M.Sc Thesis

M.Sc StudentYohan Kamoun
SubjectFictitious Source Method for the Analysis of Noise Level
from a Distant Source on Ground with Variable
Impedance and Topography
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Givoli Dan


The analysis of noise level emanating from a distant source is necessary in various applications, most notably in environmental engineering. The sound pressure level (SPL) distribution is desired, e.g., due to the acute effects of noise on community. To this end, one has to solve a typically large-scale acoustic problem: a moving source over ground with given impedance and topography.

Since the human hearing bandwidth is quite wide, one has to repeatedly solve the Helmholtz equation in the upper half space for many different wave lengths, with given impedance boundary condition imposed on the ground. In order to do so an efficient Helmholtz equation solver must be used.

In recent years, fictitious source methods (FSM) have been developed and applied for numerous problems, ranging from acoustics to electromagnetics wave problems. For a flat ground with zero or infinite impedance, basic fictitious sources method implementation can easily give a semi-analytical solution to the Helmholtz problem, using mirror image method. For nonzero impedance or for a ground with given topography, the problem becomes much more complex, and numerical solution is then necessary. The use of the FSM was formerly proven to be efficient for the case of flat ground with constant impedance.

In current work we present an extension to the previous work in the following main aspects:

a.         The ground impedance may be a function of location.

b.        Topography: the ground may be non-flat

c.         In contrast to the previous works, where only the residual was calculated, it is now possible to estimate the error generated by the fictitious source method using a dedicated algorithm.