Multiresolution Methods in Scattered Data Modelling
Edition: 1 edition
Publisher: Springer
Published: May 14, 2004
Language: eng
Format: Paperback
Number of pages: 204
ISBN-13: 9783540204794
Subjects: Databases & data structures; Mathematics; Data structures (Computer scie; Science/Mathematics; Relational databases; Number Systems; Differential Equations; Programming - General; Computers : Programming - General; Mathematics / Number Systems; Mathematics : Differential Equations; digital image compression; meshfree methods for fluid flow simulation; multiresolution methods; radial basis functions; scattered data modelling; Computer algorithms; Applied; Computer Engineering; Data structures (Computer science)
First sentence: Much of the following discussion in this work relies on standard tools from computational geometry, approximation theory, and computer programming.
Description: 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.