Space-Filling Curves

An Introduction with Applications in Scientific Computing

Inbunden, Engelska, 2012

AvMichael Bader

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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.

Produktinformation

Utgivningsdatum2012-10-14
Mått155 x 235 x 21 mm
Vikt592 g
FormatInbunden
SpråkEngelska
SerieTexts in Computational Science and Engineering
Antal sidor285
Upplaga2013
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783642310454

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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.

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

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)