PRECONDITIONING SUBSPACE ITERATION FOR LARGE EIGENVALUE PROBLEMS WITH AUTOMATED MULTI-LEVEL SUB-STRUCTURING

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Published: 2015-12-04

Page: 136-150


HEINRICH VOSS *

Institute of Mathematics, Hamburg University of Technology, D-Hamburg 21073, Germany.

JIACONG YIN

State Key Laboratory of Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, 100871 Beijing, China.

PU CHEN

State Key Laboratory of Turbulence and Complex Systems and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, 100871 Beijing, China.

*Author to whom correspondence should be addressed.


Abstract

The subspace iteration method (SIM) is a numerical procedure for normal mode analysis which has shown to be robust and reliable for solving very large general eigenvalue problems. Although its classical form as introduced by Bathe in the seventies of the last century is less efficient than the Lanczos iteration method in terms of CPU time, it is beneficial in terms of storage use if a very large number (say hundreds) of eigenmodes are needed and good approximations to the wanted eigenvectors are at hand. In this paper we take advantage of the automated multi-level sub-structuring (AMLS) to construct an accurate initial subspace for SIM. Along with the AMLS reduction we derive a very efficient preconditioning method for SIM which solves the linear systems for a transformed system with block diagonal system matrix whereas the multiplication with the mass matrix is executed in the original variables.

Keywords: Large eigenvalue problem, subspace iteration;, automated multi{level sub{structuring, preconditioning.


How to Cite

VOSS, H., YIN, J., & CHEN, P. (2015). PRECONDITIONING SUBSPACE ITERATION FOR LARGE EIGENVALUE PROBLEMS WITH AUTOMATED MULTI-LEVEL SUB-STRUCTURING. Asian Journal of Mathematics and Computer Research, 10(2), 136–150. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/262

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