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

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.

Keywords

Partial symmetric generalized eigenvalue problem (GEP) / Modal analysis / Lanczos algorithm / Mathematical Sciences / Numerical and Computational Mathematics

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Funding

Russian Science Support Foundation(22-21-00318)

RIGHTS & PERMISSIONS

Shanghai University