Reduced Order Methods for Modeling and Computational Reduction

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed 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.

This book details advances and developments in reduced order methods for modeling and computational reduction of complex parametrized systems held by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques. <br>

1 W. H. A. Schilders, A. Lutowska: A novel approach to model order reduction for coupled multiphysics problems.- 2 A. C. Ionita, A. C. Antoulas: Case study. Parametrized Reduction using Reduced-Basis and the Loewner Framework.- 3 M. Bebendorf, Y. Maday, B. Stamm: Comparison of some reduced representation approximations.- 4 H. Antil, M. Heinkenschloss, D. C. Sorensen: Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric System.- 5 K. Urban, S. Volkwein, O. Zeeb: Greedy Sampling using Nonlinear Optimization.- 6 P. Benner, L. Feng: A Robust Algorithm for Parametric Model Order Reduction based on Implicit Moment Matching.- 7 F. Chen, J. S. Hesthaven, X. Zhu: On the use of reduced basis methods to accelerate and stabilize the Parareal method.- 8 C. Farhat, D. Amsallem: On the stability of reduced-order linearized computational fluid dynamics models based on POD and Galerkin projection: descriptor vs non-descriptor forms.- 9 T. Lassila, A. Manzoni, A. Quarteroni, G. Rozza: Model Order Reduction in Fluid Dynamics: Challenges and Perspectives.- 10 L. Grinberg, M. Deng, A. Yakhot, G. Karniadakis: Window Proper Orthogonal Decomposition. Application to Continuum and Atomistic Data.- 11 M. Bergmann, T. Colin, A. Iollo, D. Lombardi, O. Saut, H. Telib: Reduced order models at work in Aeronautics and Medicine.