A combinatorial model reduction method for the finite element analysis of wind instruments

Abstract

A high‐fidelity finite element model is proposed for the complete simulation of the time‐harmonic acoustic propagation in wind instruments. The challenge is to meet the extremely high accuracy required by professional musicians, in a complex domain, for all fingerings and over a wide frequency range, within an affordable computational time. Several modelling assumptions are made to limit the numerical complexity of the problem while preserving all relevant physics. A dedicated high‐performance solution strategy is also proposed, based on partitioning, condensation and model order reduction, exploiting the combinatorial nature of wind instrument fingerings. Finally, the proposed approach is applied to the simulation of an alto saxophone. An order of magnitude reduction in memory and computational cost is achieved.