Use of the Laplace Transform and the direct interpolation Boundary Element Method for acoustic wave simulation

This work applies the Boundary Element Method to obtain responses in acoustic wave propagation problems using the Laplace Transform. This technique eliminates the time variable and successfully solves transient heat transfer problems. However, the accurate return to the original variable is still a significant challenge in the dynamics since many usual techniques for inversion are inaccurate. Here, Durbin’s inverse method, based on the Fourier series, is used to overcome this issue. Concerning spatial discretization, the direct interpolation boundary element technique (DIBEM) is used to solve numerically the resulting pseudo-Helmholtz partial differential equation in the transformed domain with relevant gain in accuracy and performance relative to other BEM methodologies. This technique is based on approximating the entire kernel of the reactive domain integral through a sequence of radial basis functions, and its results have demonstrated superiority compared to similar methods in solutions of Helmholtz, Poisson, and Diffusive-advective problems. Simulations performed in this work indicate that coupling DIBEM with the Laplace Transform using Durbin’s technique for solving wave propagation makes numerical solutions advantageous, producing stable, precise solutions. Emphasis is placed on convergence tests regarding the effect of the number of terms in the Fourier series used in the Durbin scheme by comparison with the results given by the available analytical solutions.