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Proper Orthogonal Decomposition Methods for Partial Differential Equations

  • 1st Edition - November 26, 2018
  • Latest edition
  • Authors: Zhendong Luo, Goong Chen
  • Language: English

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computati… Read more

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Description

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.

Key features

  • Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns
  • Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics
  • Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Readership

Graduate students and researchers in mathematically intensive environments who perform large scale computations

Table of contents

1. Reduced-Order Extrapolation Finite Difference Schemes Based on Proper Orthogonal Decomposition2. Reduced-Order Extrapolation Finite Element Methods Based on Proper Orthogonal Decomposition3. Reduced-Order Extrapolation Finite Volume Element Methods Based on Proper Orthogonal Decomposition4. Epilogue and Outlook

Review quotes

"This book details the application of the Proper Orthogonal Decomposition (POD) to instationary problems whose spatial semidiscretization is done either by Finite Difference (FD), Finite Element (FE) or Finite Volume (FV) methods. These three discretization methods correspond to the 3 main chapters of the book."—zbMATH

Product details

  • Edition: 1
  • Latest edition
  • Published: December 3, 2018
  • Language: English

About the authors

ZL

Zhendong Luo

Zhendong Luo is Professor of Mathematics at North China Electric Power University, Beijing, China. Luo is heavily involved in the areas of Optimizing Numerical Methods of PDEs; Finite Element Methods; Finite Difference Scheme; Finite Volume Element Methods; Spectral-Finite Methods; and Computational Fluid Dynamics. For the last 12 years, Luo has worked mainly on Reduced Order Numerical Methods based on Proper Orthogonal Decomposition Technique for Time Dependent Partial Differential Equations.
Affiliations and expertise
North China Electric Power University, Beijing, China

GC

Goong Chen

Affiliations and expertise
Professor of Mathematics and Aerospace Engineering, Texas A & M University

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