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The use of model-based numerical simulation of wave propagation in rooms forengineering applications requires that acoustic conditions for multipleparameters are evaluated iteratively and this is computationally expensive. Wepresent a reduced basis methods (RBM) to achieve a computational cost reductionrelative to a traditional full order model (FOM), for wave-based room acousticsimulations with parametrized boundary conditions. In this study, the FOMsolver is based on the spectral element method, however other numerical methodscould be applied. The RBM reduces the computational burden by solving theproblem in a low-dimensional subspace for parametrized frequency-independentand frequency-dependent boundary conditions. The problem is formulated andsolved in the Laplace domain, which ensures the stability of the reduced ordermodel based on the RBM approach. We study the potential of the proposed RBMframework in terms of computational efficiency, accuracy and storagerequirements and we show that the RBM leads to 100-fold speed-ups for a 2D casewith an upper frequency of 2kHz and around 1000-fold speed-ups for an analogous3D case with an upper frequency of 1kHz. While the FOM simulations needed toconstruct the ROM are expensive, we demonstrate that despite this cost, the ROMhas a potential of three orders of magnitude faster than the FOM when fourdifferent boundary conditions are simulated per room surface. Moreover, resultsshow that the storage model for the ROM is relatively high but affordable forthe presented 2D and 3D cases.

Reduced basis methods for numerical room acoustic simulations with parametrized boundaries