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Data structure properties for scientific computing: an algebraic topology library

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René HeinzlAuthors Info & Claims

POOSC '09: Proceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing

Article No.: 5, Pages 1 - 6

https://doi.org/10.1145/1595655.1595660

Published: 07 July 2009 Publication History

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Abstract

Cell and complex properties are introduced in order to derive a common specification environment for properties of data structures. Only topological properties are used, thereby separating the actual data storage structure from the stored data. Several theoretical topological property concepts are introduced, and traversal and boundary operations are presented and accompanied by selected examples.

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Cited By

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Juba SBaumann P(2010)A coverage representation model based on explicit topologyProceedings of the 14th east European conference on Advances in databases and information systems10.5555/1885872.1885896(278-288)Online publication date: 20-Sep-2010
https://dl.acm.org/doi/10.5555/1885872.1885896
Juba SBaumann P(2010)A Coverage Representation Model Based on Explicit TopologyAdvances in Databases and Information Systems10.1007/978-3-642-15576-5_22(278-288)Online publication date: 2010
https://doi.org/10.1007/978-3-642-15576-5_22
Sonderfeld RHeinzl RDavis|Chair K(2009)A generic and self-optimizing polynomial libraryProceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing10.1145/1595655.1595666(1-4)Online publication date: 7-Jul-2009
https://dl.acm.org/doi/10.1145/1595655.1595666

Index Terms

Data structure properties for scientific computing: an algebraic topology library
1. Computing methodologies
  1. Symbolic and algebraic manipulation
2. Software and its engineering
  1. Software notations and tools
    1. Context specific languages
      1. Domain specific languages
  2. Software organization and properties
    1. Software system structures
      1. Abstraction, modeling and modularity
      2. Software architectures

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Reviews

Reviewer: Wolfgang Schreiner

A reason for the success of the C++ standard template library (STL) is the concept of iterators, which allow for the processing of different kinds of data structures in a uniform way. In this paper, Heinzl generalizes this idea to the application area of physical simulation, by providing a unifying theoretical framework and corresponding C++ library for the representation of spatial domain decompositions. The core idea is to apply concepts from algebraic topology to the structured representation of spatial cells, using their topological properties; thus, a three-dimensional (3D) cell is related to its two-dimensional (2D) facets, which are related to their one-dimensional (1D) boundary lines, which are ultimately related to their corner points. This representation is applied to complexes of cells whose topologies are described by the adjacency of each element. For example, topological operators decompose a complex into its boundary elements or evaluate real-valued functions over a complex. Based on these concepts, a C++ template library is developed that allows the definition of various kinds of representations of n -dimensional spaces that can be processed in a uniform way by topological operators. The paper presents an interesting and useful approach. Unfortunately, it is not easily accessible without prior background knowledge. This is partially due to sub-optimal organization; in particular, the introduction does not describe well the concrete context of the work, and some basic notions are used before they are defined. However, the paper refers to a number of more detailed resources, in particular Heinzl's dissertation. I advise the reader to consult these for more information. Online Computing Reviews Service

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Published In

POOSC '09: Proceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing

July 2009

85 pages

ISBN:9781605585475

DOI:10.1145/1595655

Conference Chair:
Kei Davis|Chair
Computer Science for High Performance Computing, Los Alamos National Laboratory, Los Alamos, NM

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 07 July 2009

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ECOOP '09

ECOOP '09: European Conference on Object-Oriented Programming

July 7, 2009

Genova, Italy

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Juba SBaumann P(2010)A coverage representation model based on explicit topologyProceedings of the 14th east European conference on Advances in databases and information systems10.5555/1885872.1885896(278-288)Online publication date: 20-Sep-2010
https://dl.acm.org/doi/10.5555/1885872.1885896
Juba SBaumann P(2010)A Coverage Representation Model Based on Explicit TopologyAdvances in Databases and Information Systems10.1007/978-3-642-15576-5_22(278-288)Online publication date: 2010
https://doi.org/10.1007/978-3-642-15576-5_22
Sonderfeld RHeinzl RDavis|Chair K(2009)A generic and self-optimizing polynomial libraryProceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing10.1145/1595655.1595666(1-4)Online publication date: 7-Jul-2009
https://dl.acm.org/doi/10.1145/1595655.1595666

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A generic topology library

On some paracompactness-type properties of fuzzy topological spaces

Weak Hausdorff separation axiom in I-fuzzy topological spaces and its application

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