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

• Main Author: Bader, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Texts in Computational Science and Engineering, 9
• Subjects: Mathematics.; Computer science > Mathematics.; Applied mathematics.; Engineering mathematics.; Algorithms.; Computer mathematics.; Computational Science and Engineering.; Applications of Mathematics.; Math Applications in Computer Science.

­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, an...

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 .