|M.Sc Thesis||Department of Applied Mathematics|
|Supervisor:||Prof. Givoli Dan|
The approximation of complex systems by simpler systems is one of the fundamental problems of linear system theory. We will look at a main-system attached to a sub-system. Our goal is to reduce the number of Degrees of Freedom (DOFs) of the sub-system such that the impact of the reduction on the dynamics of the main-system is minimized in some norm. The reduction is based on modal truncation. Namely, the original sub-system if first decomposed into its eigenmodes ; then a small number of these eigenmodes is retained to represent the sub-system, whereas all the other modes are discarded. The following question then arises: ‘Which of the modes should be retained?’ The Optimal Modal Reduction (OMR) method was devised in 2003 to answer this question and to provide an optimal algorithm for sub-system reduction.
In this thesis, we extend the OMR method and suggest some modifications which improve its performance significantly. We compare its performance with that of other methods, including Standard Modal Reduction (SMR) and subsystem mesh coarsening. The OMR algorithm was devised only to undamped systems ; here we generalize OMR to systems with Rayleigh damping. We investigate how the presence of Rayleigh damping affects the results of the reduction and emphasize the differences from the undamped case.