Generalized finite element analysis using the preconditioned conjugate gradient method

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 high quality with an addition of only small 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 methods such as the LU and Cholesky factorization methods.