Combining theory with practice in a multidisciplinary context, Efficient Time-Dependent PDE Computation using MATLAB and SCILAB presents techniques of algorithmic reduction with a focus on reduced-order models like proper orthogonal decomposition (POD). The book offers a comprehensive introduction to numerical optimization and addresses both degree-of-freedom reduction and dimensionality reduction issues. It also presents stochastic process modeling using probabilistic density functions (PDF) to demonstrate how dimensionality limits computations to only a few random variables. MATLAB (R) and SCILAB codes are used to implement several of the algorithms discussed.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Professional
Illustrationen
50 s/w Abbildungen
50 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
ISBN-13
978-1-58488-927-4 (9781584889274)
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Schweitzer Klassifikation
Ecole Centrale PARIS, Chatenay-Malabry cedex, France Ecole Centrale Paris, Chatenay Malabry, France University of Greenwich, London, UK
Autor*in
Ecole Centrale PARIS, Chatenay-Malabry cedex, France
Principal Component Analysis and POD. POD for the Navier-Stoke Equations. Numerical Techniques for Unconstrained Optimization. Equality-constrained Optimization. Adaptive Trust-Region POD. Variational Data Assimilation. Constrained Variational Data Assimilation. Data Size Reduction/Inflation using POD. Stochastic Processes and PDE. Spectral Method and Reduced-Order Basis. Numerical Quadrature using Sparse Grids. Reduced-order Implicit Algorithms. Parareal in Time Algorithms. Combining Parareal in Time and POD.
