Design Methodology for Real-Time FPGA-Based Sound Synthesis

Explicit finite difference (FD) schemes can realise highly realistic physical models of musical instruments but are computationally complex. A design methodology is presented for the creation of FPGA-based micro-architectures for FD schemes which can be applied to a range of applications with varying computational requirements, excitation and output patterns and boundary conditions. It has been applied to membrane and plate-based sound producing models, resulting in faster than real-time performance on a Xilinx XC2VP50 device which is 10 to 35 times faster than general purpose and DSP processors. The models have developed in such a way to allow a wide range of interaction (by a musician) thereby leading to the possibility of creating a highly realistic digital musical instrument.

Numerical analysis of bodyworn UHF antenna systems

Bodyworn antennas are found in a wide range of medical, military and personal communication applications, yet reliable communication from the surface of the human body still presents a range of engineering challenges. At UHF and microwave frequencies, bodyworn antennas can suffer from reduced efficiency due to electromagnetic absorption in tissue, radiation pattern fragmentation and variations in feed-point impedance. The significance and nature of these effects are system specific and depend on the operating frequency, propagation environment and physical constraints on the antenna itself. This paper describes how numerical electromagnetic modelling techniques such as FDTD (finite-difference time-domain) can be used in the design of bodyworn antennas. Examples are presented for 418 MHz, 916 .5 MHz and 2 . 45 GHz, in the context of both biomedical signalling and wireless personal-area networking applications such as the Bluetooth(TM)* wireless technology.

Radiowave propagation from a tissue-implanted source at 418 MHz and 916.5 MHz

Tissue-implanted ultra-high frequency (UHF) radio devices are being employed in both humans and animals for telemetry and telecommand applications, This paper describes the experimental measurement and electromagnetic modeling of propagation from 418-MHz and 916.5-MHz sources placed in the human vagina. Whole-body homogeneous and semi-segmented software models were constructed using data from the Visible Human Project. Bodyworn radiation efficiencies for a vaginally placed 418-MHz source were calculated using finite-difference time-domain and ranged between 1.6% and 3.4% (corresponding to net body losses of between 14.7 and 18.0 dB), Greater losses were encountered at 916.5 MHz, with efficiencies between 0.36% and 0.46% (net body loss ranging between 23.4 and 24.4 dB), Practical measurements were in good agreement with simulations, to within 2 dB at 418 MHz and 3 dB at 916.5 MHz. The degree of tissue-segmentation for whole-body models was found to have a minimal effect on calculated azimuthal radiation patterns and bodyworn radiation efficiency, provided the region surrounding the implanted source was sufficiently detailed.

Periodic FDTD analysis of a 2-D leaky-wave planar antenna based on dipole frequency selective surfaces

A periodic finite-difference time-domain (FDTD) analysis is presented and applied for the first time in the study of a two-dimensional (2-D) leaky-wave planar antenna based on dipole frequency selective surfaces (FSSs). First, the effect of certain aspects of the FDTD modeling in the modal analysis of complex waves is studied in detail. Then, the FDTD model is used for the dispersion analysis of the antenna of interest. The calculated values of the leaky-wave attenuation constants suggest that, for an antenna of this type and moderate length, a significant amount of power reaches the edges of the antenna, and thus diffraction can play an important role. To test the validity of our dispersion analysis, measured radiation patterns of a fabricated prototype are presented and compared with those predicted by a leaky-wave approach based on the periodic FDTD results.

Coupled heat and moisture transfer in multi-layer building materials

A dynamic mathematical model for simulating the coupled heat and moisture migration through multilayer porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The discretization of the governing equations was done by the finite difference approach. A new experimental set-up was also developed in this study. The evolution of transient temperature and moisture distributions inside specimens were measured. The method for determining the temperature gradient coefficient was also presented. The moisture diffusion coefficient, temperature gradient coefficient, sorption–desorption isotherms were experimentally evaluated for some building materials (sandstone and lime-cement mortar). The model was validated by comparing with the experimental data with good agreement. Another advantage of the method lies in the fact that the required transport properties for predicting the non-isothermal moisture flow only contain the vapor diffusion coefficient and temperature gradient coefficient. They are relatively simple, and can be easily determined.

Two-dimensional hygrothermal transfer in porous building materials

A two-dimensional mathematical model for evaluating the simultaneous heat and moisture migration in porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The numerical solution was based on the control volume finite difference technique with fully implicit scheme in time. Two validation experiments were developed in this study. The evolution of transient moisture distributions in both one-dimensional and two-dimensional cases was measured. A comparison between experimental results and those obtained by the numerical model proves that they are fully consistent with each other. The model can be easily integrated into a whole building heat, air and moisture transfer model. Another main advantage of the present numerical method lies in the fact that the required moisture transport properties are comparatively simple and easy to determine.

