Efficient Time-dependent PDE Computation Using MATLAB and SCILAB
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[registered] and SCILAB codes are used to implement several of the algorithms discussed.
- Hardback | 306 pages
- 156 x 235mm
- 26 Apr 2011
- Taylor & Francis Ltd
- Chapman & Hall/CRC
- United States
- 50 black & white illustrations
Table of contents
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.
About Florian De Vuyst
Ecole Centrale PARIS, Chatenay-Malabry cedex, France Ecole Centrale Paris, Chatenay Malabry, France University of Greenwich, London, UK