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

doi:10.1007/s42967-025-00487-1

Abstract

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

CLC Number:

65F15
65F10

Galina V. Muratova, Tatiana S. Martynova, Pavel A. Oganesyan. Numerical Solution of Partial Symmetric Generalized Eigenvalue Problems in Piezo Device Modal Analysis[J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 1002-1015.

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