Connects the different techniques to describe space-filling curves to corresponding algorithms
Connects space-filling curves and respective orders to regular and adaptive meshes for discretisation
Describes parallelisation and cache-efficient algorithms based on space-filling curves
Provides a section on references to both pioneering and current research on space-filling curves in scientific computing?
Includes supplementary material: sn.pub/extras
Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 9)
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Table of contents (15 chapters)
About this book
The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings.
The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.
- Hilbert curve, Peano curve, Sierpinski curve
- adaptive meshes
- algorithms in scientific computing
- space-filling curves
From the reviews:
“This book concentrates on low-dimensional, two or three at most, curves used for linearly ordering points on the 2D or 3D grid with applications in computer graphics and data structures. … Each section ends with indications for further reading and exercises. This is a new book in the field of computer science which should be a valuable resource for advanced undergraduate and graduate students as well as more experienced researchers.” (Ewa Skubalska-Rafajłowicz, Mathematical Reviews, January, 2014)
“Bader’s book … provides an introduction to the algorithmics of space-filling curves. … The book has many color illustrations and can be used as a textbook and as reference monograph for research.” (Luiz Henrique de Figueiredo, MAA Reviews, April, 2013)“This is a gentle introduction to space filling curves. Emphasis is on the representation, implementation and application in computer science. … It is clear that the author has a long teaching experience with this subject. He had found the right balance between motivation, rigor, application, implementation, in just the right pace to take the reader/student along climbing up the hill towards of increasing complexity as academic examples are left and one approaches the real life applications.” (A. Bultheel, The European Mathematical Society, December, 2012)
Authors and Affiliations
, Department of Informatics, Munich Center of Advanced Computing, Garching, Germany
About the author
computing platforms. A large part of his work is dedicated to exploiting locality properties of space-filling curves for simulation tasks in science and engineering.
Book Title: Space-Filling Curves
Book Subtitle: An Introduction with Applications in Scientific Computing
Authors: Michael Bader
Series Title: Texts in Computational Science and Engineering
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-31045-4Published: 14 October 2012
Softcover ISBN: 978-3-662-52236-3Published: 23 August 2016
eBook ISBN: 978-3-642-31046-1Published: 13 October 2012
Series ISSN: 1611-0994
Series E-ISSN: 2197-179X
Edition Number: 1
Number of Pages: XIII, 285
Topics: Computational Science and Engineering, Algorithms, Applications of Mathematics, Mathematical Applications in Computer Science