Multiresolution Methods in Scattered Data Modelling

  • Armin Iske

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 37)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Armin Iske
    Pages 1-6
  3. Armin Iske
    Pages 7-30
  4. Armin Iske
    Pages 31-65
  5. Armin Iske
    Pages 67-125
  6. Armin Iske
    Pages 127-141
  7. Armin Iske
    Pages 143-169
  8. Back Matter
    Pages 171-188

About this book

Introduction

This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi­ levelapproximation schemes, and meshfree discretizations for transport equa­ tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur­ face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.

Keywords

Approximation Interpolation data modelling digital image compression meshfree methods for fluid flow simulation multiresolution methods radial basis functions scattered data modelling simulation

Authors and affiliations

  • Armin Iske
    • 1
  1. 1.Lehrstuhl Numerische Mathematik und Wissenschaftliches RechnenTechnische Universität MünchenGarchingGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18754-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20479-4
  • Online ISBN 978-3-642-18754-4
  • Series Print ISSN 1439-7358
  • About this book
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