Proper Orthogonal Decomposition Methods for Partial Differential Equations

This guide evaluates the potential applications of the Proper Orthogonal Decomposition (POD) reduced-order numerical methods for time-dependent partial differential equations

Zhendong Luo (Author), Goong Chen (Author)

9780128167984, Elsevier Science

Paperback, published 3 December 2018

278 pages
22.9 x 15.1 x 1.8 cm, 0.45 kg

"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

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.

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

Subject Areas: Mathematics [PB]