An Effective Method Calculating Acoustic Green's Function for Closed Rectangular Cavity Using the Ewald's Summation Technique

Acoustic problems based on Helmholtz equation require evaluation of the Green's function. The acoustic Green's function expressed by modal expansion method converges very slowly. The Ewald's summation technique is suggested to extend into acoustic problems, in which the slowly convergent modal Green's function is split into two parts using a splitting factor. Each of them represents the exponentially convergent form, which drastically reduces the iteration items of the infinite series. Based on the simulation results, the transformed Green's function achieves rapid convergence with only a small number of iterations. In contrast, the identical results can be achieved from modal method with a large number of items. Therefore Ewald's method is an effective and inexpensive method for solving Green's function and acoustic problems in the closed rectangular cavity.