vibro-Lanczos, a symmetric Lanczos solver for vibro-acoustic simulations

Journal article (2016)

Authors

U. Tabak Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering

D.J. Rixen Technische Universität München

Research Group

Dynamics of Micro and Nano Systems (Mechanical, Maritime and Materials Engineering) (TU Delft)

Lanczos Partial reorthogonalization Symmetric Vibro-acoustics

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Published Date

2016

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Dynamics of Micro and Nano Systems

Abstract

An efficient symmetric Lanczos method for the solution of vibro-acoustic eigenvalue problems is presented in this paper. Although finite element discretization results in real but nonsymmetric system matrices, we show that an efficient iteration scheme on a symmetric representation can be built up by using a transformation matrix. In order to decrease the numerical costs of the orthogonalizations performed, we propose to use a partial orthogonalization scheme for the symmetric case. The proposed method is tested on two large problems in order to demonstrate its efficiency and accuracy.