Multiscale Wavelet Methods for Partial Differential Equations

Abstract

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.