A dual interpolation boundary face method for exterior acoustic problems based on the Burton-Miller formulation

A dual interpolation boundary face method (DiBFM) based on the Burton-Miller formulation for solving exterior acoustic problems is presented. The method is able to unify the conforming and nonconforming BFM. In DiBFM implementation, the nodes of a conforming element are divided into two categories: source nodes (inside the element) and virtual nodes (on the boundary of the element). Acoustic pressure and its derivative are approximated using conforming elements, in the same way as conforming BFM. However, the Burton-Miller integral equations are just collocated at source nodes, in the same way as nonconforming BFM. To arrive at a square linear system, additional constraint equations established by the moving least-squares approximation are provided to condense the degrees of freedom relating to virtual nodes. Several numerical examples demonstrate the accuracy and efficiency of the proposed method.