Half Space Acoustic Problems Analysis by Fast Multipole Boundary Face Method

In this paper, a half space adaptive fast multipole boundary face method (FMBFM) is presented for solving the three-dimensional half space exterior acoustic problems. In the presented method, the Burton-Miller equation based on the conventional boundary integral equation (CBIE) and its hyper-singular boundary integral equation (HBIE) is used to deal with the fictitious eigenfrequencies problem. The half space Green's function is employed, thus the tree structure in the fast multipole method can be used only for the real domain. The higher order elements and an adaptive tree structure are used to improve the efficiency of the FMBFM. This half space adaptive FMBFM for half space acoustic problems is an extension of the adaptive FMBFM for full space acoustic problems developed by the authors. Numerical examples for half space acoustic problems in this paper demonstrate the efficiency and validity of this method.