In our day life we are all exposed to all kind of sounds, from pleasant sounds coming from loudspeakers or musical instruments, to annoying and sometimes damaging sounds like noise from industrial machines. Most of these sounds are basically generated by mechanical vibrations of an object (membranes, plates, structures, etc) that makes sound propagate through the space. There are many different applications where accurate and fast modeling of this process is needed, and the goal of this project is to develop an efficient method for that.
Sound radiation problems are usually solved by numerical methods such as the so-called boundary element method, the method of finite differences in the time-domain, or finite element methods. The main idea behind some of these is to divide both the vibrating object and the space into small subdivisions, or elements, and solve the problem for each of those elements. This is often called a meshing process where the whole scenario is subdivided into small elements. As one may guess, the larger the number of elements, the more accurate the results will be. As it turns out, these commonly used methods come with a huge computational cost when the number of elements get larger, which might be in some cases be unaffordable. During this project, a novel method, which is computationally less demanding, has been developed combining these common used methods and an edge diffraction model. Finally, the new method has been applied to virtual reality applications where computational efficiency is particularly important.

The HYBRID project will develop, implement and validate an hybrid method for calculating the sound radiated by a vibrating structure. The approach suggested in the present proposal is to combine a volume-element method, FDTD, for modelling vibrations, with a Green's function matrix that can be computed separately. This Green's function matrix, also known as cross-impedance matrix, is a matrix connecting the vibration amplitude of all the surface nodes of the vibrating membrane with the resulting pressure of the same nodes. This matrix can be computed in a separate pre-step where a rigid model of the vibrating structure is excited point by point, and the resulting pressure is computed everywhere. Notable is that this Green's function matrix is independent of the excitation point and excitation signal on the membrane, so it can be re-used.
The Green's function matrix can be computed by a boundary element method, but this choice is not so attractive because of the BEM's high computational costs. Instead, a method based on edge source integral equation (ESIE) recently developed at the Norges Teknisk-Naturvitenskapelige Universitet will be suggested because this new method has the potential of offering an order of magnitude, even two in some cases, less computational cost than the BEM.