A comparison of a one-dimensional finite element method and the transfer matrix method for the computation of wind music instrument impedance

Robin Tournemenne 1 Juliette Chabassier 2, 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : This work presents a computation tool for the calculation of wind instrument input impedance in the context of linear planar wave propagation with viscothermal losses. The originality of the approach lies in the usage of a specific finite element method (FEM) which has a simple implementation given the one dimensional nature of the problem. The results can be arbitrarily precise and any instrument geometry can be computed. The popular Transfer Matrix Method (TMM) is also recalled and a seamless mathematical formulation of its expression is proposed which does not distinguish the cases cylinders vs. cones. In presence of viscothermal losses and for conical parts, the method is not exact and the equation which is exactly solved is exhibited. The accuracy of the two methods (FEM and TMM) and the associated computation times are assessed and compared. Although the TMM is more efficient in lossless cases and for lossy cylinders, the FEM is shown to be more efficient when targeting a specific precision in the realistic case of a lossy trumpet. Unusual physical situations are also possible to solve. All the results of this article are computed using the open-source python toolbox OpenWind.
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Submitted on : Tuesday, May 21, 2019 - 4:06:35 PM
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Robin Tournemenne, Juliette Chabassier. A comparison of a one-dimensional finite element method and the transfer matrix method for the computation of wind music instrument impedance. 2019. ⟨hal-01963674⟩

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