Space-Filling Curves
An Introduction with Applications in Scientific Computing
1st Edition
Published on 14. October 2012
Book
Hardback
XIII, 278 pages
978-3-642-31045-4 (ISBN)
Description
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.
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.
Reviews / Votes
From the reviews:
"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)More details
Product info
Book
Series
Language
English
Place of publication
Berlin, Heidelberg
Germany
Target group
Upper undergraduate
Illustrations
34
323 farbige Abbildungen, 34 s/w Abbildungen
34 schwarz-weiße und 323 farbige Abbildungen
Dimensions
Height: 247 mm
Width: 162 mm
Thickness: 25 mm
Weight
589 gr
ISBN-13
978-3-642-31045-4 (9783642310454)
DOI
10.1007/978-3-642-31046-1
Schweitzer Classification
Other editions
Additional editions
Book
08/2016
Springer
€96.29
Shipment within 7-9 days
E-Book
10/2012
1st Edition
Springer
€96.29
Available for download
Person
Michael Bader is professor for computer science at Technische Universität München, where he leads a research group on hardware-aware algorithms and software for high performance computing (located at the Leibniz Supercomputing Centre). His focus in research and teaching is on algorithmic challenges imposed by modern
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.
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.
Content
Two Motivating Examples.- How to Construct Space-Filling Curves.- Grammar-Based Description of Space-Filling Curves.- Arithmetic Representation of Space-Filling Curves.- Approximating Polygons.- Sierpinski Curves.- Further Space-Filling Curves.- Space-Filling Curves in 3D.- Refinement Trees and Space-Filling Curves.- Parallelisation with Space-Filling Curves.- Locality Properties of Space-Filling Curves.- Sierpinski Curves on Triangular and Tetrahedral Meshes.- Case Study: Cache Efficient Algorithms for Matrix Operations.- Case Study: Numerical Simulation on Spacetree Grids Using Space-Filling Curves.- Further Applications of Space-Filling Curves.- Solutions to Selected Exercises.- References.- Index