0 0.5 1 1.5 2 2.5 3 3.5 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 Mode 1 (ω=1.26e7) Mode 2,(ω=7.63e7) 0 0.5 1 1.5 2 2.5 3 3.5 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 Mode 3 (ω=9.59e7) Mode 4,(ω=−1.20e8) Fig. 7 Modes 1, 2, 3, 4 of the statically condensed dual interface problem (32). We have shown in two examples that the method allows reducing the system to a small number of degrees of freedom while keeping good accuracy on the frequencies of the system. We note that one of the major cost in the interface reduction strategy proposed here resides in the solution of the statically condensed interface problem (32). In particular the factorization of FI implies a significant computational cost. Nevertheless several options exist to reduce that cast by approximating the interface operators and find approximate interface modes. In particular the large know-how present in the field of parallel computing can be used to approximate the inverse of the interface flexibility. One could approximate that operator by a projected Dirichlet operator like it is done in the Dirichlet preconditioner of the FETI method. One could also Interface Reduction in the Dual Craig-Bampton method 327
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