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Need a hand to pull me into the world of XFEM !!

Dear all,

         I am new to X-FEM, started reading papers a couple of weeks before. I understood, functions[heaviside,sign..] are used to enrich the nodes to simulate virtually the discontinuity and asymptotic functions are used to charecterize the crack tip,other than this regular FEM nodes are there. I have few questions. 

1.what is the role of the asymptotic functions and its unknown co-efficient 'b' in charecterizing the crack tip. What are the parameters do these functions exactly charecterize means wat are the details can we extract from these fns n co-effs?

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