Multiscale wavelet methods for partial differential equations / edited by Wolfgang Dahmen, Andrew Kurdila, Peter Oswald.

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.

FEM-Like Multilevel Preconditioning: P. Oswald, Multilevel Solvers for Elliptic Problems on Domains. P. Vassilevski and J. Wang, Wavelet-Like Methods in the Design of Efficient Multilevel Preconditioners for Elliptic PDEs. Fast Wavelet Algorithms: Compression and Adaptivity: S. Bertoluzza, An Adaptive Collocation Method Based on Interpolating Wavelets. G. Beylkin and J. Keiser, An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear PartialDifferential Equations. P. Joly, Y. Maday, and V. Perrier, A Dynamical Adaptive Concept Based on Wavelet Packet Best Bases: Application to Convection Diffusion Partial Differential Equations. S. Dahlke, W. Dahmen, and R. DeVore, Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations. Wavelet Solvers for Integral Equations: T. von Petersdorff and C. Schwab, Fully Discrete Multiscale Galerkin BEM. A. Rieder, Wavelet Multilevel Solvers for Linear Ill-Posed Problems Stabilized by Tikhonov Regularization. Software Tools and Numerical Experiments: T. Barsch, A. Kunoth, and K. Urban, Towards Object Oriented Software Tools for Numerical Multiscale Methods for PDEs Using Wavelets. J. Ko, A. Kurdila, and P. Oswald, Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems. Multiscale Interaction and Applications to Turbulence: J. Elezgaray, G. Berkooz, H. Dankowicz, P. Holmes, and M. Myers, Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation. M. Wickerhauser, M. Farge, and E. Goirand, Theoretical Dimension and the Complexity of Simulated Turbulence. Wavelet Analysis of Partial Differential Operators: J-M. Angeletti, S. Mazet, and P. Tchamitchian, Analysis of Second-Order Elliptic Operators Without Boundary Conditions and With VMO or Hilderian Coefficients. M. Holschneider, Some Directional Elliptic Regularity for Domains with Cusps. Subject Index.

Includes bibliographical references and index.

Multilevel solvers for elliptic problems on domains / Peter Oswald -- Wavelet-like methods in the design of efficient multilevel preconditioners for elliptic PDEs / Panayot S. Vassilevski and Junping Wang -- An adaptive collocation method based on interpolating wavelets / Silvia Bertoluzza -- An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations / Gregory Beylkin and James M. Keiser -- A dynamical adaptive concept based on wavelet packet best bases : application to convection diffusion partial differential equations / Pascal Joly, Yvon Maday, and Valérie Perrier -- Nonlinear approximation and adaptive techniques for solving elliptic operator equations / Stephan Dahlke, Wolfgang Dahmen, and Ronald A. DeVore -- Fully discrete multiscale Galerkin BEM / Tobias von Petersdorff and Christoph Schwab -- Wavelet multilevel solvers for linear ill-posed problems stabilized by Tikhonov regularization / Andreas Rieder -- Towards object oriented software tools for numerical multiscale methods for PDEs using wavelets / Titus Barsch, Angela Kunoth, and Karsten Urban -- Scaling function and wavelet preconditioners for second order elliptic problems / Jeonghwan Ko, Andrew J. Kurdila, and Peter Oswald -- Local models and large scale statistics of the Kuramoto-Sivashinsky equation / Juan Elezgaray [and others] -- Theoretical dimension and the complexity of simulated turbulence / Mladen V. Wickerhauser, Marie Farge, and Eric Goirand -- Analysis of second order elliptic operators without boundary conditions and with VMO or Hölderian coefficients / Jean-Marc Angeletti, Sylvain Mazet, and Philippe Tchamitchian -- Some directional elliptic regularity for domains with cusps / Matthias Holschneider.

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