Comparative Study of Two Different Fmm–bem Methods in Solving 2-d Acoustic Transmission Problems With A Multilayered Obstacle

The fast multipole method (FMM) is an effective approach for accelerating the computation efficiency of the boundary element method (BEM) in solving problems that are computationally intensive. This paper presents two different BEMs, i.e., Kress' and Seydou's methods, for solving two-dimensional (2D) acoustic transmission problems with a multilayered obstacle, along with application of the FMM to solution of the related boundary integral equations. Conventional BEM requires O(MN²) operations to compute the equations for this problem. By using the FMM, both the amount of computation and the memory requirement of the BEM are reduced to order O(MN), where M is the number of layers of the obstacle. The efficiency and accuracy of this approach in dealing with the acoustic transmission problems containing a multilayered obstacle are demonstrated in the numerical examples. It is confirmed that this approach can be applied to solving the acoustic transmission problems for an obstacle with multilayers.