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Abstract We study a framework that allows to solve the coarse problem in the FETI‐DP method approximately. It is based on the saddle‐point formulation of the FETI‐DP system with a block‐triangular preconditioner. One of the blocks approximates the coarse problem, for which we use the multilevel BDDC method as the main tool. This strategy then naturally leads to a version of multilevel FETI‐DP method, and we show that the spectra of the multilevel FETI‐DP and BDDC preconditioned operators are essentially the same. The theory is illustrated by a set of numerical experiments, and we also present a few experiments when the coarse solve is approximated by algebraic multigrid.more » « less
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