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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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The Mixed Finite Element Analysis for Porous Media using Domain Decomposition Method

영역 분할기법을 이용한 포화 다공질매체의 혼합유한요소해석

  • 이경재 (한양대학교 건설환경공학과) ;
  • 탁문호 (한양대학교 건설환경공학과) ;
  • 강윤식 (한양대학교 건설환경공학과) ;
  • 박대효 (한양대학교 건설환경공학과)
  • Received : 2010.06.07
  • Accepted : 2010.08.03
  • Published : 2010.08.31
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Abstract

The mixed finite element analysis is the most widely used method for saturated porous media. Generally, in this method, direct method and iterative method are proposed to obtain unknown variable, however, the iterative method is recommended because the method provide numerical stability and accuracy under the material properties for solid and fluid are different. In this paper, we introduce staggered method which has strong numerical stability, and FETI(Finite Element Tearing and Interconnecting) which is one of decomposition methods are applied into the method in order to obtain numerical efficiency. In which, Lagrange Multipliers and conjugated gradient method to solve decomposed domain are proposed, and then, the proposed method is verified numerical efficiency by point to point MPI(Message Passing Interface) library.

포화된 다공질매체의 수치해석에서는 일반적으로 고체영역과 유체영역을 동시에 고려한 혼합유한요소해석(Mixed Finite Element Analysis)이 쓰인다. 여기서 고체영역과 유체영역에서의 변수를 계산하기 위해서는 직접법(Direct Method) 또는 반복법(Iterative method)을 사용할 수 있으나, 각 구성물질의 상이한 물리적 특성 때문에 수치안정성을 확보하기 위해서는 대부분 스태거드 방법(Staggered method)이 제안된다. 본 논문에서는 수치안정성을 높인 스태거드 방법에서 영역 분할기법 중 하나인 FETI(Finite Element Tearing and Interconnecting)기법을 고체영역에 접목시켜 수치효율성을 증대시키는 방법이 제안되었다. 고체영역에서 라그랑지 승수와 Conjugated Gradient Method를 이용해 영역 분할이 진행되고 MPI(Message Passing Interface) 라이브러리를 사용하여 수치 효율성을 검증하였다.

Keywords

References

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