Modelling the mechanical response of the Reed-mouthpiece-lip system of a clarinet. Part I. A one-dimensional distributed model

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time-domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece Jay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated.

Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations

A new method for modeling-frequency-dependent boundaries in finite-difference time-domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations is presented. The proposed approach allows the direct incorporation of a digital impedance filter (DIF) in the Multidimensional (2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a Suitable recursive formulation. The method is analyzed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which matches locally reacting surface (LRS) theory closely. Furthermore a numerical boundary analysis (NBA) formula is provided as a technique for an analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations

In this paper, a method for modeling diffusive boundaries in finite difference time domain (FDTD) room acoustics simulations with the use of impedance filters is presented. The proposed technique is based on the concept of phase grating diffusers, and realized by designing boundary impedance filters from normal-incidence reflection filters with added delay. These added delays, that correspond to the diffuser well depths, are varied across the boundary surface, and implemented using Thiran allpass filters. The proposed method for simulating sound scattering is suitable for modeling high frequency diffusion caused by small variations in surface roughness and, more generally, diffusers characterized by narrow wells with infinitely thin separators. This concept is also applicable to other wave-based modeling techniques. The approach is validated by comparing numerical results for Schroeder diffusers to measured data. In addition, it is proposed that irregular surfaces are modeled by shaping them with Brownian noise, giving good control over the sound scattering properties of the simulated boundary through two parameters, namely the spectral density exponent and the maximum well depth.

Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

A comparison of nonstaggered compact FDTD schemes for the 3D wave equation

This paper aims at providing a better insight into the 3D approximations of the wave equation using compact finite-difference time-domain (FDTD) schemes in the context of room acoustic simulations. A general family of 3D compact explicit and implicit schemes based on a nonstaggered rectilinear grid is analyzed in terms of stability, numerical error, and accuracy. Various special cases are compared and the most accurate explicit and implicit schemes are identified. Further considerations presented in the paper include the direct relationship with other numerical approaches found in the literature on room acoustic modeling such as the 3D digital waveguide mesh and Yee's staggered grid technique.

The RMT method for many-electron atomic systems in intense short-pulse laser light

We describe a new ab initio method for solving the time-dependent Schrödinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We call the method the R-matrix with time-dependence (RMT) method. Our starting point is a finite-difference numerical integrator (HELIUM), which has proved successful at describing few-electron atoms and atomic ions in strong laser fields with high accuracy. By exploiting the R-matrix division-of-space concept, we bring together a numerical method most appropriate to the multi-electron finite inner region (R-matrix basis set) and a different numerical method most appropriate to the one-electron outer region (finite difference). In order to exploit massively parallel supercomputers efficiently, we time-propagate the wavefunction in both regions by employing Arnoldi methods, originally developed for HELIUM.

FDTD analysis of close-coupled 418 MHz radiating devices for human biotelemetry

This paper describes the finite-difference time-domain (FDTD) analysis of antenna-body interaction effects occurring when chest-mounted 418 MHz radio transmitters are used for medical telemetry applications. Whole-body software models (homogeneous, layered and tissue-segmented) were developed for an adult male subject. Using an electrically small (300 mm(2)) planar loop antenna, calculated radiation efficiencies ranged between 33.5% and 39.2% for a whole-body model, and between 60.7% and 66.1% for a torso; radiation patterns were found to be largely independent of model composition. The computed radiation efficiency for a 21.5 kg phantom representing a six-year-old female was within 1.1 dB of measured results (actual body mass 28 kg) and well-correlated azimuthal radiation patterns were noted.

A virtual inspection framework for precision manufacturing of aerofoil components

The finite element method plays an extremely important role in forging process design as it provides a valid means to quantify forging errors and thereby govern die shape modification to improve the dimensional accuracy of the component. However, this dependency on process simulation could raise significant problems and present a major drawback if the finite element simulation results were inaccurate. This paper presents a novel approach to assess the dimensional accuracy and shape quality of aeroengine blades formed from finite element hot-forging simulation. The proposed virtual inspection system uses conventional algorithms adopted by modern coordinate measurement processes as well as the latest free-form surface evaluation techniques to provide a robust framework for virtual forging error assessment. Established techniques for the physical registration of real components have been adapted to localise virtual models in relation to a nominal Design Coordinate System. Blades are then automatically analysed using a series of intelligent routines to generate measurement data and compute dimensional errors. The results of a comparison study indicate that the virtual inspection results and actual coordinate measurement data are highly comparable, validating the approach as an effective and accurate means to quantify forging error in a virtual environment. Consequently, this provides adequate justification for the implementation of the virtual inspection system in the virtual process design, modelling and validation of forged aeroengine blades in industry.