The analysis of noise level emanating from a distant source is needed in a number of applications, most notably in environmental engineering. The sound pressure level (SPL) distribution is desired, e.g., due to the acute effects of sound on community. To this end, one has to solve a typically large-scale acoustics 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. To this end, an efficient Helmholtz equation solver must be used.

In recent years, fictitious source methods (FSM) have been developed and applied for various problems such as acoustic and electromagnetic wave problems. For a flat ground with a zero or infinite impedance, basic fictitious source implementation can easily give a semi-analytical solution to the Helmholtz problem using the mirror image method. For a variable impedance or for ground with given topography, the problem becomes much more complex, and a numerical solution is required. The use of the FSM was previously proven to be efficient for the case of a flat ground with a constant impedance.

In this Seminar we will present an extension to the previous work in the following main aspects:

- The ground impedance may be a function of location.
- Topography: the ground may be non-flat

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