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.
- J. Siek, L.-Q. Lee, and A. Lumsdaine. The Boost Graph Library: User Guide and Reference Manual. Addison-Wesley, 2002. Google ScholarDigital Library
- R. Heinzl. Concepts for Scientific Computing. Dissertation, Technische Universität Wien, Austria, 2007.Google Scholar
- R. Heinzl, P. Schwaha, and S. Selberherr. A High Performance Generic Scientific Simulation Environment. In B. Kaagström et al., editor, Lecture Notes in Computer Science, volume 4699/2007, pages 996--1005. Springer, Berlin, June 2007. Google Scholar
- R. Heinzl, P. Schwaha, F. Stimpfl, and S. Selberherr. Parallel Library-Centric Application Design by a Generic Scientific Simulation Environment. In Proc. of the POOSC, Paphos, Cyprus, July 2008.Google Scholar
- B. A. Davey and H. A. Priestley. Introduction to Lattices and Order. Cambridge, 1990.Google Scholar
- Boost. Boost Graphics Image Library (GIL), 2005. http://www.boost.org/.Google Scholar
- P. Gottschling and D. Lindbo. Generic Compressed Sparse Matrix Insertion: Algorithms and Implementations in MTL4 and FEniCS. In POOSC 2009 Workshop at ECOOP09, ACM Digital Library, 2009. Google ScholarDigital Library
- P. Gross and P. R. Kotiuga. Electromagnetic Theory and Computation: A Topological Approach. Cambridge University Press, 2004.Google ScholarCross Ref
- C. Mattiussi. The Geometry of Time-Stepping. In F. L. Teixeira, editor, Geometric Methods in Computational Electromagnetics, PIER 32, pages 123--149. EMW Publishing, Cambridge, Mass., 2001.Google Scholar
- A. Hatcher. Algebraic Topology. Cambridge University Press, 2002.Google Scholar
- J. Hocking and G. Young. Topology. Addison-Wesley, Dover Publications, New York, 1961.Google Scholar
- A. J. Zomorodian. Topology for Computing. In Cambridge Monographs on Applied and Computational Mathematics, 2005. Google ScholarDigital Library
- T. Dey, H. Edelsbrunner, and S. Guha. Computational Topology. In J. E. G. B. Chazelle and R. Pollack, editors, Advances in Discrete and Computational Geometry, Contemporary Mathematics. Providence, RI, USA, 1998.Google Scholar
- E. Tonti. The Reason for Analogies between Physical Theories. Appl. Math. Modelling, 1(1):37--50, 1976/77.Google ScholarCross Ref
- P. Bochev and M. Hyman. Principles of Compatible Discretizations. In Proc. of IMA Hot Topics Workshop on Compatible Discretizations, volume IMA 142, pages 89--120. Springer, 2006.Google ScholarCross Ref
- Boost. Boost Phoenix 2, 2006. http://spirit.sourceforge.net/.Google Scholar
- G. Berti. Generic Software Components for Scientific Computing. Dissertation, Technische Universität Cottbus, 2000.Google Scholar
- R. Heinzl, P. Schwaha, M. Spevak, and T. Grasser. Performance Aspects of a DSEL for Scientific Computing with C++. In Proc. of the POOSC Conf., pages 37--41, Nantes, France, July 2006.Google Scholar
Index Terms
- Data structure properties for scientific computing: an algebraic topology library
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