Journal of Mechanical Science and Technology

  • 제20권1호
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  • Pages.110-124
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  • 2006
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  • 1738-494X(pISSN)
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  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

Implementation Strategy for the Numerical Efficiency Improvement of the Multiscale Interpolation Wavelet-Galerkin Method

  • Seo Jeong Hun (School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University) ;
  • Earmme Taemin (School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University) ;
  • Jang Gang-Won (School of Mechanical Engineering, Kunsan National University) ;
  • Kim Yoon Young (School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University)
  • 발행 : 2006.01.01
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초록

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.

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