Márquez, A.; Meddahi, S.; Selgas, V. A new BEM-FEM coupling strategy for two-dimensional fluid-solid interaction problems. (English) Zbl 1127.74328 J. Comput. Phys. 199, No. 1, 205-220 (2004). Summary: We present a numerical method to solve a fluid–solid interaction problem posed in the plane. In this scheme, we use a finite element method to approximate the solid vibrations and the near wave field. The far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle. The boundary unknown involved in our formulation is approximated by a spectral method. We obtain a fully discrete Galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals. We provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique. Cited in 18 Documents MSC: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 74S05 Finite element methods applied to problems in solid mechanics 74S15 Boundary element methods applied to problems in solid mechanics 76M10 Finite element methods applied to problems in fluid mechanics 76M15 Boundary element methods applied to problems in fluid mechanics Keywords:Exterior boundary value problem; Helmholtz equation; Elastodynamic equation; Integral equations; Finite elements; Spectral methods PDFBibTeX XMLCite \textit{A. Márquez} et al., J. Comput. Phys. 199, No. 1, 205--220 (2004; Zbl 1127.74328) Full Text: DOI References: [1] Bielak, J.; MacCamy, R. C., Symmetric finite element and boundary integral coupling methods for fluid-solid interaction, Quart. Appl. Math., 49, 107-119 (1991) · Zbl 0731.76043 [2] Costabel, M., Symmetric methods for the coupling of finite elements and boundary elements, The Mathematics of Finite Elements and Applications IV (1988), Academic Press: Academic Press London · Zbl 0687.73034 [3] Givoli, D., Numerical Methods for Problems in Infinite Domains (1992), Elsevier: Elsevier Amsterdam · Zbl 0788.76001 [4] Hsiao, G., The coupling of BEM and FEM - a brief review, Boundary Elements X, vol. 1 (1988), Springer: Springer New York, pp. 431-445 [5] Ihlenburg, F., Finite Element Analysis of Acoustic Scattering (1998), Springer: Springer New York · Zbl 0908.65091 [6] Kress, R., Linear Integral Equations (1999), Springer: Springer New York [7] Luke, C. J.; Martin, P. A., Fluid-solid interaction: acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55, 904-922 (1995) · Zbl 0832.73045 [8] McLean, W., Strongly Elliptic Systems and Boundary Integral Equations (2000), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0948.35001 [9] Meddahi, S., An optimal iterative process for the Johnson-Nedelec method of coupling boundary and finite elements, SIAM J. Numer. Anal., 35, 1393-1415 (1998) · Zbl 0912.65096 [10] Meddahi, S.; Sayas, F.-J., A fully discrete BEM-FEM for the exterior Stokes problem in the plane, SIAM J. Numer. Anal., 37, 2082-2102 (2000) · Zbl 0981.65129 [11] Meddahi, S.; González, M.; Pérez, P., On a FEM-BEM formulation for an exterior quasilinear problem in the plane, SIAM J. Numer. Anal., 37, 1820-1837 (2000) · Zbl 0986.65113 [12] Meddahi, S.; Márquez, A., New implementation techniques for the exterior Stokes problem in the plane, J. Comput. Phys., 172, 685-703 (2001) · Zbl 0988.65104 [13] Meddahi, S.; Márquez, A., A combination of spectral and finite elements methods for an exterior problem in the plane, Appl. Numer. Math., 43, 275-295 (2002) · Zbl 1015.65061 [14] Meddahi, S.; Márquez, A.; Selgas, V., Computing acoustic waves in an inhomogeneous medium of the plane by a coupling of spectral and finite elements, SIAM J. Numer. Anal., 41, 1729-1750 (2003) · Zbl 1056.65119 [15] Saranen, J.; Vainikko, G., Periodic Integral and Pseudodifferential Equations with Numerical Approximation (2002), Springer: Springer Berlin · Zbl 0991.65125 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.