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. Foreword and Introduction - p. xi 2. Chapter 1: Reduced-Order Extrapolation Finite Difference Schemes Based on Proper Orthogonal Decomposition - p. xvi 3. Chapter 2: Reduced-Order Extrapolation Finite Element Methods Based on Proper Orthogonal Decomposition - p. 56 4. Chapter 3: Reduced-Order Extrapolation Finite Volume Element Methods Based on Proper Orthogonal Decomposition - p. 155 5. Chapter 4: Epilogue and Outlook - p. 244 6. Bibliography - p. 247 7. Index - p. 257
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. Foreword and Introduction - p. xi 2. Chapter 1: Reduced-Order Extrapolation Finite Difference Schemes Based on Proper Orthogonal Decomposition - p. xvi 3. Chapter 2: Reduced-Order Extrapolation Finite Element Methods Based on Proper Orthogonal Decomposition - p. 56 4. Chapter 3: Reduced-Order Extrapolation Finite Volume Element Methods Based on Proper Orthogonal Decomposition - p. 155 5. Chapter 4: Epilogue and Outlook - p. 244 6. Bibliography - p. 247 7. Index - p. 257
