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Implementaion of the Lanczos Method for Structural Vibration Analysis on a Parallel Computer


Bostic, S.W.; Fulton, R.E. (1987) Computers and Structures, Vol. 25, No. 3, 395-403.


Vibrations, Computer Aided Analysis, Structural Anal ysis - Computer Aided Analysis, Computer Systems, Digital - Parallel Processing, Mathematical Techniques - Eigenvalues And Eigenfunctions, Computer Programming - Algorithms, Structural Vibration Analysis


This paper reports on experiences from a study involving the implementation of the C. Lanczos method on a parallel computer. The results of this study show that introducing shifts, assigning each processor a different region in the eigenvalue spectrum, and implementing the Lanczos calculation steps in parallel is an effective strategy for speeding up calculations. This approach provides good parallel performance and easy balance of processor workload. Two example vibration problems were solved to assess the behavior of the Lanczos implementation. The test-problem results include examples of the Lanczos phenomenon where lack of orthogonality in the vectors can result in spurious eigenvalues. Tests were incorporated in the parallel calculations which detected these spurious eigenvalues. The parallel eigenvalue algorithm demonstrates that significant speedups in calculation time can be realized over traditional sequential methods.