Zhang, Y., and Harichandran, R. S. (1989). "Eigenproperties of
large-scale structures by finite element partitioning and homotopy
continuation." International Journal of Numerical Methods in
Engineering, 28, 2113- 2122.
Abstract
Finite element partitioning (or substructuring) is employed to estimate
the eigenproperties of large-scale structural systems. A homotopy
equation is constructed and its solutions are characterized by a number
of curves which connect the eigensolutions of the partitions with those
of the complete system. A step-by-step tracing procedure is developed to
follow these curves. At each step, prediction and correction are
performed. The Rayleigh-Ritz procedure and the conjugate gradient method
are used as predictor and corrector, respectively. Compared with the
sole use of either the Rayleigh-Ritz or gradient methods, the proposed
method is more reliable and more efficient for large-scale problems.
Numerical implementation is well suited for supercomputers.