Multiresolution Methods in Scattered Data Modelling

Iske, Armin; Arnold, V.I.

ISBN 10: 3540204792 / ISBN 13: 9783540204794

Editore: Springer, 2004

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Titolo: Multiresolution Methods in Scattered Data ...

Casa editrice: Springer

Data di pubblicazione: 2004

Legatura: Rilegato

Condizione: New

Descrizione articolo

Riassunto:

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. The resulting multiresolution methods are thinning algorithms, multilevel approximation schemes, and meshfree discretizations for transport equations. The utility of the algorithmic approach taken in this research is supported by the wide range of applications, including image compression, hierarchical surface 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.

Contenuti:

Introduction: Scattered Data Modelling, Multiresolution Methods, Multilevel Methods, Adaptive Irregular Sampling.- Algorithms and Data Structures: Triangulation Methods, Delaunay Triangulations, Voronoi Diagrams, Data-Dependent Triangulations, Heaps and Priority Queues, Quadtrees.- Radial Basis Functions: Interpolation, Conditionally Positive Definite Functions, Optimal Recovery, Pointwise Optimality, Error Estimates, Numerical Stability, Uncertainty Principle, Polyharmonic Splines, Optimal Point Sampling, Least Squares Approximation.- Thinning Algorithms: Preliminary Remarks, Generic Formulation, Non-Adaptive Thinning, Scattered Data Filtering, Adaptive Thinning, Adaptive Thinning in Digital Image Compression.- Multilevel Approximation Schemes: Generic Formulation, Multilevel Interpolation, Adaptive Multilevel Approximation, Hierarchical Surface Visualization.- Meshfree Methods for Transport Equations: Transport Equations, Meshfree Method of Backward Characteristics, Adaption Rules, Multiscale Flow Simulation.