Journal of Computational Acoustics

One-dimensional analyses provide novel definitions of the Galerkin/least-squares stability parameter for quadratic interpolation. A new approach to the dispersion analysis of the Lagrange multiplier approximation in discontinuous Galerkin methods is presented. A series of computations comparing the performance of Galerkin and GLS methods with Q-8-2 DGM on large-scale problems shows superior DGM results on analogous meshes, both structured and unstructured. The degradation of the GLS stabilization on unstructured meshes may be a consequence of inadequate one-dimensional analysis used to derive the stability parameter.

Coupled finite-infinite element computations are very efficient for modeling large scale acoustics problems. Parallel algorithms, like sub-structuring and domain decomposition methods, have shown to be very efficient for solving huge linear systems arising from acoustics. In this paper, a coupled finite-infinite element method is described, formulated and analyzed for parallel computations purpose. New numerical results illustrate the efficiency of this method for academic test cases and industrial problems alike.

In this paper, we consider the numerical method for the voice generation problem. The basic mathematical model for the voice generation is the Helmholtz equation in an unbounded region. Introducing an artificial boundary, we divide the unbounded region into a bounded region and the rest unbounded one with a simple shape. We apply the finite element method for the equation in the bounded region imposing an artificial boundary condition given through the Dirichlet to Neumann (DtN) mapping on the artificial boundary. We then compute the frequency response function or the formant curve by which we can simulate the voice generation process for various vowels. The complex eigenvalues related to the Helmholtz equation control the peaks of the frequency response function known as formants. We give the variational formulas for the complex eigenvalues with respect to the variation of vocal tract boundary.

A general Discontinuous Galerkin framework is introduced for symmetric systems of conservations laws. It is applied to the three-dimensional electromagnetic wave propagation in heterogeneous media, and to the propagation of aeroacoustic perturbations of either uniform or nonuniform, steady solutions of the three-dimensional Euler equations. In all these linear contexts, the time evolution of some quadratic wave energy is given in a balance equation, with a volumic source term for aeroacoustics in a nonuniform flow. An explicit leap-frog time scheme along with centered numerical fluxes are used in the proposed Discontinuous Galerkin Time Domain (DGTD) method, in order to achieve a discrete equivalent of the balance equation for the wave energy. The scheme introduced is genuinely nondissipative. Numerical first-order boundary conditions are developed to bound the domain and stability is proved on arbitrary unstructured meshes and discontinuous finite elements, under some CFL-like stability condition on the time step. Numerical results obtained with a parallel implementation of the method based on mesh partitioning and message passing are presented to show the potential of the method.

The use of Fast Multipole Methods (FMM) combined with embedded Krylov solvers preconditioned by a sparse approximate inverse is investigated for the solution of large linear systems arising in industrial acoustic and electromagnetic simulations. We use a boundary element integral equation method to solve the Helmholtz and the Maxwell equations in the frequency domain. The resulting linear systems are solved by iterative solvers using FMM to accelerate the matrix-vector products. The simulation code is developed in a distributed memory environment using message passing and it has out-of-core capabilities to handle very large calculations. When the calculation involves one incident wave, one linear system has to be solved. In this situation, embedded solvers can be combined with an approximate inverse preconditioner to design extremely robust algorithms. For radar cross section calculations, several linear systems have to be solved. They involve the same coefficient matrix but different right-hand sides. In this case, we propose a block variant of the single right-hand side scheme. The efficiency, robustness and parallel scalability of our approach are illustrated on a set of large academic and industrial test problems.

In this paper we are interested in studying the development of parallel algorithms to solve nonlinear wave equations. Both synchronous and asynchronous algorithms contexts are considered. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Experiments are carried out in both homogeneous and heterogeneous grid environments. According to the configuration environment, the behaviors of parallel synchronous and asynchronous algorithms are analyzed. Experiments allow us to draw some conclusions about the use of parallel iterative algorithms in grid computing environment.

Sound waves are propagating pressure fluctuations and are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes (RANS) equations do not resolve the acoustic fluctuations. Direct numerical simulation of turbulent flow is still a prohibitively expensive tool to perform noise analysis. This paper proposes a distributed algorithm, based on the acoustic correction method, which leads to an efficient method for computational aeroacoustics and noise analysis. Software issues and advantages are discussed. Numerical experiments on a flow induced noise problem are included.