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Hierarchical Meshing for the Adaptive Finite Elements

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ECCOMAS Multidisciplinary Jubilee Symposium

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 14))

This paper presents a method of generation of adaptive meshes for the finite elements using a level-of-detail for the mesh data structure. To achieve the level-of-detail, we perform the hierarchical regional partitions using the Ward's method. The meshes using this data structure are changeable in a very fast manner. This method is successfully applied to the adaptive analyses of fracture mechanics and fluid dynamics.

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References

  1. Anderberg M. R., In Cluster Analysis for Applications, Academic, New York, 1973

    MATH  Google Scholar 

  2. Clark J., Hierarchical geometric models for visible surface algorithms, In Communications of the ACM 19, 547– 554, October 1976

    Article  MATH  Google Scholar 

  3. Deering M., Geometry compression, In Computer Graphics, SIGGRAPH'95 Proceedings, 13– 20, 1995

    Google Scholar 

  4. Funkhouser T., Seequin C., Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments, In Computer Graphics, SIGGRAPH'93 Proceedings, 247– 254, 1993

    Google Scholar 

  5. Garland M., Heckbert P., Surface simplification using quadric error metrics, In Computer Graphics, SIGGRAPH'97 Proceedings, 1997

    Google Scholar 

  6. Hoppe H., Progressive meshes, In Computer Graphics, SIGGRAPH'96 Proceedings, 99–108, 1996

    Google Scholar 

  7. Hoppe H., DeRose T., Duchamp T., McDonald J., Stuetzle W., Mesh optimization, In Computer Graphics, SIGGRAPH'93 Proceedings, 19– 26, 1993

    Google Scholar 

  8. Jain A. K., Dubes R. C, In Algorithms for Clustering Data, Prentice-Hall, Englewood Cliffs, NJ, 1988

    MATH  Google Scholar 

  9. Lee C. K., Shuai Y. Y., An automatic adaptive refinement procedure for the reproducing kernel particle method. Part II: Adaptive refinement, In Comp. Mech. 40, 415– 427, 2007

    Article  MathSciNet  Google Scholar 

  10. Ronfard R., Rossignac J., Full-range approximation of triangulated polyhedra, In Computer Graphics Forum, Proceedings of Eurographics'96, 67– 76, 1996

    Google Scholar 

  11. Rossignac J., Borrel P., Multi-resolution 3D approximations for rendering complex scenes, In Modeling in Computer Graphics, Falcidieno B., Kunii T. L., eds., Springer, Genova, Italy, pp. 455– 465, 1993

    Google Scholar 

  12. Schaufler G., Sturzlinger W., Generating multiple levels of detail from polygonal geometry models, In Virtual Environments'95, Eurographics Workshop, Gobel M., ed., Springer, Barcelona, Spain, pp. 33– 41, 1995

    Google Scholar 

  13. Schroeder W., Zarge J., Lorensen W., Decimation of triangle meshes, In Computer Graphics, SIGGRAPH'92 Proceedings, 65– 70, 1992

    Google Scholar 

  14. Taubin G., Rossignac J., Geometry compression through topological surgery, In Research Report RC-20340, IBM, January 1996

    Google Scholar 

  15. Ward J. H., Hierarchical Grouping to optimize an objective function, In J. Am. Statist. Associat., 58, 236– 244, 1963

    Article  Google Scholar 

  16. Wu J., Zhu Z. J., Szmelter J., Zienkiewicz O. C., Error estimation and adaptivity in Navier-Stokes incompressible flows, In Comp. Mech. 6, 259– 270, 1990

    Article  MATH  Google Scholar 

  17. Zienkiewicz O. C., Zhu Z., A simple error estimation and adaptive procedure for practical engineering analysis, In Int. J. Numer. Methods. Eng., 24, 337– 357, 1987

    Article  MATH  MathSciNet  Google Scholar 

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Murotani, K., Yagawa, G. (2009). Hierarchical Meshing for the Adaptive Finite Elements. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A., Périaux, J. (eds) ECCOMAS Multidisciplinary Jubilee Symposium. Computational Methods in Applied Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9231-2_20

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  • DOI: https://doi.org/10.1007/978-1-4020-9231-2_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9230-5

  • Online ISBN: 978-1-4020-9231-2

  • eBook Packages: EngineeringEngineering (R0)

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