An efficient boundary integral equation method for multi-frequency acoustics analysis

In this paper, a multi-frequency calculation technique based on least square approximate is introduced into the boundary integral equation method (BIEM) for 3D acoustics problems. The quadrilateral constant elements are used in multi-frequency calculation technique. In this method, the exponential term is expanded only when the source point and the field point locate in the same element. Thus, all the diagonal entries in system matrices are independent of the wave number. As a result, the integrals for the diagonal entries in all the final matrices (different frequencies) only are calculated once. Comparing with the original BIEM, the storage requirement for the presented method only adds O(n) (n is the total number of the elements). In addition, the presented method can be used to deal with the full frequency acoustic problems. Numerical examples show the accuracy and efficiency of the presented technique.