A three-dimensional acoustics model using the method of fundamental solutions
The method of fundamental solutions (MFS) is formulated in the frequency domain to model the sound wave propagation in three-dimensional (3D) enclosed acoustic spaces. In this model the solution is obtained by approximation, using a linear combination of fundamental solutions for the 3D Helmholtz equation. Those solutions relate to a set of virtual sources placed over a surface placed outside the domain in order to avoid singularities. The materials coating the enclosed space surfaces can be assumed to be sound absorbent. This effect is introduced in the model by imposing impedance boundary conditions, with the impedance being defined as a function of the absorption coefficient. To impose these boundary conditions, a set of collocation points (observation points) needs to be selected along the boundary. Time domain responses are obtained by applying an inverse Fourier transform to the former frequency domain results. In order to avoid aliasing phenomena in the time domain results, the computations introduce damping in the imaginary part of the frequency. This effect is later removed in the time domain by rescaling the response. After corroborating the present solution against the analytical solution, known in closed form for the case of a parallelepiped room bounded by rigid walls, the model is used to solve the case of a dome.
acoustic model mfs meshless three-dimensional model