Proper Orthogonal Decomposition Methods for Partial Differential Equations

By: Luo, Chen

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Paperback | 3 December 2018 | Edition Number 1

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278 Pages

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22.86 x 15.24 x 1.47

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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.

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

Industry Reviews

"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

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