Improvement of reduction method combined with sub-domain scheme in large-scale problem

For a few decades, various approximate techniques have been developed to calculate the eigenvalues in a reduced manner. In order to construct reliable reduced systems it is essential to select the proper primary degrees of freedom (PDOFs). Unless the PDOFs are selected properly, the selection of PDOFs might be localized and the eigenvalue prediction might emphasize excessively the lower modes or lose the important modes. Moreover, sometimes, it takes considerable amount of computing time to construct a reduced system in large-scale problem. These troubles in constructing reduced system can be avoided by applying reduction scheme in sub-domain level. After dividing global system into a number of subdomains, reduced system which has only the PDOFs is constructed in each sub-domain. This paper presents new algorithms to construct efficient reduction system through three different schemes. They are version 1, version 2 and version 3 systems. The version 3 system is constructed by combining the advantages of the version 1 and the version 2 systems. Numerical examples demonstrate that the proposed version 3 method saves computational cost effectively and provides a reduced system which can predict accurate eigenvalues of global system. Copyright q 2006 John Wiley & Sons, Ltd