한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)

  • 제24권4호
  • /
  • Pages.405-412
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  • 2011
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  • 1229-3059(pISSN)
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  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
권호 표지

전처리된 켤레구배법의 전체-국부 확장함수를 지닌 일반유한요소해석에의 응용

Application of the Preconditioned Conjugate Gradient Method to the Generalized Finite Element Method with Global-Local Enrichment Functions

  • 투고 : 2011.06.30
  • 심사 : 2011.07.25
  • 발행 : 2011.08.31
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초록

본 논문에서는 켤레구배법을 이용해 전체-국부 확장함수를 지닌 일반유한요소법을 해석하는 방식을 제안한다. 이 기법은 편미분방정식의 해에 대한 정보가 충분하지 않은 경우에도 수치해석적인 방법으로 일반유한요소법의 확장함수를 구성할 수 있으며, 해석과정 중 약간의 추가적인 연산만으로 좋은 성능을 지닌 전처리행렬 및 초기 추측치를 구성할 수 있어 국부적으로 복잡한 거동을 보이는 문제의 해석에 효과적이다. 본 논문에 포함된 수치해석 예제의 결과는 제안된 기법이 가우스 소거법과 같은 직접 솔버를 이용하는 경우보다 수치해석적으로 더 효율적임을 보여준다.

This paper introduces the generalized finite element method with global-local enrichment functions using the preconditioned conjugate gradient method. The proposed methodology is able to generate enrichment functions for problems where limited a-priori knowledge on the solution is available and to utilize a preconditioner and initial guess of good quality with only small addition of computational cost. Thus, it is very effective to analyze problems where a complex behavior is locally exhibited. Several numerical experiments are performed to confirm its effectiveness and show that it is computationally more efficient than the analysis utilizing direct solvers such as Gauss elimination method.

키워드

과제정보

연구 과제 주관 기관 : 한국연구재단

참고문헌

  1. Duarte, C.A., Kim, D.-J. (2008) Analysis and Applications of a Generalized Finite Element Method with Global-Local Enrichment Functions, Computer Methods in Applied Mechanics and Engineering, 197(6-8), pp.487-504. https://doi.org/10.1016/j.cma.2007.08.017
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  5. Kim, D.-J., Duarte, C.A., N.A. Sobh (2011) Parallel Simulations of Three-Dimensional Cracks using GFEM, Computational Mechanics, 47, pp.265-282. https://doi.org/10.1007/s00466-010-0546-5
  6. Kim, D.-J., Pereira, J.P., Duarte, C.A. (2010) Analysis of Three-Dimensional Fracture Mechanics Problems: A Two-Scale Approach using Coarse Generalized FEM meshes, International Journal for Numerical Methods in Engineering, 81(3), pp.335-365.
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  8. Simone, A., Duarte, C.A., van der Giessen, A. (2006) A generalized Finite Element Method for Polycrystals with Discontinuous Grain Boundaries, International Journal for Numerical Methods in Engineering, 67(8), pp.1122-1145. https://doi.org/10.1002/nme.1658