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.
Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.
This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.
Author(s): Alfio Quarteroni, Gianluigi Rozza (eds.)
Series: MS&A - Modeling, Simulation and Applications 9
Edition: 1
Publisher: Springer International Publishing
Year: 2014
Language: English
Pages: 334
Tags: Computational Mathematics and Numerical Analysis; Numeric Computing; Appl.Mathematics/Computational Methods of Engineering; Mathematical Modeling and Industrial Mathematics; Continuum Mechanics and Mechanics of Materials; Numerical and C
Front Matter....Pages i-x
A Novel Approach to Model Order Reduction for Coupled Multiphysics Problems....Pages 1-49
Case Study: Parametrized Reduction Using Reduced-Basis and the Loewner Framework....Pages 51-66
Comparison of Some Reduced Representation Approximations....Pages 67-100
Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems....Pages 101-136
Greedy Sampling Using Nonlinear Optimization....Pages 137-157
A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching....Pages 159-185
On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method....Pages 187-214
On the Stability of Reduced-Order Linearized Computational Fluid Dynamics Models Based on POD and Galerkin Projection: Descriptor vs Non-Descriptor Forms....Pages 215-233
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives....Pages 235-273
Window Proper Orthogonal Decomposition: Application to Continuum and Atomistic Data....Pages 275-303
Reduced Order Models at Work in Aeronautics and Medicine....Pages 305-332
Back Matter....Pages 333-334
