A dual interpolation Galerkin boundary face method for potential problems

Abstract A dual interpolation Galerkin boundary face method (DiGBFM) is applied in this paper by combining the newly developed dual interpolation method with the Galerkin boundary face method (BFM). The dual interpolation method unifies the conforming and nonconforming elements in the BFM implementation. It classifies the nodes of a conventional conforming element into virtual nodes and source nodes. Potentials and fluxes are interpolated using the continuous elements in the same way as conforming BFM, while boundary integral equations (BIEs) are collocated at source nodes, in the same way as nonconforming BFM. In order to arrive at a square linear system, we provide additional constraint equations, which are established by the moving least-squares (MLS) approximation, to condense the degrees of freedom relating to virtual nodes. Compared with the traditional symmetric Galerkin boundary element method (BEM), the symmetry feature of the DiGBFM equations is obtained simply through matrix manipulations, because of the use of the symmetric BEM, and no hypersingular BIE is needed in the DiGBFM. The proposed method has been implemented successfully for solving 2-D steady-state potential problems. Several numerical examples are presented in this paper to show the convergence and accuracy of this new method.