Multiscale and Multiresolution Methods: Theory and Applications

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Timothy J. Barth, Tony Chan, Robert Haimes
Springer Science & Business Media, Nov 20, 2001 - Mathematics - 394 pages
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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.
 

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Contents

Multiscale Scientific Computation
3
WaveletBased Numerical Homogenization with Applications
97
Beamlets and Multiscale Image Analysis
149
Generalized FEM for Homogenization Problems
197
Nonlinear Multiscale Transforms
239
From Conservation Laws to Image Compression
281
Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of the NavierStokes Equations
297
The Role of Multiresolution in Mining Massive Image Datasets
307
Dynamic Subgrid Modeling for Scalar ConvectionDiffusionReaction Equations with Fractal Coefficients
319
Multilevel Methods for Inverse Bioelectric Field Problems
331
N Eigenfunctions in 0N log N
347
Wavelet Galerkin BEM on Unstructured Meshes by Aggregation
359
Collected Color Plates
379
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