Elsevier S & T

Multiscale Wavelet Methods for Partial Differential Equations

Dahmen, Wolfgang; Kurdila, Andrew; Oswald, Peter

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Table of contents
  • Contentsv
  • Prefacevii
  • Contributorsxi
  • Part I: FEM-Like Multilevel Preconditioning1
  • Chapter 1. Multilevel Solvers for Elliptic Problems on Domains3
  • Chapter 2. Wavelet-Like Methods in the Design of Efficient Multilevel Preconditioners for Elliptic P59
  • Part II: Fast Wavelet Algorithms: Compression and Adaptivity107
  • Chapter 3. An Adaptive Collocation Method based on Interpolating Wavelets109
  • Chapter 4. An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial Differential Equations137
  • Chapter 5. A Dynamical Adaptive Concept Based on Wavelet Packet Best Bases: Application to Convectio199
  • Chapter 6. Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations237
  • Part III: Wavelet Solvers for Integral Equations285
  • Chapter 7. Fully Discrete Multiscale Galerkin BEM287
  • Chapter 8. Wavelet Multilevel Solvers for Linear Ill-Posed Problems Stabilized by Tikhonov Regulariz347
  • Part IV: Software Tools and Numerical Experiments381
  • Chapter 9. Towards Object Oriented Software Tools for Numerical Multiscale Methods for PDEs using Wa383
  • Chapter 10. Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems413
  • Part V: Multiscale Interaction and Applications to Turbulence439
  • Chapter 11. Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation441
  • Chapter 12. Theoretical Dimension and the Complexity of Simulated Turbulence473
  • Part VI: Wavelet Analysis of Partial Differential Operators493
  • Chapter 13. Analysis of Second Order Elliptic Operators Without Boundary Conditions and With VMO or495
  • Chapter 14. Some Directional Elliptic Regularity For Domains With Cusps541
  • Subject Index567
Book details
  • Vendor Elsevier S & T
  • SKU 9780122006753
  • ISBN-13 9780080537146
  • Author Dahmen, Wolfgang; Kurdila, Andrew; Oswald, Peter
  • Category Mathematics
  • Subject Mathematical Analysis

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Description eBook delivery & access Reviews
This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.

Key Features
* Covers important areas of computational mechanics such as elasticity and computational fluid dynamics
* Includes a clear study of turbulence modeling
* Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations
* Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications