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On the coupling of BEM and FEM
for exterior problems
for the Helmholtz equation

Author: Ruixia Li
Journal: Math. Comp. 68 (1999), 945-953
MSC (1991): Primary 65N38, 65N30, 15A06
Published electronically: February 15, 1999
MathSciNet review: 1627809
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with the coupled procedure of the boundary element method (BEM) and the finite element method (FEM) for the exterior boundary value problems for the Helmholtz equation. A circle is selected as the common boundary on which the integral equation is set up with Fourier expansion. As a result, the exterior problems are transformed into nonlocal boundary value problems in a bounded domain which is treated with FEM, and the normal derivative of the unknown function at the common boundary does not appear. The solvability of the variational equation and the error estimate are also discussed.

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  • 1. C. Johnson and J. C. Nedelec, On the coupling of boundary integral and finite element methods, Math. Comp., 35(1980), pp.1063- 1079. MR 82c:65072
  • 2. G. C. Hsiao, The coupling of BEM and FEM-a brief review, in Boundary Elements X, C. A. Brebbia et al., ed., Springer-Verlag, 1988, pp.431-445. MR 91c:65071
  • 3. Feng Kang and Yu De-hao, Canonical integral equations of elliptic boundary value problems and their numerical solutions, in Proceedings of China-France Symposium on the Finite Element Method (1982, Beijing), Science Press, Beijing, 1983, pp.211-252.
  • 4. Yu De-hao, A direct and natural coupling of BEM and FEM, in Boundary Elements XIII, C.A.Brebbia and G.S.Gipson ed., Computational Mechanics Publications, Southampton, 1991, pp.995-1004. MR 92h:65004
  • 5. J. B. Keller and D. Givoli, Exact non-reflecting boundary conditions, J.Comp. Phys., 82(1989), pp.172-192. MR 91a:76064
  • 6. A. K. Aziz and R. B. Kellogg, Finite element analysis of a scattering problem, Math. Comp., 37(1981), pp.261-272. MR 82i:65069
  • 7. I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. 1, Academic Press, New York, 1964. MR 29:3869
  • 8. V. J. Ervin, R. Kieser and W. L. Wendland, Numerical approximation of the solution for a model 2-D hypersingular integral equation, Universität Stuttgart, Math. Institut A, Bericht Nr.26, 1990; also in Computational Engineering with Boundary Elements, Vol. 1 (Proc. Fifth Internat. Conf., Newark, DE, 1990; S. Grilli et al., eds.), Comput. Mech. Publ., Southampton, 1990, pp. 85-99. MR 92i:65005
  • 9. F. Ihlenburg and I. Babu[??]ska, Finite element solution of the Helmholtz equation with high wave number - part I: The h-version of the FEM, Comp. Math. Appl., 30(1995), No.9, pp.9-37. MR 96j:65123
  • 10. A. Bayliss, C. I. Goldstein and E. Turkel, On accuracy conditions for the numerical computation of waves, J.Comp. Phys., 59(1985), pp.396-404. MR 87b:65153

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Additional Information

Ruixia Li
Affiliation: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P.R.China

Keywords: BEM, FEM, Helmholtz equation, integral equation, Fourier expansion, variational equation
Received by editor(s): November 21, 1996
Received by editor(s) in revised form: April 10, 1997, and January 22, 1998
Published electronically: February 15, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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