Titlebook: Reduced Order Methods for Modeling and Computational Reduction; Alfio Quarteroni,Gianluigi Rozza Book 2014 Springer International Publishi

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Model Order Reduction in Fluid Dynamics: Challenges and Perspectives,eral reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, es

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Reduced Order Models at Work in Aeronautics and Medicine,or a model described by partial differential equations. The empirical approximation space is usually spanned by a small number of global modes. In case of time-periodic or mainly diffusive phenomena it is shown that this approach can lead to accurate fast simulations of complex problems. In other ca

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Book 2014ned by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics..Several topics are covered, including: design, optimization, and control theory in real-time with applic

OTTER

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On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method,op this approach to solve both linear and nonlinear problems and highlight the minimal changes required to utilize this algorithm to accelerate existing implementations. We illustrate the advantages through algorithmic design, through analysis of stability, convergence, and computational complexity, and through several numerical examples.

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Greedy Sampling Using Nonlinear Optimization,snapshot and to update the reduced basis. We show the well-posedness of this nonlinear optimization problem and derive first- and second-order optimality conditions. Numerical comparisons with the standard Greedy-training method are shown.

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