Multilevel fast multipole boundary element method for 2D acoustic problems and its applications

Since the memory requirement and computation cost of solving conventional boundary element method have quadratic ratio with respect,to the freedoms,it makes the conventional boundary element method unsuitable for large scale problems.A multilevel fast multipole boundary element of 2D acoustic wave problems is developed.Based on the introduction of kernel expansion theory of 2D Helmholtz equation,the formulations of moment computation,moment to moment,moment to local and local to local transformation are derived.The fast multipole method algorithm for 2D acoustic problems is described in detail.Fast Fourier interpolation is used to transfer the moments and local expansion coefficients from level to level.Left preconditioner based on block diagonal method is adopted to improve the condition number of the corresponding linear equations.At the end.numerical experiments and applications are used to verify the accurate and the efficiency of the algorithm.