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Vierendeels. The quasi-newton least squares method: A new and fast secant method analyzed for linear systems. SIAM J. Numer. , 47:2347–2368, 2009. 5. C. H. Brummelen, and R. de Borst. An interface Newton-Krylov solver for fluidstructure interaction. Int. J. for Num. Meth. in Fluids, 47(10-11):1189–1195, 2005. 6. P. A. Wall, and E. Ramm. Accelerated iterative substructure schemes for instationary fluid-structure interaction. In First MIT Conference on Computational Fluid and Solid Mechanics, pages 1325–1328, 2001.

For coupling of an inviscid fluid (in particular, an acoustic fluid) to an elastic structure the gluing field is a scalar, which was called Bn in Sect. 3. g. [22]. This is inevitable for general fluid models, which are not derivable from variational principles. In the present context, however, we will restrict those equations to be based on the functional ˘BM of (4), a variational framework that preserves symmetry. The only field to be discretized is the scalar multiplier function Bn on B . Physically this is the normal-to-the-interface surface traction, also known as wet wall pressure.

11 gives the following fluid-to-structure force transfer fBS D TSF fBF and the structure-to-fluid motion transfer uBF D UF S uBS : fBS uBF 9 8 fF 1 > 0 03ˆ = < fF 2 2 40 ; 05 3 ˆ ; : fF 3 > 1 0 0 3 1 fF 4 3 2 8 9 1 0 0 8 9 u ˆ < F1 > = 6 1 3 0 7 < uS1 = uF 2 4 4 7 D D6 4 0 3 1 5 : uS2 ; : ˆ : uF 3 > ; 4 4 uS3 uF 4 0 0 1 8 9 < fS1 = D fS2 D : ; fS3 21 1 3 2 3 (22) It is easily checked that (22) pass both the stress and rigid-motion patch tests. However since TSF is not the transpose of UF S , interface energy conservation is not verified.

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