### Abstract

We develop and analyze efficient methods for computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy. The discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem. Numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on Raviart-Thomas finite elements for the displacement field. The trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem (GEP) of the form Ax=λBx. For solving the GEP we apply Arnoldi algorithm to two different types of single matrices B-1A and AB-1. Numerical accuracy shows that the application of Arnoldi on AB-1 is better than that on B-1A.

Original language | English |
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Pages (from-to) | 2189-2206 |

Number of pages | 18 |

Journal | Journal of Computational Physics |

Volume | 230 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2011 Mar 1 |

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### Keywords

- Arnoldi algorithm
- Finite elements
- Fluid-structure interaction
- Rational eigenvalue problem
- Trimmed linearization

### ASJC Scopus subject areas

- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational Physics*,

*230*(5), 2189-2206. https://doi.org/10.1016/j.jcp.2010.12.022