In seeking to model realistic room acoustics, direct numerical simulation can be employed. This paper presents 3D Finite Difference Time Domain schemes that incorporate losses at boundaries and due to the viscosity of air. These models operate within a virtual room designed on a detailed floor plan. The schemes are computed at 44.1kHz, using large-scale data sets containing up to 100 million points each. A performance comparison is made between serial computation in C, and parallel computation using CUDA on GPUs, showing up to 80 times speed-ups. Testing on two different Nvidia Tesla cards shows the benefits of the latest FERMI architecture for double precision floating-point computation.

Nonlinear vibrations of thin rectangular plates are considered, using the von Kármán equations in order to take into account the effect of geometric nonlinearities. Solutions are derived through an expansion over the linear eigenmodes of the system for both the transverse displacement and the Airy stress function, resulting in a series of coupled oscillators with cubic nonlinearities, where the coupling coefficients are functions of the linear eigenmodes. A general strategy for the calculation of these coefficients is outlined, and the particular case of a simply supported plate with movable edges is thoroughly investigated. To this extent, a numerical method based on a new series expansion is derived to compute the Airy stress function modes, for which an analytical solution is not available. It is shown that this strategy allows the calculation of the nonlinear coupling coefficients with arbitrary precision, and several numerical examples are provided. Symmetry properties are derived to speed up the calculation process and to allow a substantial reduction in memory requirements. Finally, analysis by continuation allows an investigation of the nonlinear dynamics of the first two modes both in the free and forced regimes. Modal interactions through internal resonances are highlighted, and their activation in the forced case is discussed, allowing to compare the nonlinear normal modes (NNMs) of the undamped system with the observable periodic orbits of the forced and damped structure.

mdw.ac.at/proceedings/index.html> Link: Link to publication record in Edinburgh Research Explorer

Synthesis using physical modeling has a long history. As computational costs for physical modeling synthesis are often much greater than for conventional synthesis methods, most techniques currently rely on simplifying assumptions. These include digital waveguides, as well as modal synthesis methods. Although such methods are efficient, it can be difficult to approach some of the more detailed behavior of musical instruments in this way, including strongly nonlinear interactions. Mainstream time-stepping simulation methods, despite being computationally costly, allow for such detailed modeling. In this article, the results of a five-year research project, Next Generation Sound Synthesis, are presented, with regard to algorithm design for a variety of sound-producing systems, including brass and bowed-string instruments, guitars, and large-scale environments for physical modeling synthesis. In addition, 3-D wave-based modeling of large acoustic spaces is discussed, as well as the embedding of percussion instruments within such spaces for full spatialization. This article concludes with a discussion of some of the basics of such time-stepping methods, as well as their application in audio synthesis.

The computation of large-scale virtual acoustics using the 3D finite difference time domain (FDTD) is prohibitively computationally expensive, especially at high audio sample rates, when using traditional CPUs. In recent years the computer gaming industry has driven the development of extremely powerful Graphics Processing Units (GPUs). Through specialised development and tuning we can exploit the highly parallel GPU architecture to make such FDTD computations feasible.This paper describes the simultaneous use of multiple NVIDIA GPUs to compute schemes containing over a billion grid points. We examine the use of asynchronous halo transfers between cards, to hide the latency involved in transferring data,and overall computation time is considered with respect to variation in the size of the partition layers. As hardware memory poses limitations on the size of the room to be rendered, we also investigate the use of single precision arithmetic.This allows twice the domain space, compared with double precision, but results in phase shifting of the output with possible audible artefacts. Using these techniques, large-scale spaces of several thousand cubic metres can be computed at 44.1kHz in a useable time frame, making their use in room acoustics rendering and auralization applications possible in the near future.