Proper Orthogonal Decomposition Methods for Partial Differential Equations Mathematics in Science and Engineering Series
Auteurs : Luo Zhendong, Chen Goong
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
Graduate students and researchers in mathematically-intensive environments who perform large scale computations
- 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
Date de parution : 12-2018
Ouvrage de 278 p.
15x22.8 cm
Thème de Proper Orthogonal Decomposition Methods for Partial... :
Mots-clés :
2D Sobolev equation; Assistive technologies; Cauchy�Schwarz inequality; Computation efficiency; Correlation coefficient; Difference operator; Error estimate; FD scheme stability; FE approximation; Finite difference scheme; Finite volume element method; H�lder and Cauchy�Schwarz inequalities; Human computer interactions; Human machine interface; Linear differential operator; Linear system of equations; Machine learning; Monitoring; Nonstationary incompressible Boussinesq equation; Numerical simulation; Numerical solutions; Reynolds number; Ritz projection; Root mean square error; Semidiscretization; Smart sensor; User centred design; User involvement; User profile; Von Neumann stability analysis