A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures

A phase-space boundary integral method is developed for modelling stochastic high-frequency acoustic and vibrational energy transport in both single and multi-domain problems. The numerical implementation is carried out using the collocation method in both the position and momentum phase-space variables. One of the major developments of this work is the systematic convergence study, which demonstrates that the proposed numerical schemes exhibit convergence rates that could be expected from theoretical estimates under the right conditions. For the discretisation with respect to the momentum variable, we employ spectrally convergent basis approximations using both Legendre polynomials and Gaussian radial basis functions. The former have the advantage of being simpler to apply in general without the need for preconditioning techniques. The Gaussian basis is introduced with the aim of achieving more efficient computations in the weak noise case with near-deterministic dynamics. Numerical results for a series of coupled domain problems are presented, and demonstrate the potential for future applications to larger scale problems from industry.