Geometric-integration tools for the simulation of musical sounds
DOI10.1007/s13160-017-0292-6zbMath1405.37088OpenAlexW2782769218MaRDI QIDQ1756717
Dominik L. Michels, Ai Ishikawa, Takaharu Yaguchi
Publication date: 21 December 2018
Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s13160-017-0292-6
geometric integrationsymplectic integrationpartitioned Runge-Kutta methodsseparable Hamiltonian systemacoustic simulationacoustic phenomenamusical soundssound renderingsound simulation
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Mathematics and music (00A65)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- New conservative schemes with discrete variational derivatives for nonlinear wave equations
- Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations
- Compact finite difference schemes with spectral-like resolution
- A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation
- Spatially accurate dissipative or conservative finite difference schemes derived by the discrete variational method
- High-order schemes for conservative or dissipative systems
- Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
- Second order conformal symplectic schemes for damped Hamiltonian systems
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Time integration and discrete Hamiltonian systems
- Physically inspired models for the synthesis of stiff strings with dispersive waveguides
- Time domain simulation of a piano. Part 2: numerical aspects
- Time domain simulation of a piano. Part 1: model description
- Discrete Variational Derivative Method
- Geometric investigation of the discrete gradient method for the Webster equation with a weighted inner product
- Geometric integration using discrete gradients
- Backward Error Analysis for Numerical Integrators
- Discrete gradient methods for solving ODEs numerically while preserving a first integral
- Symplectic Partitioned Runge–Kutta Methods for Constrained Hamiltonian Systems
- Geometric Numerical Integration
- Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
This page was built for publication: Geometric-integration tools for the simulation of musical sounds
