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Space-Filling Curves: An Introduction with Applications in Scientific ComputingOctober 2012
- Author:
- Michael Bader
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Abstract
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.
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- Saurabh K, Ishii M, Fernando M, Gao B, Tan K, Hsu M, Krishnamurthy A, Sundar H and Ganapathysubramanian B Scalable adaptive PDE solvers in arbitrary domains Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, (1-15)
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- Suh H and Isaac T Evaluation of a minimally synchronous algorithm for 2:1 octree balance Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, (1-12)
- Mascagni M, Al-Kharusi I and Walker D (2020). Locality properties of 3D data orderings with application to parallel molecular dynamics simulations, International Journal of High Performance Computing Applications, 33:5, (998-1018), Online publication date: 1-Sep-2019.
- Weinzierl T (2019). The Peano Software—Parallel, Automaton-based, Dynamically Adaptive Grid Traversals, ACM Transactions on Mathematical Software, 45:2, (1-41), Online publication date: 30-Jun-2019.
- Van Steenkiste T, Van Der Herten J, Deschrijver D and Dhaene T (2019). ALBATROS, Engineering with Computers, 35:2, (537-550), Online publication date: 1-Apr-2019.
- Uher V, Gajdoš P and Snášel V A Hybrid Point Indexing Structure Based on Orthogonal and Hexagonal Grids Proceedings of the 11th International Conference on Computer Modeling and Simulation, (151-156)
- Weinzierl M and Weinzierl T (2018). Quasi-matrix-free Hybrid Multigrid on Dynamically Adaptive Cartesian Grids, ACM Transactions on Mathematical Software, 44:3, (1-44), Online publication date: 30-Sep-2018.
- von Looz M, Tzovas C and Meyerhenke H Balanced k-means for Parallel Geometric Partitioning Proceedings of the 47th International Conference on Parallel Processing, (1-10)
- Galántai A (2018). Always convergent methods for nonlinear equations of several variables, Numerical Algorithms, 78:2, (625-641), Online publication date: 1-Jun-2018.
- Franco P, Nguyen G, Mullot R and Ogier J (2018). Alternative patterns of the multidimensional Hilbert curve, Multimedia Tools and Applications, 77:7, (8419-8440), Online publication date: 1-Apr-2018.
- LEcuyer P, Munger D, Lcot C and Tuffin B (2018). Sorting methods and convergence rates for Array-RQMC, Mathematics and Computers in Simulation, 143:C, (191-201), Online publication date: 1-Jan-2018.
- alik B, Mongus D, alik K and Luka N (2017). Boolean operations on rasterized shapes represented by chain codes using space filling curves, Journal of Visual Communication and Image Representation, 49:C, (420-432), Online publication date: 1-Nov-2017.
- Reps B and Weinzierl T (2017). Complex Additive Geometric Multilevel Solvers for Helmholtz Equations on Spacetrees, ACM Transactions on Mathematical Software, 44:1, (1-36), Online publication date: 24-Jul-2017.
- Fernando M, Duplyakin D and Sundar H Machine and Application Aware Partitioning for Adaptive Mesh Refinement Applications Proceedings of the 26th International Symposium on High-Performance Parallel and Distributed Computing, (231-242)
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- Mo-Hellenbrand A, Comprés I, Meister O, Bungartz H, Gerndt M and Bader M A Large-Scale Malleable Tsunami Simulation Realized on an Elastic MPI Infrastructure Proceedings of the Computing Frontiers Conference, (271-274)
- Nishimura S and Yokota H QUILTS Proceedings of the 2017 ACM International Conference on Management of Data, (1525-1537)
- Mohamed R, Aly H and Youssef M (2017). Accurate Real-time Map Matching for Challenging Environments, IEEE Transactions on Intelligent Transportation Systems, 18:4, (847-857), Online publication date: 1-Apr-2017.
- Christodoulou G and Sgouritsa A An improved upper bound for the universal TSP on the grid Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, (1006-1021)
- Kong L, Pan J, Sung T, Tsai P, Snášel V and De Marco G (2017). An Energy Balancing Strategy Based on Hilbert Curve and Genetic Algorithm for Wireless Sensor Networks, Wireless Communications & Mobile Computing, 2017, Online publication date: 1-Jan-2017.
- Perović N, Frisch J, Salama A, Sun S, Rank E and Mundani R (2017). Multi-scale high-performance fluid flow, Advances in Engineering Software, 103:C, (85-98), Online publication date: 1-Jan-2017.
- Wang C, Wei W, Lin H, Jiang H and Lui J (2016). BLOW-UP, ACM Transactions on Sensor Networks, 12:4, (1-20), Online publication date: 17-Nov-2016.
- Tsuzuki S and Aoki T Effective dynamic load balance using space-filling curves for large-scale SPH simulations on GPU-rich supercomputers Proceedings of the 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, (1-8)
- Uher V, Gajdoš P, Radecký M and Snášel V A proposal of hierarchical vertex clustering based on the Gosper curve 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC), (000632-000637)
- Aly H and Youssef M semMatch Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems, (1-10)
- Sarje A, Song S, Jacobsen D, Huck K, Hollingsworth J, Malony A, Williams S and Oliker L (2015). Parallel Performance Optimizations on Unstructured Mesh-based Simulations, Procedia Computer Science, 51:C, (2016-2025), Online publication date: 1-Sep-2015.
- Yuxin Zheng , Zhifeng Bao , Lidan Shou and Tung A (2015). INSPIRE: A Framework for Incremental Spatial Prefix Query Relaxation, IEEE Transactions on Knowledge and Data Engineering, 27:7, (1949-1963), Online publication date: 1-Jul-2015.
- Grandin M (2015). Data structures and algorithms for high-dimensional structured adaptive mesh refinement, Advances in Engineering Software, 82:C, (75-86), Online publication date: 1-Apr-2015.
- Nivarti G, Salehi M and Bushe W (2015). A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries, Journal of Computational Physics, 281:C, (352-364), Online publication date: 15-Jan-2015.
- Zheng Y, Bao Z, Shou L and Tung A (2014). MESA, Proceedings of the VLDB Endowment, 7:13, (1545-1548), Online publication date: 1-Aug-2014.
Index Terms
- Space-Filling Curves: An Introduction with Applications in Scientific Computing
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