High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: O(1)\mathcal{O}(1) Sampling Cost via Incident-Field Windowing and Recentering

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily-long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time $T$ at $\mathcal{O}(1)$-bounded sampling cost, for arbitrarily large values of $T$, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization, time-domain integral equations, and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now including direct comparisons to existing CQ and TDIE solver implementations) (Part I of II

Acoustic modeling using the digital waveguide mesh

The digital waveguide mesh has been an active area of music acoustics research for over ten years. Although founded in 1-D digital waveguide modeling, the principles on which it is based are not new to researchers grounded in numerical simulation, FDTD methods, electromagnetic simulation, etc. This article has attempted to provide a considerable review of how the DWM has been applied to acoustic modeling and sound synthesis problems, including new 2-D object synthesis and an overview of recent research activities in articulatory vocal tract modeling, RIR synthesis, and reverberation simulation. The extensive, although not by any means exhaustive, list of references indicates that though the DWM may have parallels in other disciplines, it still offers something new in the field of acoustic simulation and sound synth

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

Fast and Accurate Simulation Technique for Large Irregular Arrays

A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique to compute the interactions between MBFs. The Harmonic-polynomial (HARP) model is established for the near-field interactions in a modified system of coordinates. For extremely large arrays made of complex antennas, two approaches assuming a limited radius of influence for mutual coupling are considered: one is based on a sparse-matrix LU decomposition and the other one on a tessellation of the array in the form of overlapping sub-arrays. The computation of all embedded element patterns is sped up with the help of the non-uniform FFT algorithm. Extensive validations are shown for arrays of log-periodic antennas envisaged for the low-frequency SKA (Square Kilometer Array) radio-telescope. The analysis of SKA stations with such a large number of elements has not been treated yet in the literature. Validations include comparison with results obtained with commercial software and with experiments. The proposed method is particularly well suited to array synthesis, in which several orders of magnitude can be saved in terms of computation time.Comment: The paper was submitted to IEEE Transaction on Antennas and Propagation on 01 - Feb.- 2017. The paper is 12 pages with 18 figure

Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity

We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant $\varepsilon_{r}\left(\mathbf{x}\right), \ \mathbf{x}\in \mathbb{R}^{3}$, which is an unknown coefficient in the Maxwell's equations, from time-dependent backscattering experimental radar data associated with a single source of electric pulses. The refractive index is$n\left(\mathbf{x}\right) =\sqrt{\varepsilon_{r}\left(\mathbf{x}\right)}.$The coefficient$\varepsilon_{r}\left(\mathbf{x}\right) $ is reconstructed using a two-stage reconstruction procedure. In the first stage an approximately globally convergent method proposed is applied to get a good first approximation of the exact solution. In the second stage a locally convergent adaptive finite element method is applied, taking the solution of the first stage as the starting point of the minimization of the Tikhonov functional. This functional is minimized on a sequence of locally refined meshes. It is shown here that all three components of interest of targets can be simultaneously accurately imaged: refractive indices, shapes and locations

An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method

In this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in or external gradient-based optimization procedures. For speed, a model order reduction technique is used and the gradient computation is achieved by perturbation with geometry deformation, processed on the level of the individual mesh nodes. To maximize performance, the framework is targeted to multicore CPU architectures and its extended version can also use multiple GPUs. To illustrate the accuracy and high efficiency of the framework, we provide examples of simulations of a dielectric resonator antenna and full-wave design by optimization of two diplexers involving tens of unknowns, and show that the design can be completed within the duration of a few simulations using industry-standard FEM solvers. The accuracy of the design is confirmed by measurements

Efficient Synthesis of Room Acoustics via Scattering Delay Networks

An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation of unequal and frequency-dependent wall absorption, as well as directional sources and microphones. The reverberator renders the first-order reflections exactly, while making progressively coarser approximations of higher-order reflections. The rate of energy decay is close to that obtained with the image method (IM) and consistent with the predictions of Sabine and Eyring equations. The time evolution of the normalized echo density, which was previously shown to be correlated with the perceived texture of reverberation, is also close to that of IM. However, its computational complexity is one to two orders of magnitude lower, comparable to the computational complexity of a feedback delay network (FDN), and its memory requirements are negligible

Simulation of Single Reed Instruments Oscillations Based on Modal Decomposition of Bore and Reed Dynamics

This paper investigates the sound production in a system made of a bore coupled with a reed valve. Extending previous work (Debut, 2004), the input impedance of the bore is projected on the modes of the air column. The acoustic pressure is therefore calculated as the sum of modal components. The airrrflow blown into the bore is modulated by reed motion, assuming the reed to be a single degree of freedom oscillator. Calculation of self-sustained oscillations controlled by time-varying mouth pressure and player's embouchure parameter is performed using ODE solvers. Results emphasize the par ticipation of the whole set of components in the mode locking process. Another impor tant feature is the mutual innnfluence of reed and bore resonance during growing blowing pressure transients, oscillation threshold being altered by the reed natural frequency and the reed damping. Steady-state oscillations are also investigated and compared with results given by harmonic balance method and by digital sound synthesis