The Boundary Element Method as a State-Space Realization Problem

From 01-01-2024 to 31-12-2027

Description

The boundary element method (BEM) is a numerical method for modeling wave propagation
problems. In this proposal, we address two particular problems related to the BEM, both of which are
impeding the application of the BEM to our area of interest, that is, sound propagation in enclosures,
i.e., room acoustics.
Firstly, the BEM is most often applied in the frequency domain, representing a steady-state solution
to a wave propagation problem. However, in order to represent wave fields generated by
spatiotemporally nonstationary sources, a time-domain approach is needed. Time-domain BEM has
only been scarcely considered as it is prone to instability problems. Secondly, the accuracy of the
BEM solution is highly dependent on an accurate formulation of the boundary conditions, hence
requiring a detailed characterization of the material properties of the enclosure, which is often
infeasible.
Both problems will be addressed by exploiting a formulation of the BEM that has remained
underexplored in literature. The time-domain boundary integral equation from which the BEM is
derived, can be rewritten into a continuous-time, discrete-space state-space model. This
representation will firstly allow to understand how stability can be preserved when moving from
continuous to discrete time. Secondly, it naturally leads to the formulation of a state-space
realization problem that yields the perspective to estimate the boundary conditions from impulse
response measurements.

Team

• Randall Azhar Ali, Co-promoter
• Toon van Waterschoot, Coordinator

Financing

Funding: FWO - Research Foundation - Flanders

Program/Grant Type: FWO Project - FWO Research Project