  The use of model-based numerical simulation of wave propagation in rooms for
engineering applications requires that acoustic conditions for multiple
parameters are evaluated iteratively and this is computationally expensive. We
present a reduced basis methods (RBM) to achieve a computational cost reduction
relative to a traditional full order model (FOM), for wave-based room acoustic
simulations with parametrized boundary conditions. In this study, the FOM
solver is based on the spectral element method, however other numerical methods
could be applied. The RBM reduces the computational burden by solving the
problem in a low-dimensional subspace for parametrized frequency-independent
and frequency-dependent boundary conditions. The problem is formulated and
solved in the Laplace domain, which ensures the stability of the reduced order
model based on the RBM approach. We study the potential of the proposed RBM
framework in terms of computational efficiency, accuracy and storage
requirements and we show that the RBM leads to 100-fold speed-ups for a 2D case
with an upper frequency of 2kHz and around 1000-fold speed-ups for an analogous
3D case with an upper frequency of 1kHz. While the FOM simulations needed to
construct the ROM are expensive, we demonstrate that despite this cost, the ROM
has a potential of three orders of magnitude faster than the FOM when four
different boundary conditions are simulated per room surface. Moreover, results
show that the storage model for the ROM is relatively high but affordable for
the presented 2D and 3D cases.
