Reduction of dynamic systems and subsystems

Abstract eng:
Large dynamic systems appear in many applications, including the analysis of large structures, where the motivation for the present work arises. Often a detailed time-dependent computational model leads to such a large semi-discrete system that precludes solution in a reasonable time or poses unattainable memory requirements. In those cases it is standard to seek a reduced model. Model reduction is a very active and rich field of research, especially, but not exclusively, in the contexts of robust control and structural analysis. A special class of model reduction problems is that associated with the reduction of subsystems, where the goal is to reduce only certain parts of the system while affecting the dynamic behavior of the rest of the structure to the minimal extent possible. In this talk, which presents work done jointly with P. Barbone, I. Patlashenko and S. Tayeb, the general subject of model reduction will be briefly reviewed, and the special characteristics of the problem of subsystem reduction will be outlined. Then the method of Optimal Modal Reduction (OMR) of Barbone and Givoli will be discussed. In addition, recent advances related to this method will be presented, including an improved OMR formulation, comparison of OMR with a reduction based on mesh coarsening, and an extension to damped systems. Numerical examples will be used to demonstrate these advances.

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