Efficient Arnoldi-type algorithms for rational eigenvalue problems arising in fluid-solid systems

Authors:
So-Hsiang Chou;Tsung-Ming Huang;Wei-Qiang Huang;Wen-Wei Lin
Affiliations:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403-0221, USA;Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan;Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan;Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
Venue:
Journal of Computational Physics
Year:
2011

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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=@lBx. 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.