A Two Grid Method for Coupling Fem and Bem in Elasticity

  • Karsten Türke
  • Eckart Schnack
Chapter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 50)

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.

Keywords

Boundary Element Method Coarse Grid Domain Decomposition Boundary Integral Equation Fine Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© yen 1996

Authors and Affiliations

  • Karsten Türke
    • 1
  • Eckart Schnack
    • 1
  1. 1.Institute of Solid MechanicsUniversity of Karlsruhe (TH)KarlsruheGermany

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