## Multiscale and Multiresolution Methods: Theory and ApplicationsTimothy J. Barth, Tony Chan, Robert Haimes 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 |

### Other editions - View all

Multiscale and Multiresolution Methods: Theory and Applications Timothy J. Barth,Tony Chan,Robert Haimes No preview available - 2011 |

### Common terms and phrases

accuracy Achi Brandt algorithm analysis applied approach approximation attraction basins beamlet graph Bloch waves boundary conditions Brandt calculated child(r cluster coarse grid coarse-level coarsening compression computational configuration convergence corresponding CP table curve decomposition defined denote derived described detection dimensional discretization domain dyadic square efficient eigenfunctions eigenvalues elliptic error example fast filter fine-level finer finite element finite element method global Haar homogenized operator integral interpolation inverse problem iterations large-scale lifting scheme line segment linear Mathematics matrix mesh micro monodromy multigrid methods multigrid solver multilevel multiresolution multiresolution analysis multiscale Navier-Stokes equations noise nonlinear obtained optimal parameters piecewise pixels polygonal curve potential procedure Radon transform reconstruction Rehovot relaxation representation residual scale scheme shape functions SIAM simulations smooth solution solving space statistics step structure subgrid model techniques threshold tion values variables vector wavelet coefficients wavelet transform

### References to this book

Advances in Chemical Engineering: Mathematics and Chemical Engineering and ... Limited preview - 2008 |