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

Choi, Won-Jeong (경희대학교 건축공학과)
Kim, Min-Sook (경희대학교 건축공학과)
Kim, Dae-Jin (경희대학교 건축공학과)
Lee, Young-Hak (경희대학교 건축공학과)
Kim, Hee-Cheul (경희대학교 건축공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.24, no.4, 2011 , pp. 405-412 More about this Journal
Abstract
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.
Keywords
generalized finite element method; global-local enrichment functions; conjugate gradient method; preconditioner; direct solver;
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