Reduced Order Methods for Modeling and Computational Reduction

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Alfio Quarteroni, Gianluigi Rozza
Springer, Jun 5, 2014 - Mathematics - 334 pages
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.

 

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Contents

1 A Novel Approach to Model Order Reductionfor Coupled Multiphysics Problems
1
Parametrized Reduction UsingReducedBasis and the Loewner Framework
50
3 Comparison of Some Reduced Representation Approximations
67
4 Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems
101
5 Greedy Sampling Using Nonlinear Optimization
137
6 A Robust Algorithm for Parametric ModelOrder Reduction Based on Implicit Moment Matching
159
7 On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method
186
Descriptor vs NonDescriptor Forms ProjectionDescriptor vs NonDescriptor Forms
215
Challenges and Perspectives
235
Application to Continuum and Atomistic Data
274
11 Reduced Order Models at Work in Aeronautics and Medicine
305
MSA Modeling Simulation and Applications
333
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