An Introduction with Applications in Scientific Computing
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.
No one who reads this book will ever again think of his or her own death in the same way. The first part of the book consists of a thought-provoking essay, in which Fingarette examines the metaphors which mislead us: death as parting, death as sleep, immortality as the denial of death, and selflessness as a kind of consolation. He…
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.
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