Space-Filling Curves: An Introduction with Applications in Scientific Computing by Michael BaderSpace-Filling Curves: An Introduction with Applications in Scientific Computing by Michael Bader

Space-Filling Curves: An Introduction with Applications in Scientific Computing

byMichael Bader

Hardcover | October 14, 2012

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­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.

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 moderncomputing platforms....
Title:Space-Filling Curves: An Introduction with Applications in Scientific ComputingFormat:HardcoverDimensions:285 pages, 23.5 × 15.5 × 0.01 inPublished:October 14, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3642310451

ISBN - 13:9783642310454

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Table of Contents

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

Editorial Reviews

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-Rafajlowicz, 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)