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.

通过将新开发的双插值方法与Galerkin边界面方法（BFM）相结合，应用了双插值Galerkin边界面方法（DiGBFM）。双插值方法统一了BFM实现中的合格和不合格元素。它将常规一致性元素的节点分类为虚拟节点和源节点。使用连续元素以与符合BFM相同的方式对电位和通量进行插值，而边界积分方程（BIE）与不符合BFM相同的方式并置在源节点处。为了得出平方线性系统，我们提供了附加的约束方程，这些方程由移动最小二乘（MLS）近似建立，以压缩与虚拟节点有关的自由度。与传统的对称Galerkin边界元方法（BEM）相比，由于使用了对称BEM，因此可以通过矩阵操作简单地获得DiGBFM方程的对称特征，并且在DiGBFM中不需要超奇异BIE。所提出的方法已经成功地用于解决二维稳态潜在问题。本文提供了几个数值示例，以证明该新方法的收敛性和准确性。