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For physical modelling sound synthesis, many techniques are available; time-stepping methods (e.g., finite-difference time-domain (FDTD) methods) have an advantage of flexibility and generality in terms of the type of systems they can model. These methods do, however, lack the capability of easily handling smooth parameter changes while retaining optimal simulation quality and stability, something other techniques are better suited for. In this paper, we propose an efficient method to smoothly add and remove grid points from a FDTD simulation under sub-audio rate parameter variations. This allows for dynamic parameter changes in physical models of musical instruments. An instrument such as the trombone can now be modelled using FDTD methods, as well as physically impossible instruments where parameters such as e.g. material density or its geometry can be made time-varying. Results show that the method does not produce (visible) artifacts and stability analysis is ongoing.

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Nonlinear interactions between different parts of musical instruments present several challenges regarding the formulation of reliable and efficient numerical sound synthesis models. This paper focuses on a numerical collision model that incorporates impact damping. The proposed energy-based approach involves an iterative solver for the solution of the nonlinear system equations. In order to ensure the efficiency of the presented algorithm a bound is derived for the maximum number of iterations required for convergence. Numerical results demonstrate energy conservation as well as convergence within a small number of iterations, which is usually much lower than the predicted bound. Finally, an application to music acoustics, involving a clarinet simulation, shows that including a loss mechanism during collisions may have a significant effect on sound production.

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Due to recent increases in computational power, physical modeling synthesis is now possible in real time even for relatively complex models. We present here a modular physical modeling instrument design, intended as a construction framework for string- and bar- based instruments, alongside a mechanical network allowing for arbitrary nonlinear interconnection. When multiple nonlinearities are present in a feedback setting, there are two major concerns. One is ensuring numerical stability, which can be approached using an energy-based framework. The other is coping with the computational cost associated with nonlinear solvers—standard iterative methods, such as Newton-Raphson, quickly become a computational bottleneck. Here, such iterative methods are sidestepped using an alternative energy conserving method, allowing for great reduction in computational expense or, alternatively, to real-time performance for very large-scale nonlinear physical modeling synthesis. Simulation and benchmarking results are presented.

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