Multiscale Wavelet Methods for Partial Differential Equations

✍ Scribed by Wolfgang Dahmen, Andrew J. Kurdila and Peter Oswald (Eds.)

• Publisher: Academic Press
• Year: 1997
• Tongue: English
• Leaves: 587
• Series: Wavelet Analysis and Its Applications 6
• Edition: 1st
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content:
Preface
Pages vii-x
Wolfgang Dahmen, Andrew J. Kurdila, Peter Oswald

Contributors
Pages xi-xiv

Multilevel solvers for elliptic problems on domains Original Research Article
Pages 3-58
Peter Oswald

Wavelet-like methods in the design of efficient multilevel preconditioners for elliptic PDEs Original Research Article
Pages 59-105
Panayot S. Vassilevski, Junping Wang

An adaptive collocation method based on interpolating wavelets Original Research Article
Pages 109-135
Silvia Bertoluzza

An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations Original Research Article
Pages 137-197
Gregory Beylkin, James M. Keiser

A dynamical adaptive concept based on wavelet packet best bases: Application to convection diffusion partial differential equations Original Research Article
Pages 199-235
Pascal Joly, Yvon Maday, Valérie Perrier

Nonlinear approximation and adaptive techniques for solving elliptic operator equations Original Research Article
Pages 237-283
Stephan Dahlke, Wolfgang Dahmen, Ronald A. DeVore

Fully discrete multiscale galerkin BEM Original Research Article
Pages 287-346
Tobias von Petersdorff, Christoph Schwab

Wavelet multilevel solvers for linear Ill-posed problems stabilized by Tikhonov regularization Original Research Article
Pages 347-380
Andreas Rieder

Towards object oriented software tools for numerical multiscale methods for PDEs using wavelets Original Research Article
Pages 383-412
Titus Barsch, Karsten Urban, Angela Kunoth

Scaling function and wavelet preconditioners for second order elliptic problems Original Research Article
Pages 413-438
Jeonghwan Ko, Andrew J. Kurdila, Peter Oswald

Local models and large scale statistics of the kuramoto–sivashinsky equation Original Research Article
Pages 441-471
Juan Elezgaray, Gal Berkooz, Harry Dankowicz, Philip Holmes, Mark Myers

Theoretical dimension and the complexity of simulated turbulence Original Research Article
Pages 473-492
Mladen Victor Wickerhauser, Marie Farge, Eric Goirand

Analysis of second order elliptic operators without boundary conditions and with VMO or Hölderian coefficients Original Research Article
Pages 495-539
J.M. Angeletti, S. Mazet, P. Tchamitchian

Some directional elliptic regularity for domains with cusps Original Research Article
Pages 541-565
Matthias Holschneider

Subject index
Pages 567-570