This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEM~(g1)) and the Stable GFEM~(g1). The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for example, the evolution of interfaces and fractures. The performance of the conjugate gradient method with the proposed preconditioner is investigated. A 3-D fracture problem is adopted for the numerical experiments.
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