Summary
This paper presents a coupling algorithm of FEM and BEM for solving mixed boundary value problems in elastostatics. A domain decomposition of the bounded domain Ω leads to a basic substructure Ω1 with a skeleton H, where the FEM is applied, and several macroelements Ωi (i = 2,…, p), where the BEM is used on a fine grid h.
As fundamental equations the well known energy bilinear form is used for the whole domain Ω and, additionally, a second bilinear form on the macroelements Ωi as a coupling condition. This way a symmetric and nonconforming (i.e. different, independent grids H and h) coupling algorithm can be obtained. This can be realized by applying the Poincaré-Steklov operator on the macroelement surfaces in the strong singular form and by avoiding the use of the hypersingular boundary integral equation.
The construction of a robust and reliable numerical algorithm depends on the adaptive control of symmetry and definiteness of the coupling matrix. Therefore we use an iterative method for solving the boundary integral equation by expanding the Calderon projector in a Neumann series. Finally the convergence of this expansion is proved, on the basis of the fundamental work of Kupradze et.al. [13].
Numerical results in 2D and 3D will show the preciseness and efficiency of the method.
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References
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Türke, K., Schnack, E. (1996). A Two Grid Method for Coupling Fem and Bem in Elasticity. In: Hackbusch, W., Wittum, G. (eds) Boundary Elements: Implementation and Analysis of Advanced Algorithms. Notes on Numerical Fluid Mechanics (NNFM), vol 50. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89941-5_20
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DOI: https://doi.org/10.1007/978-3-322-89941-5_20
Publisher Name: Vieweg+Teubner Verlag
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