메뉴 건너뛰기




Volumn , Issue , 2009, Pages 135-145

Discrete physics using metrized chains

Author keywords

Discrete calculus; Geometric and physical modeling; I.3.5 computational geometry and object modeling : physically based modeling; J.2 physical sciences and engineering : engineering

Indexed keywords

CELL COMPLEXES; CIRCUIT DESIGNS; DISCRETE CALCULUS; DISCRETE DIFFERENTIAL GEOMETRY; DISCRETE EXTERIOR CALCULUS; DISCRETE MEASURE; DISCRETIZATION METHOD; FINITE DIFFERENCE; FINITE ELEMENT; FINITE VOLUME; FIRST-PRINCIPLES; GENERAL RELATIVITY; GEOMETRIC AND PHYSICAL MODELING; GEOMETRIC INTEGRATION; GEOMETRIC MODELS; I.3.5 [COMPUTATIONAL GEOMETRY AND OBJECT MODELING]: PHYSICALLY BASED MODELING; INNER PRODUCT; J.2 [PHYSICAL SCIENCES AND ENGINEERING]: ENGINEERING; MATHEMATICAL STRUCTURE; NETWORK ANALYSIS; PHYSICAL MODELING; PHYSICAL THEORY; PHYSICALLY BASED; PHYSICS-BASED SIMULATION; REGGE CALCULUS; THEORETIC STRUCTURES; TOPOLOGICAL APPROACH; TOPOLOGICAL PROPERTIES; WHITNEY;

EID: 70350633956     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1629255.1629273     Document Type: Conference Paper
Times cited : (16)

