This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.

本文结合Poisson方程的双重插值界面方法（DiBFM），提出了双重互易方法（DRM）的新实现。在DiBFM中，元素的节点分为两类：（i）源节点（ii）虚拟节点。第一层插值用于插值物理变量，而边界积分仅在源节点上求值。此外，使用了移动最小二乘（MLS）插值，并提供了其他约束方程式来建立源节点与虚拟节点之间的关系。此外，增强的薄板样条（ATPS）用于更好地内插非均匀项。最后，据称所提出的方法对于具有不同几何形状的泊松型方程，特别是对于复杂几何形状，比DRM要好得多。