## Abstract

Two algorithms for eigenvalue problems in piezoelectric finite element analyses are introduced. The first algorithm involves the use a Lanczos eigensolver, while the second algorithm uses a Rayleigh quotient iteration scheme. In both solution methods, schemes are implemented to reduce storage requirements and solution time. Also, both solution methods seek to preserve the sparsity structure of the stiffness matrix to realize major savings in memory. In the Lanczos solution method, the structural pattern of the consistent mass matrix is exploited to gain savings in both memory and solution time. In the Rayleigh quotient iteration method, an algorithm for generating good initial eigenpairs is employed to improve significantly its overall convergence rate, and convergence stability in the regions of closely spaced eigenvalues and repeated eigenvalues.

Original language | English (US) |
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Pages (from-to) | 1057-1062 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Ultrasonics Symposium |

Volume | 2 |

State | Published - 1994 |

Event | Proceedings of the 1994 IEEE Ultrasonics Symposium. Part 1 (of 3) - Cannes, Fr Duration: Nov 1 1994 → Nov 4 1994 |

## All Science Journal Classification (ASJC) codes

- Acoustics and Ultrasonics