References (37)
  • 1
    • 33646721932 scopus 로고    scopus 로고
    • Finite element exterior calculus, homological techniques, and applications
    • D. Arnold, R. Falk, and R. Winther. Finite element exterior calculus, homological techniques, and applications. Acta Numerica, 15:1-155, 2006.
    • (2006) Acta Numerica , vol.15 , pp. 1-155
    • Arnold, D.1    Falk, R.2    Winther, R.3
  • 2
    • 33747361289 scopus 로고    scopus 로고
    • A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, editors, Birkhäuser Verlag AG
    • A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, editors. Discrete Differential Geometry, volume 38. Birkhäuser Verlag AG, 2008.
    • (2008) Discrete Differential Geometry , vol.38
  • 3
    • 0024104484 scopus 로고
    • Whitney forms: A class of finite elements for three-dimensional computations in electromagnetism. Science, Measurement and Technology
    • A. Bossavit. Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. Science, Measurement and Technology, IEE Proceedings A, 135(8):493-500, 1988.
    • (1988) IEE Proceedings A , vol.135 , Issue.8 , pp. 493-500
    • Bossavit, A.1
  • 5
    • 0035787875 scopus 로고    scopus 로고
    • On the notion of anisotropy in constitutive laws: Some implications of the 'Hodge implies metric' result
    • A. Bossavit. On the notion of anisotropy in constitutive laws: some implications of the 'Hodge implies metric' result. COMPEL, 20(1):233-239, 2001.
    • (2001) COMPEL , vol.20 , Issue.1 , pp. 233-239
    • Bossavit, A.1
  • 6
    • 70350670779 scopus 로고    scopus 로고
    • A uniform rationale for whitney forms on various supporting shapes
    • in press
    • A. Bossavit. A uniform rationale for whitney forms on various supporting shapes. Mathematics and Computers in Simulation, 2009. (in press).
    • (2009) Mathematics and Computers in Simulation
    • Bossavit, A.1
  • 7
    • 0002678388 scopus 로고
    • The algebraic-topological basis for network analogies and the vector calculus
    • Polytechnic Institute of Brooklyn
    • F. H. Branin. The algebraic-topological basis for network analogies and the vector calculus. In Proceeding of the Symposium on Generalized Networks, volume 16, pages 453-491. Polytechnic Institute of Brooklyn, 1966.
    • (1966) Proceeding of the Symposium on Generalized Networks , vol.16 , pp. 453-491
    • Branin, F.H.1
  • 10
    • 84869640589 scopus 로고    scopus 로고
    • M. Desbrun, E. Grinspun, P. Schröder, and M. Wardetzky. Discrete differential geometry: An applied introduction. In Course Notes (3rd Edition). SIGGRAPH Asia, 2008.
    • M. Desbrun, E. Grinspun, P. Schröder, and M. Wardetzky. Discrete differential geometry: An applied introduction. In Course Notes (3rd Edition). SIGGRAPH Asia, 2008.
  • 11
    • 1542355827 scopus 로고    scopus 로고
    • Discrete exterior calculus. arXiv:math/0508341v2
    • August
    • M. Desbrun, A. H. Hirani, M. Leok, and J. E. Marsden. Discrete exterior calculus. arXiv:math/0508341v2, August 2005.
    • (2005)
    • Desbrun, M.1    Hirani, A.H.2    Leok, M.3    Marsden, J.E.4
  • 12
    • 77952611086 scopus 로고    scopus 로고
    • Discrete differential forms for computational modeling
    • A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, editors, Birkhäuser Verlag AG
    • M. Desbrun, E. Kanso, and Y. Tong. Discrete differential forms for computational modeling. In A. I. Bobenko, P. Schröder, J. M. Sullivan, and G. M. Ziegler, editors, Discrete Differential Geometry, volume 38, pages 287-323. Birkhäuser Verlag AG, 2008.
    • (2008) Discrete Differential Geometry , vol.38 , pp. 287-323
    • Desbrun, M.1    Kanso, E.2    Tong, Y.3
  • 16
    • 33749678097 scopus 로고    scopus 로고
    • Lectures on chainlet geometry - new topological methods in geometric measure theory
    • arXiv:math-ph/0505063, May
    • J. Harrison. Lectures on chainlet geometry - new topological methods in geometric measure theory. arXiv:math-ph/0505063, May 2005.
    • (2005)
    • Harrison, J.1
  • 21
    • 0031570250 scopus 로고    scopus 로고
    • An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology
    • C. Mattiussi. An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology. Journal of Computational Physics, 133:289-309, 1997.
    • (1997) Journal of Computational Physics , vol.133 , pp. 289-309
    • Mattiussi, C.1
  • 25
    • 0000061804 scopus 로고
    • Chain models of physical behavior for engineering analysis and design
    • R. Palmer and V. Shapiro. Chain models of physical behavior for engineering analysis and design. Research in Engineering Design, 5(3):161-184, 1993.
    • (1993) Research in Engineering Design , vol.5 , Issue.3 , pp. 161-184
    • Palmer, R.1    Shapiro, V.2
  • 26
    • 51649208939 scopus 로고
    • General relativity without coordinates
    • T. Regge. General relativity without coordinates. Nuovo Cimento 19, 1961.
    • (1961) Nuovo Cimento , vol.19
    • Regge, T.1
  • 27
    • 0019284740 scopus 로고
    • Representations for rigid solids: Theory, methods, and systems
    • A. Requicha. Representations for rigid solids: Theory, methods, and systems. Computing Surveys, 12(4):437-464, 1980.
    • (1980) Computing Surveys , vol.12 , Issue.4 , pp. 437-464
    • Requicha, A.1
  • 30
    • 0010953453 scopus 로고
    • On the formal structure of physical theories
    • Istituto di Matematica del Politecnico di Milano
    • E. Tonti. On the formal structure of physical theories. Quaderno dei gruppi di ricerca matematica del cnr, Istituto di Matematica del Politecnico di Milano, 1975.
    • (1975) Quaderno dei gruppi di ricerca matematica del cnr
    • Tonti, E.1
  • 31
    • 0001221130 scopus 로고    scopus 로고
    • A direct discrete formulation of field laws: The cell method
    • E. Tonti. A direct discrete formulation of field laws: The cell method. Computer Modeling in Engineering & Sciences, 2(2):237-258, 2001.
    • (2001) Computer Modeling in Engineering & Sciences , vol.2 , Issue.2 , pp. 237-258
    • Tonti, E.1
  • 32
    • 84887430723 scopus 로고    scopus 로고
    • Finite formulation of the electromagnetic field
    • Geometric Methods for Computational Electromagnetics
    • E. Tonti. Finite formulation of the electromagnetic field. Geometric Methods for Computational Electromagnetics, 32:1-42, 2001. PIER Mon. Ser.
    • (2001) PIER Mon. Ser , vol.32 , pp. 1-42
    • Tonti, E.1
  • 34
    • 0001751343 scopus 로고
    • Regge calculus: A brief review and bibliography
    • R. M. Williams and P. A. Tuckey. Regge calculus: a brief review and bibliography. Class. Quantum Grav., 9:1409-1422, 1992.
    • (1992) Class. Quantum Grav , vol.9 , pp. 1409-1422
    • Williams, R.M.1    Tuckey, P.A.2
  • 35
    • 70350682888 scopus 로고    scopus 로고
    • Geometric structures on the cochains of a manifold. arXiv:math/0505227v2
    • August
    • S. O. Wilson. Geometric structures on the cochains of a manifold. arXiv:math/0505227v2, August 2005.
    • (2005)
    • Wilson, S.O.1
  • 36
    • 34247263420 scopus 로고    scopus 로고
    • Cochain algebra on manifolds and convergence under refinement
    • S. O. Wilson. Cochain algebra on manifolds and convergence under refinement. Topology and its Applications, 154(9):1898-1920, 2007.
    • (2007) Topology and its Applications , vol.154 , Issue.9 , pp. 1898-1920
    • Wilson, S.O.1
  • 37
    • 40349085800 scopus 로고    scopus 로고
    • On geometric discretization of elasticity
    • A. Yavari. On geometric discretization of elasticity. Journal of Mathematical Physics, 49(2):1-36, 2008.
    • (2008) Journal of Mathematical Physics , vol.49 , Issue.2 , pp. 1-36
    • Yavari, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.