An iterative method using FEM and BEM for the analysis of electrostatic field and structure interaction problems is presented. For the analysis of electrostatic field problem, it is often required to discretize the air-space surrounding the conductors. In the case, if the space is to be discretized only by finite elements, the number of d.o.fs of the problem significantly increases thereby reducing computational efficiency. In this reason, BEM is used for the analysis of electrostatic field. The surrounding unbounded space is treated by the BEM and structure bodies are described by the FEM. First, BEM domains can be solved with electric potentials as a boundary condition. Using electrostatic force obtained in the BEM calculation, FEM domain can be solved. The electrostatic force and structure deformation are updated at each step. The iteration can be ended when the solutions are converged. The matrix obtained in FEM can be solved fast because the matrix is symmetric. In BEM part, we used a generalized conjugated residual iterative algorithm with a multipole approximation for the efficient calculation.
In the matter of the electrostatic problems, the reference potential have to be considered to obtain the charge distribution exactly. This consideration for the reference potential have an important meaning about the principle of conservation of charge. In this paper, the method to consider the reference potential is proposed. Using linear properties of the electrostatic field problem, the reference potential can be obtained by several operations. Several numerical example problems are solved to demonstrate the verification of the scheme.
For the analysis of a electrostatic field and structure interaction problem, the effectiveness of the multipole expansion algorithm considering the reference potential is demonstrated by solving two real problems.