Symmetric finite element and boundary integral coupling methods for fluid-solid interaction
Authors:
J. Bielak and R. C. MacCamy
Journal:
Quart. Appl. Math. 49 (1991), 107-119
MSC:
Primary 65N30; Secondary 65N12, 73D25, 73K70, 73V05, 76M10, 76M25, 76Q05
DOI:
https://doi.org/10.1090/qam/1096235
MathSciNet review:
MR1096235
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Abstract: This paper presents a coupled finite element and boundary integral method for solving the time-periodic oscillation and scattering problem of an inhomogeneous elastic body immersed in a compressible, inviscid, homogeneous fluid. By using integral representations for the solution in the infinite exterior region occupied by the fluid, the problem is reduced to one defined only over the finite region occupied by the solid, with associated nonlocal boundary conditions. This problem is then given a family of variational formulations, including a symmetric one, which are used to derive finite-dimensional Galerkin approximations. The validity of the method is established explicitly, and results of an error analysis are discussed, showing optimal convergence to a classical solution.
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M. C. Junger and D. Feit, Sound, Structures and Their Interaction, MIT Press, Cambridge, MA, 1986
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G. S. Sammelmann, D. H. Trivett, and R. H. Hackman, The acoustic scattering by a submerged spherical shell I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave, J. Acoust. Soc. Amer. 85, 114–124 (1989)
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A. Barry, J. Bielak, and R. C. MacCamy, On absorbing boundary conditions for wave propagation, J. Comput. Phys 79, 449–468 (1988)
A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations, Comm. Pure Appl. Math. 33, 707–725 (1980)
D. E. Beskos, Potential theory, Boundary Element Methods in Mechanics, (D. E. Beskos, ed.), Elsevier, Amsterdam, 1987, pp. 23–106
J. Bielak and R. C. MacCamy, An exterior interface problem in two-dimensional elastodynamics, Quart. Appl. Math. 41, 143–159 (1983)
A. J. Burton and G. F. Miller, The application of integral equation methods to the numerical solutions of some exterior boundary-value problems, Proc. Royal Soc. London Ser. A 323, 201–210 (1971)
B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31, 629–651 (1977)
S. Hildebrandt and E. Weinholz, Construction proofs of representation theorems in separable Hilbert space, Comm. Pure Appl. Math. 17, 369–373 (1964)
G. Hsiao, The coupling of BEM and FEM—A brief review, Boundary Elements X, Vol.1, Springer-Verlag, New York, 1988, pp. 431–445
C. Johnson and J. C. Nedelec, On the coupling of boundary integral and finite element methods, Math. Comp. 35, 1063–1079 (1980)
M. C. Junger and D. Feit, Sound, Structures and Their Interaction, MIT Press, Cambridge, MA, 1986
R. C. MacCamy and E. Stephan, A boundary element method for an exterior problem for three-dimensional Maxwell’s equation, Appl. Anal 10, 141–163 (1983)
G. S. Sammelmann, D. H. Trivett, and R. H. Hackman, The acoustic scattering by a submerged spherical shell I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave, J. Acoust. Soc. Amer. 85, 114–124 (1989)
H. A. Schenk, Improved integral formulation for acoustic radiation problems, J. Acoust. Soc. Amer. 44, 41–58 (1968)
O. C. Zienkiewicz, D. W. Kelly, and P. Bettes, The coupling of the finite element method and boundary solution procedures, Internat. J. Numer. Methods Engrg. 11, 335–375 (1977)
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Article copyright:
© Copyright 1991
American Mathematical Society