Abstract
In several engineering problems, especially the ones associated with the unbounded domains, the coupling of the finite element method (FEM) and the boundary element method (BEM) improves the efficiency of the numerical analysis. Due to the complexity of direct coupling techniques, iterative domain decomposition method became a popular approach. However, in the conventional domain decomposition algorithms, the boundary conditions at the interface boundary must be of one type, i.e., Neumann/Dirichlet. In this paper a new algorithm is presented for the iterative coupling of the FEM and the BEM. Both Dirichlet and Neumann boundary conditions are assumed simultaneously in different parts of the interface boundary and an iterative procedure is conducted by two relaxation parameters to solve the coupled problem. To demonstrate the accuracy of the proposed method, some numerical examples are investigated at the end of the paper.
Similar content being viewed by others
References
Zienkiewicz O.C., Kelly D.W., Bettess P.: The coupling of the finite element method and boundary solution procedures. Int. J. Numer. Methods Eng. 11, 355–375 (1977)
Brebbia C.A., Georgious P.: Combination of boundary and finite elements for elastostatics Appl. Math. Model. 3, 212–220 (1979)
Beer, G.; Meek, J.L.: The coupling of the boundary and finite element methods for infinite domain problems in elastoplasticity. In: Brebbia, C.A. (ed.) Boundary Element Methods. Springer, Berlin, pp. 575–591 (1981)
Fukui, T.: Time marching BE–FE method in 2-D elastodynamic problem. In: International Conference BEM IX, Stuttgart (1987)
Estorff O.V., Kausel E.: Coupling of boundary and finite elements for soil–structure interaction problems. Earthq. Eng. Struct. Dyn. 18, 1065–1075 (1989)
Elleithy W.M., Al-Gahtani H.J., El-Gebeily M.: Iterative coupling of BE and FE methods in elastostatics. Eng. Anal. Bound. Elem. 25, 685–695 (2001)
Kanarachos, A.; Provatidis, C.: On the symmetrization of the BEM formulation. Comput. Methods Appl. Mech. Eng. 71, 151–165 (1988)
Ameen, M.: Computational Elasticity; Theory of Elasticity and Finite and Boundary Element Methods. Alpha Science International, UK, p. 509 (2005)
Sutradhar, A.; Paulino, G.; Gray, L.J.: Symmetric Galerkin Boundary Element Method. Springer-Verlag, Berlin (2008)
Jaswon, M.A.; Symm, G.T.: Integral Equation Methods in Potential Theory and Elastostatics. Academic Press, London (1977)
Massonnet, C.E.: Numerical use of integral procedures, in stress analysis In: Zienkiewicz, O.C.; Holister, G.S. (eds.) Wiley, London (1965)
Estorff O.V., Firuziaan M.: Coupled BEM/FEM approach for nonlinear soil/structure interaction. Eng. Anal. Bound. Elem. 24, 715–725 (2000)
Mullen R.L., Rencis J.J.: Iterative methods for solving boundary element equations. Comput. Struct. 25(5): 713–723 (1987)
Araujo, F.C.; Mansur, W.J.: Iterative solvers for BEM systems of equations. In: Brebbia, C.A.; Connor, J.J. (eds.) International Conference BEM XI, Vol 1. Computational Mechanics Publications, Southampton, pp. 263–274 (1989)
Mansur W.J., Araujo F.C., Malaghini J.E.B.: Solution of BEM systems of equations via iterative techniques. Int. J. Numer. Methods Eng. 33, 1823–1841 (1992)
Araujo, F.C.; Mansur, W.J.: Iterative solvers for BEM systems of equations. In: Brebbia, C.A.; Connor, J.J. (eds.) Advances in Boundary Elements, Vol 1. Springer- Verlag, Berlin, pp. 263–274 (1989)
Izzuddin B.A., Zolghadr Jahromi H., Zdravkovic L.: Partitioned analysis of nonlinear soil–structure interaction using iterative coupling. Interact. Multiscale Mech. 1(1): 33–51 (2007)
Elleithy W.: Analysis of problems in elasto-plasticity via an adaptive FEM-BEM coupling method. Comput. Methods Appl. Mech. Eng. 197(45–48): 3687–3701 (2008)
Li, M.; Zhu, J.: A domain decomposition method combining a boundary element method with a meshless local Petrov–Galerkin method. In: Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, Vol. 78, pp. 391–398 (2011)
Toselli, A.; Widlund, O.B.: Domain Decomposition Methods—Algorithms and Theory. Springer-Verlag, New York (2005)
El-Gebeily M., Elleithy W.M., Al-Gahtani H.J.: Convergence of the domain decomposition finite element–boundary element coupling methods. Comput. Methods Appl. Mech. Eng. 191, 4851–4867 (2002)
Lin, C.-C.; Lawton, E.C.; Caliendo, J.A.; Anderson, L.R.: An iterative finite element–boundary element algorithm. Comput. Struct. 39, 899–909 (1996)
Bathe, K.J.: Finite Element Procedures. Prentice-Hall Inc., Upper Saddle River, p. 07458 (1996)
Feng Y.T., Owen D.R.J.: Iterative solution of coupled FE/BE discretization for plate–foundation interaction problems. Int. J. Numer. Methods Eng. 39, 1889–1901 (1996)
Kamiya N., Iwase H.: BEM and FEM combination parallel analysis using conjugate gradient and condensation. Eng. Anal. Bound. Elem. 20, 319–326 (1997)
Kamiya N., Iwase H., Kita E.: Parallel computing for the combination method of BEM and FEM. Eng. Anal. Bound. Elem. 18, 221–229 (1996)
Davis, R.O.; Selvadurai, A.P.S.: Elasticity and Geomechanics. Cambridge University Press, Cambridge (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Haghighat, A.E., Binesh, S.M. Domain Decomposition Algorithm for Coupling of Finite Element and Boundary Element Methods. Arab J Sci Eng 39, 3489–3497 (2014). https://doi.org/10.1007/s13369-014-0995-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-014-0995-9