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

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Development of Finite Element Domain Decomposition Method Using Local and Mixed Lagrange Multipliers

국부 및 혼합 Lagrange 승수법을 이용한 영역분할 기반 유한요소 구조해석 기법 개발

  • Kwak, Jun Young (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Cho, Hae Seong (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Shin, Sang Joon (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Bauchau, Olivier A. (Department of Mechanical Engineering, University of Michigan-Shanghai Jiao Tong University Joint Institute)
  • 곽준영 (서울대학교 기계항공공학부) ;
  • 조해성 (서울대학교 기계항공공학부) ;
  • 신상준 (서울대학교 기계항공공학부) ;
  • 올리비에 보쇼 (미시간-상해교통대 연합대학교 기계공학부)
  • Received : 2012.10.30
  • Accepted : 2012.12.01
  • Published : 2012.12.31
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Abstract

In this paper, a finite element domain decomposition method using local and mixed Lagrange multipliers for a large scal structural analysis is presented. The proposed algorithms use local and mixed Lagrange multipliers to improve computational efficiency. In the original FETI method, classical Lagrange multiplier technique was used. In the dual-primal FETI method, the interface nodes are used at the corner nodes of each sub-domain. On the other hand, the proposed FETI-local analysis adopts localized Lagrange multipliers and the proposed FETI-mixed analysis uses both global and local Lagrange multipliers. The numerical analysis results by the proposed algorithms are compared with those obtained by dual-primal FETI method.

본 논문에서는 대규모 구조해석을 위하여 국부(local) 및 전역-국부 혼합(mixed) Lagrange 승수(Lagrange multiplier)를 이용한 새로운 유한요소 영역분할 기법을 제시한다. 제시되는 FETI 알고리즘은 계산 효율성을 향상시키기 위하여 기존의 FETI 기법들에서 사용되어 온 전통적인 Lagrange 승수법과는 달리, 국부 및 전역-국부 혼합 Lagrange 승수를 도입하고 ALF(Augmented Lagrangian Formulation)과의 결합을 유도하여 공유면 문제(interface problem)의 해의 수렴성을 향상 시켰다. 추가적으로, 몇 가지 수치예제 계산을 통해 기존의 FETI-DP 기법과 비교하여 유연도 행렬의 조건수, 계산 시간 그리고 메모리 사용량에 대한 계산결과를 제시하였다.

Keywords

References

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  2. Domain Decomposition Approach Applied for Two- and Three-dimensional Problems via Direct Solution Methodology vol.16, pp.2, 2015, https://doi.org/10.5139/IJASS.2015.16.2.177