Geometric-integration tools for the simulation of musical sounds
type: Item
instance of: scholarly article
title: Geometric-integration tools for the simulation of musical sounds
zbMATH Open document ID: 1405.37088
author: Ai Ishikawa
author: Dominik L. Michels
author: Takaharu Yaguchi
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2018-12-21T00:00:00Z
review text: The authors introduce a procedure for deriving numerical schemes for models of musical instruments. The approach relies on a combination of the variational semi-discretization by \textit{E. Celledoni} et al. [J. Comput. Phys. 231, No. 20, 6770--6789 (2012; Zbl 1284.65184)] and the symplectic Runge-Kutta methods. This technique automatically derives a semi-discrete scheme preserving the Hamiltonian structure. In this way, geometric integrators can be immediately applied without any additional steps. Following this procedure the authors derive a series of explicit integration algorithms for a simple model describing piano sounds as a representative example for virtual instruments.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 00A65
zbMATH DE Number: 6996760
zbMATH Keywords: acoustic phenomena
zbMATH Keywords: acoustic simulation
zbMATH Keywords: geometric integration
zbMATH Keywords: musical sounds
zbMATH Keywords: partitioned Runge-Kutta methods
zbMATH Keywords: separable Hamiltonian system
zbMATH Keywords: sound rendering
zbMATH Keywords: sound simulation
zbMATH Keywords: symplectic integration
MaRDI profile type: Publication
full work available at URL: s13160-017-0292-6
OpenAlex ID: W2782769218
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DOI: 10.1007/S13160-017-0292-6
description: scientific article; zbMATH DE number 6996760