국부 및 혼합 Lagrange 승수법을 이용한 영역분할 기반 유한요소 구조해석 기법 개발
Development of Finite Element Domain Decomposition Method Using Local and Mixed Lagrange Multipliers
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초록
본 논문에서는 대규모 구조해석을 위하여 국부(local) 및 전역-국부 혼합(mixed) Lagrange 승수(Lagrange multiplier)를이용한 새로운 유한요소 영역분할 기법을 제시한다. 제시되는 FETI 알고리즘은 계산 효율성을 향상시키기 위하여 기존의FETI 기법들에서 사용되어 온 전통적인 Lagrange 승수법과는 달리, 국부 및 전역-국부 혼합 Lagrange 승수를 도입하고ALF(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.
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.
참고문헌 (14)
- Bauchau, O.A, "Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations", Journal of Computational and Nonlinear Dynamics, 4 (2009)
- Bauchau, O.A., "Parallel Computation Approaches for Flexible Multibody Dynamics Simulations", Journal of the Franklin Institute, 347, pp.53~68 (2010)
- Bathe, K.-J., "Finite Element Procedures in Engineering Analysis" (1996), Prentice Hall
- Duff, S., "The Multifrontal Solution of Indefinite Sparse Symmetric Linear Equations", ACM Trans. Math. Software, 9, pp.302~325 (1973)
- Farhat, C., "The Two-level FETI Method. Part I: anOptimal Iterative Solver for Biharmonic Systems", Computer Methods and Applied Mechanics andEngineering, 155, pp.129~151 (1998)
- Farhat, C., "The Two-level FETI Method. Part II:Extension to Shell Problems, Parallel Implementationand Performance Results", Computer Methodsand Applied Mechanics and Engineering, 155, pp.153~179 (1998)
- Farhat, C., "FETI-DP: a Dual-primal Unified FETI method PartI: A Faster Alternative to the Two-level FETI Method", International Journal for Numerical Methods in Engineering, 50, pp.1523~1544 (2001)
- Farhat, C., "Optimal Convergence Properties of the FETI Domain Decomposition Method", Computer Methods and Applied Mechanics and Engineering, 115, pp.367~388 (1994)
- Farhat, C., "The Second Generation FETI Methods and their Application to the Parallel Solution of Large-scale Linear and Geometrically Non-linear Structural Analysis Problems", Computer Methods in Applied Mechanics and Engineering, 184, pp.333~374 (2000)
- Farhat, C., "A Method of Finite Element Tearing and Interconnecting and Its Parallel Solution Algorithm", International Journal for Numerical Methods in Engineering, 32, pp.1205~1227 (1991)
- Gill, P., "Sequential Quadratic Programming Methods for Nonlinear Programming", Computer Methods in Applied Mechanics and Engineering, 71, pp.183~195 (1988)
- 김현기, "축소 의사역행렬을 이용한 영역분할 기반 축소모델구축기법 연구", 한국전산구조공학회논문집, 22(22), pp.173~179 (2009), 한국전산구조공학회
- 이경재, "영역 분할기법을 이용한 포화 다공질매체의 혼합유한요소해석", 한국전산구조공학회논문집, 23(4), pp.369~378 (2010), 한국전산구조공학회
- Park, K. C., "A localized version of the method of Lagrange multipliers and its applications", Computational Mechanics, 24, pp.476~490 (2000)