Efficient Time-dependent PDE Computation Using MATLAB and SCILAB

Efficient Time-dependent PDE Computation Using MATLAB and SCILAB

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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.
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Product details

  • Hardback | 306 pages
  • 156 x 235mm
  • Chapman & Hall/CRC
  • United States
  • English
  • 50 black & white illustrations
  • 1584889276
  • 9781584889274

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.
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About Florian De Vuyst

Ecole Centrale PARIS, Chatenay-Malabry cedex, France Ecole Centrale Paris, Chatenay Malabry, France University of Greenwich, London, UK
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