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100   $a20121025d2013      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aSpace-Filling Curves $eAn Introduction with Applications in Scientific Computing /$fby Michael Bader
205   $a1st ed. 2013.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013.
215   $a1 online resource (285 p.)
225 1 $aTexts in Computational Science and Engineering,$x1611-0994 ;$v9
300   $aDescription based upon print version of record.
311   $a3-642-31045-1 
320   $aIncludes bibliographical references and index.
327   $aTwo 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 .
330   $a­The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings. ­The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.
410  0$aTexts in Computational Science and Engineering,$x1611-0994 ;$v9
606   $aComputer science$xMathematics
606   $aAlgorithms
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aComputer science?Mathematics
606   $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026
606   $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
606   $aMath Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17044
615  0$aComputer science$xMathematics.
615  0$aAlgorithms.
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615  0$aComputer science?Mathematics.
615 14$aComputational Science and Engineering.
615 24$aAlgorithms.
615 24$aApplications of Mathematics.
615 24$aMath Applications in Computer Science.
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