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
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1. Reduced-Order Extrapolation Finite Difference Schemes Based on Proper Orthogonal Decomposition 2. Reduced-Order Extrapolation Finite Element Methods Based on Proper Orthogonal Decomposition 3. Reduced-Order Extrapolation Finite Volume Element Methods Based on Proper Orthogonal Decomposition 4. Epilogue and Outlook
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.