A parallel method of eigenvalue analysis using dynamic substructuring and homotopy continuation

Abstract

A parallel method to solve large eigenvalue problems using dynamic substructuring and homotopy continuation is presented. Unlike the conventional approaches in substructuring, the non-linear term is not neglected for improved accuracy. Therefore, instead of solving the approximated condensed problems, full exact condensed forms are treated. Homotopy continuation method is introduced to solve the non-linear reduced eigenvalue problem. In the process small number of substructure modes are used to reduce the original eigenvalue problem, and additional degrees of freedom, besides those at interfaces, are selected. The whole procedures are implemented to workstation cluster using PVM. To show how the method works, simple two-dimensional numerical examples are solved. It is demonstrated that the method yields highly accurate results and good parallel efficiency. (C) 1998 John Wiley & Sons, Ltd.