Multiscale and Multiresolution Methods

Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.

Inhalt

Invited Papers: A. Brandt: Multiscale Scientific Computation: Review 2001.- B. Engquist, O. Runborg: Wavelet-Based Numerical Homogenization with Applications.- D.L. Donoho, X. Huo: Beamlets and Multiscale Image Analysis.- C. Schwab, A.-M. Matache: Generalized FEM for Homogenization Problems.- J.-L. Starck: Nonlinear Multiscale Transforms. Contributed Papers: F. Arandiga, G. Chiavassa, R. Donat: Application of Harten's Framework for Multiresolution: From Conservation Laws to Image Compression.- F. Fairag: A Two Level Finite Element Technique for Pressure Recovery from the Stream Function Formulation of the Navier-Stokes Equations.- I.K. Fodor, C. Kamath: The Role of Multiresolution in Mining Massive Image Datasets.- J. Hoffman: Dynamic Subgrid Modeling for Scalar Convection-Diffusion-Reaction Equations with Fractal Coefficients.- C.R. Johnson, M. Mohr, U. Rüde, A. Samsonov, K. Zyp: Multilevel Methods for Inverse Bioelectric Field Problems.- O.E. Livne, A. Brandt: Multiscale Eigenbasis Calculations: N Eigenfunctions in O(N log N).- G. Schmidlin, C. Schwab: Wavelet Galerkin BEM on Unstructures Meshes by Aggregation. Appendix: Collected Color Figures