By L. I. Sedov, J. R. M. Radok
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Extra resources for A course in continuum mechanics, vol. 1: Basic equations and analytical techniques
41) has as many rows as the number of trial vectors undergoing iteration. It can be shown rather easily that the partitions (U;)T KUp and (U;f MUp , which are rectangular, consist of null submatrices on the left, and square submatrices on the right that are given by Eqs. (43) and (44), at least in perfect arithmetic. Due to roundoff error, it can be anticipated that the set of trial vectors that have not converged will not remain orthogonal to exact lower eigenvectors, so that the null submatrices in these partitions should be nonzero to reflect this.
2), F is given by F = M'U p • The preceding development Berves itS it basis for ll. gimpll! substructure-based algorithm for subspace iteration, which will be described in the following. This algorithm is based on the assumption that there are n •• substructures and there is a processor assigned to the computation associated with each substructure, and that another processor is available for structure-level computation. It is further assumed that stiffness and mass matrices are available for each of the substructures, and are stored in such a way that substructure-level processors have access to them.
Mahajan, U. , "Three Parallel Computation Methods for Structural Vibration Analysis," Proc. of 29th Structures, Struc. , April 1988, pp. 1401-1410. 3. Hurty, W. , "Vibrations of Structural Systems by Component-Mode Synthesis," J. of the Engineering Mechanics Division, ASCE, Vol. 86, Aug. 1960, pp. 51-69. 4. Hurty, W. , "Dynamic Analysis of Structural Systems Using Component Modes," AIAA Journal, Vol. 4, 1965, pp. 678-685. 5. Craig, R. R. Jr. and Bampton, M. C. , "Coupling of Substructures for Dynamic Analysis," AIAA Journal, Vol.