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Goal-Oriented, Model-Constrained Optimization for Reduction of Large-Scale Systems

By T. Bui-Thanh, K. Willcox, O. Ghattas and B. van Bloemen Waanders


Optimization-oriented reduced-order models should target a particular output func-tional, span an applicable range of dynamic and parametric inputs, and respect the underlying governing equations of the system. To achieve this goal, we present an approach for determining a projection basis that uses a goal-oriented, model-constrained optimization framework. The mathematical framework permits con-sideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems. Results for a simple linear model problem of the two-dimensional heat equation demonstrate the ability of the goal-oriented approach to target a particular output functional of interest. Application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady Euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition

Year: 2006
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