I. I. Institute of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don 344090, Russia
  • Received:2023-12-07 Revised:2024-05-09 Accepted:2024-06-05 Online:2025-09-20 Published:2025-05-23
  • Supported by:
    This study was funded by a grant of the Russian Science Foundation N 22-21-00318, https://rscf.ru/project/22-21-00318/ at Southern Federal University.

摘要: 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 shiftand-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.

关键词: Partial symmetric generalized eigenvalue problem (GEP), Modal analysis, Lanczos algorithm

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 shiftand-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.

Key words: Partial symmetric generalized eigenvalue problem (GEP), Modal analysis, Lanczos algorithm

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