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    3d Modeling and simulation of a harpsichord

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    cembalo_paper2.pdf
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    Type
    Article
    Authors
    Larisch, Lukas
    Lemke, Babett
    Wittum, Gabriel
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Date
    2020-04-29
    Online Publication Date
    2020-04-29
    Print Publication Date
    2020-12
    Embargo End Date
    2021-04-29
    Submitted Date
    2019-07-29
    Permanent link to this record
    http://hdl.handle.net/10754/662800
    
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    Abstract
    The mathematical characterization of the sound of a musical instrument still follows Schumann’s laws (Schumann in Physik der klangfarben, Leipzig, 1929). According to this theory, the resonances of the instrument body, “the formants”, filter the oscillations of the sound generator (e.g., strings) and produce the characteristic “timbre” of an instrument. This is a strong simplification of the actual situation. It applies to a point source and can be easily performed by a loudspeaker, disregarding the three dimensional structure of music instruments. To describe the effect of geometry and material of the instruments, we set up a 3d model and simulate it using the simulation system UG4 (Vogel et al. in Comput Vis Sci 16(4):165–179, 2013; Reiter et al. in Comput Vis Sci 16(4):151–164, 2014). We aim to capture the oscillation behavior of eigenfrequencies of a harpsichord soundboard and investigate how well a model for the oscillation behavior of the soundboard approximates the oscillation behavior of the whole instrument. We resolve the complicated geometry by several unstructured 3d grids and take into account the anisotropy of wood. The oscillation behavior of the soundboard is modeled following the laws of linear orthotropic elasticity with homogenous boundary conditions. The associated eigenproblem is discretized using FEM and solved with the iterative PINVIT method using an efficient GMG preconditioner (Neymeyr in A hierarchy of preconditioned eigensolvers for elliptic differential operators. Habilitation dissertation, University of Tübingen, 2001). The latter allows us to resolve the harpsichord with a high resolution hybrid grid, which is required to capture fine modes of the simulated eigenfrequencies. We computed the first 16 eigenmodes and eigenfrequencies with a resolution of 1.8 billion unknowns each on Shaheen II supercomputer (https://www.hpc.kaust.edu.sa/content/shaheen-ii). To verify our results, we compare them with measurement data obtained from an experimental modal analysis of a real reference harpsichord.
    Citation
    Larisch, L., Lemke, B., & Wittum, G. (2020). 3d Modeling and simulation of a harpsichord. Computing and Visualization in Science, 23(1-4). doi:10.1007/s00791-020-00326-1
    Sponsors
    The support by Merzdorf GmbH and Polytec GmbH is gratefully acknowledged. For computing time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. Furthermore, we would like to thank Rossitza Piperkova for setting up an initial geometry of the soundboard.
    Publisher
    Springer Nature
    Journal
    Computing and Visualization in Science
    DOI
    10.1007/s00791-020-00326-1
    Additional Links
    http://link.springer.com/10.1007/s00791-020-00326-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00791-020-00326-1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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